# Why Is C Major Called A "Diatonic" Scale"? What Does "Diatonic" Mean?



## millionrainbows

*Why Is C Major Called A "Diatonic" Scale"? What Does "Diatonic" Mean?*

Why Is C Major Called A "Diatonic" Scale"? What Does "Diatonic" Mean?

Any "takers?" Heh heh....


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## isorhythm

Diatonic doesn't mean "two tonics" - the Greek preposition "dia" is not the prefix "di-" has nothing to do with the number two. I really hope you don't choose to double down on this basic error.

I also hope you're aware that all of the white-key scales, including Lydian, are called diatonic.


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## EdwardBast

The term diatonic comes from Ancient Greek theory, where it designates one of three standard genera of tetrachords. Tetrachords are four note series dividing the interval of a perfect fourth. The three standard genera were diatonic, chromatic, and enharmonic. Diatonic tetrachords comprise two tones and a semitone. Chromatic tetrachords comprise a minor third and two semitones. Enharmonic tetrachords comprise a major third and two quarter tones. The Greeks built modes by stacking tetrachords. For example, if one stacks the tetrachord B-C-D-E on top of the tetrachord E-F-G-A, one has the complete set of pitches to define a mode. This is a diatonic mode because both tetrachords are diatonic. 

When carried over into modern theory, the term diatonic indicates any mode or scale of seven notes comprising two diatonic tetrachords. This includes major and natural minor scales and all the standard Greek-named modes. C major is among this group and so is a diatonic scale.


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## millionrainbows

isorhythm said:


> Diatonic doesn't mean "two tonics" - the Greek preposition "dia" is not the prefix "di-" has nothing to do with the number two. I really hope you don't choose to double down on this basic error.
> 
> I also hope you're aware that all of the white-key scales, including Lydian, are called diatonic.



Thank you, BabyGiraffe, I'll take that into consideration.
 The English word diatonic is ultimately from the Greek διατονικός (diatonikós), itself from διάτονος (diátonos), which may mean (as OEDclaims) "through the tones" (taking τόνος, tónos, to mean interval of a tone), or perhaps stretched out (as recorded in Liddell and Scott's Greek Lexicon). See also Barsky (Chromaticism, Barsky, Vladimir, Routledge, 1996, p. 2): "There are two possible ways of translating the Greek term 'diatonic': (1) 'running through tones', i.e. through the whole tones; or (2) a 'tensed' tetrachord filled up with the widest intervals". The second interpretation would be justified by consideration of the pitches in the diatonic tetrachord, which are more equally distributed ("stretched out") than in the chromatic and enharmonic tetrachords, and are also the result of tighter stretching of the two variable strings. It is perhaps also sounder on linguistic morphological grounds. (See also Merriam-Webster Online.)
A completely separate explanation of the origins of *the term diatonic appeals to the generation of the diatonic scale from "two tones"*: "Because the musical scale is based entirely on octaves and fifths, that is, two notes, it is called the 'diatonic scale' " (Phillips, Stephen, "Pythagorean aspects of music", in Music and Psyche, Vol. 3, available also online. *But this ignores the fact that it is the element di- that means "two", not the element dia-,* which has "through" among its meanings (see Liddell and Scott). *There is a Greek term δίτονος (dítonos), which is applied to an interval equivalent to two tones. It yields the English words ditone and ditonic (see Pythagorean comma), but it is quite distinct from διάτονος.*
*Yet another derivation assumes the sense "through the tones" for διάτονος, but interprets tone as meaning individual note of the scale: "The word diatonic means 'through the tones' (i.e., through the tones of the key)" (Gehrkens, 1914, see below; see also the Prout citation, at the same location). This is not in accord with any accepted Greek meaning, and in Greek theory it would fail to exclude the other tetrachords.*
*The fact that τόνος itself has at least four distinct meanings in Greek theory of music contributes to the uncertainty of the exact meaning and derivation of διατονικός, even among ancient writers. *(See Solon Michaelides, The Music of Ancient Greece: An Encyclopaedia (London; Faber and Faber, 1978), pp. 335-40: "Tonos".
Τόνος may refer to a pitch, an interval, a *"key"* or register of the voice, or a mode.) For more information, especially concerning the various exact tunings of the diatonic tetrachord, see Diatonic genus.

Hmm, two tones, two tetrachords, two semitones, two keys...


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## Bwv 1080

The Greek etymology is irrelevant, what matter in regards to western music theory is the definition given to it over the past few hundred years which is the scale <013568A> pattern of the white keys of the piano.


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## EdwardBast

millionrainbows said:


> Hmm, two tones, two tetrachords, two semitones, two keys...





Why did you end with the above? None of these readings is justified by what you quoted. Instead of just admitting that isorhythm and BabyGiraffe are right - "two" has nothing to do with it - you chose to obfuscate.

Edit: Oh, I see! You made a mistake in another thread … :

"Diatonic" means "two tonics." The C major scale is "diatonic" because it has C and F as strong tonics."

… and you're trying to cover it up.

So the substance of your elaborate post is that the term diatonic as applied to C major derives from Greek tetrachord theory, a fact you were told in the other thread and above in #3.


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## millionrainbows

I'd like to express my sincere appreciation to BabyGiraffe for posting an edited-out statement of mine. Thanks a lot, dude!


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## millionrainbows

EdwardBast said:


> Why did you end with the above? None of these readings is justified by what you quoted. Instead of just admitting that isorhythm and BabyGiraffe are right - "two" has nothing to do with it - you chose to obfuscate.


If you read carefully, there is no definite meaning of the Greek root. It could mean "two," referring to fifths and octaves.


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## EdwardBast

millionrainbows said:


> If you read carefully, there is no definite meaning of the Greek root. It could mean "two," referring to fifths and octaves.


It doesn't mean two. And this is beside the point. The term diatonic comes directly from Greek tetrachord theory where it is used in opposition to chromatic. We use it the same way. There is no mystery here. It certainly has nothing to do with your half-baked theory.


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## isorhythm

millionrainbows said:


> If you read carefully, there is no definite meaning of the Greek root. It could mean "two," referring to fifths and octaves.


It couldn't. It has a meaning unrelated to the number two and comes up in quite a few Greek-derived words. Think dialectic, dialogue, diagnosis, dialysis....

What I still don't understand is where you thought you were going with this. Did you think diatonic only referred to the Ionian (eg C major) scale?


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## Woodduck

Diatonic is something one takes to cure diarrhea. Of the verbal sort, in the case of this thread.


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## isorhythm

Woodduck said:


> Diatonic is something one takes to cure *diarrhea*. Of the verbal sort, in the case of this thread.


Another good example of a dia- word.


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## Becca

Woodduck said:


> Diatonic is something one takes to cure diarrhea. Of the verbal sort, in the case of this thread.


It is surely diabolical


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## millionrainbows

It could mean "dirreah," referring to EdwardBast and Woodduck.


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## millionrainbows

The diatonic scale is obtained from a chain of six successive fifths. For instance, the seven natural pitches that form the C-major scale can be obtained from a chain of fifths starting from F (F-C-G-D-A-E-B).
True or false?


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## isorhythm

millionrainbows said:


> The diatonic scale is obtained from a chain of six successive fifths. For instance, the seven natural pitches that form the C-major scale can be obtained from a chain of fifths starting from F (F-C-G-D-A-E-B).
> True or false?


Obtained by whom, when?

In general, false, but I suppose some theorists have obtained it that way.


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## millionrainbows

Originally Posted by *millionrainbows* 
_

The diatonic scale is obtained from a chain of six successive fifths. For instance, the seven natural pitches that form the C-major scale can be obtained from a chain of fifths starting from F (F-C-G-D-A-E-B).

True or false?_



isorhythm said:


> Obtained by whom, when?
> 
> In general, false, but I suppose *some theorists *have obtained it that way.


So there really is no unanimous, definitive answer?

Well, that's a Wikepedia quote. 
If you say that tetrachords were how diatonic scales were formed, then how do you explain the 12-note collection? 
It's easily explained by fifths, since the circle of fifths and the chromatic circle are closely related.


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## Bwv 1080

> There is evidence that the Sumerians and Babylonians used a version of the diatonic scale.[2][3] This derives from surviving inscriptions that contain a tuning system and musical composition. Despite the conjectural nature of reconstructions of the piece known as the Hurrian songs from the surviving score, the evidence that it used the diatonic scale is much more soundly based. This is because instructions for tuning the scale involve tuning a chain of six fifths, so that the corresponding circle of seven major and minor thirds are all consonant-sounding, and this is a recipe for tuning a diatonic scale.


https://en.wikipedia.org/wiki/Diatonic_scale

the Babylonians derived the diatonic scale from 5ths, therefore everything George Russell ever said is true!


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## Bwv 1080

Lydian Chromatic is the Dianetics of Music Theory


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## isorhythm

million,

I've got a true or false question for you as well. Here goes.

The intervals of a diatonic scale can be described by the following ratios:

1:1
9:8
5:4
4:3
3:2
5:3
15:8
2:1

True or false?


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## EdwardBast

millionrainbows said:


> So there really is no unanimous, definitive answer?
> 
> Well, that's a Wikepedia quote.
> If you say that tetrachords were how diatonic scales were formed, then how do you explain the 12-note collection?
> It's easily explained by fifths, since the circle of fifths and the chromatic circle are closely related.


You started this thread and yet you can't seem to remember what it's about. It isn't about where 12-note collections came from, it's about why C major is called a diatonic scale and what diatonic means. Once again, the name comes from diatonic tetrachord theory and it applies to major and minor scales because the Greeks used similar scales and modes, which they built from tetrachords they called diatonic.


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## Guest

You can waste a lot of time on numerology. The scale we have is a kluge. If you take the chromatic scale, breaking the octave into 12 equal steps, you end up with intervals which are close enough to the simple ratios 3:2, 4:3, 5:4. If you divide the octave differently, into 10, 11, 13, 14, 15 equal steps you end up with intervals which are farther from the simple ratios. So the 12 tone is a lucky numerical coincidence. If you want two notes at once you use the 1st and 5th. If you want 3 note chords you would naturally include the major third, which is the next simplest ratio (5:4). The scale we have is what you get if you ask for the minimum number of tones that allows you to make a triad based on the root, the dominant, and the subdominant. It's convenient. It's the minimum toolkit for writing a three-chord pop song.

The pythagorean bit, building the scale from repeated 5ths, is a red herring. When you come around the full circle you don't end up with the same note. Doing c-g-d-a-e-b-f#-c#-a flat-e flat-b flat-f-c your final c is mistuned from your initial c. It doesn't work. Sure, each tone has a perfect relationship with a tone a 5th up or down, but the other notes do not have good relationships with each other. You can torture it into generating a scale if you value numerology over music that sounds good.

There is no perfect mathematical basis for the common practice system of harmony.


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## Bwv 1080

Baron Scarpia said:


> There is no perfect mathematical basis for the common practice system of harmony.


I don't know about that - if you map integers to letters, the complete texts of all major religious works are encoded in the digits of the ratio between equal tempered semitones (2^(1/12))

Within the ratio of an equal-tempered major third, you can find every novel that has been published or ever will be published

who knows what you could find in other intervals...


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## Woodduck

EdwardBast said:


> You started this thread and yet you can't seem to remember what it's about.


A clear case of diamentia.


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## Guest

EdwardBast said:


> *You started this thread and yet you can't seem to remember what it's about.* It isn't about where 12-note collections came from, it's about why C major is called a diatonic scale and what diatonic means. Once again, the name comes from diatonic tetrachord theory and it applies to major and minor scales because the Greeks used similar scales and modes, which they built from tetrachords they called diatonic.


The proposition that any thread on this site is _about_ something is questionable.


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## Guest

Bwv 1080 said:


> I don't know about that - if you map integers to letters, the complete texts of all major religious works are encoded in the digits of the ratio between equal tempered semitones (2^(1/12))
> 
> Within the ratio of an equal-tempered major third, you can find every novel that has been published or ever will be published
> 
> who knows what you could find in other intervals...


They why am I wasting my money on Kindle books.


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## Guest

Here. Want to know the "deep" meaning of the pythagorean tuning. Every time you go up by an octave you multiply the frequency of the tone by 2. The octaves are 2, 2^2 = 4, 2^3 = 8, etc.

Now, take the perfect fifth, which has a frequency ratio 3/2. Go up 12 perfect fifths from C, you apply the ratio (3/2) 12 times. You get (3/2)^12 = 129.7463. Well seven octaves is 2^7 = 128. and 129.7463 is close to 128. That coincidence is the reason the circle of fifths gives you the chromatic scale, _almost_. The approximation of C you get after going around the circle of fifths is 1/4 of the way between C and C#. The music of the spheres, except the gears are grinding a bit.

Math is fun!


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## EdwardBast

Baron Scarpia said:


> Here. Want to know the "deep" meaning of the pythagorean tuning. Every time you go up by an octave you multiply the frequency of the tone by 2. The octaves are 2, 2^2 = 4, 2^3 = 8, etc.
> 
> Now, take the perfect fifth, which has a frequency ratio 3/2. Go up 12 perfect fifths from C, you apply the ratio (3/2) 12 times. You get (3/2)^12 = 129.7463. Well seven octaves is 2^7 = 128. and 129.7463 is close to 128. That coincidence is the reason the circle of fifths gives you the chromatic scale, _almost_. The approximation of C you get after going around the circle of fifths is 1/4 of the way between C and C#. *The music of the spheres, except the gears are grinding a bit.*
> 
> Math is fun!


Yes. And seeing it almost worked they decided to bend it so it did. The warping was within acceptable tolerances, for most of us anyway.


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## Becca

And they call this theory? I'm not sure whether to :lol: or  Well I suppose it is better than 'social science'.


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## EdwardBast

Becca said:


> And they call this theory? I'm not sure whether to :lol: or  Well I suppose it is better than 'social science'.


No Becca, this _is_ social science.


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## BabyGiraffe

12 is a composite number = 2^2 x 3, so only 1/11 or 5/7 can serve as generators for the cyclic group of 12 pitches. 
Compare to 34 equal (which is better than *any *meantone tuning in terms of harmonic accuracy) where the circle of fifths gives us...17 equal, so obviously tonal modulation and chord patterns there are different than these in 12 equal music theory.

(12 equal has subgrous C2, C3, C4 and C6. A coset of Cn is obtained by adding to each element of Cn the same element of Cn. Example: tempered fully diminished chord is C4 in 12 equal and is represented in atonal integer notation as (0,3,6,9). The other cosets are 1,4,7,10 and 2,5,8, 11. Obviously in 34 equal we have 17 equal and tritones (of course, any tuning, divisible by 2 has this one) as subgroups. We can construct all the modes of limited transposition, various looping chord progressions and represent various other elements as generated by these cosets or intervals in them. For reference, check any abstract algebra/group theory text/wikipedia.)

From
https://en.wikipedia.org/wiki/Modulatory_space

"Toroidal modulatory spaces

If we divide the octave into n parts, where n = rs is the product of two relatively prime integers r and s, we may represent every element of the tone space as the product of a certain number of "r" generators times a certain number of "s" generators; in other words, as the direct sum of two cyclic groups of orders r and s. We may now define a graph with n vertices on which the group acts, by adding an edge between two pitch classes whenever they differ by either an "r" generator or an "s" generator (the so-called Cayley graph of Z 12 with generators r and s). The result is a graph of genus one, which is to say, a graph with a donut or torus shape. Such a graph is called a toroidal graph.

An example is equal temperament; twelve is the product of 3 and 4, and we may represent any pitch class as a combination of thirds of an octave, or major thirds, and fourths of an octave, or minor thirds, and then draw a toroidal graph by drawing an edge whenever two pitch classes differ by a major or minor third.

We may generalize immediately to any number of relatively prime factors, producing graphs can be drawn in a regular manner on an n-torus. "

Translated in more normal language we can say that every interval in 12 equal can be decomposed into major thirds and minor thirds -example: P5=M3 + m3

So we don't need chains or circles of generators to get to diatonic or 12 tone (tuned to equal, meantone, just intonation, diaschismic like 34, schismic or whatever temperament). Of course, there exist even more different methods to construct 7note diatonic/12 equal.

If we are that concerned about very good perfect fifths, the only alternative to diatonic scale actually is 17 notes and this is based on some patterns of log3 base2 - we get 8 major chords, 8 minor chords and one dissonant chord. Pythagorean/syntonic commas becomes a small step in this tuning. I guess this is similar to some kind of Indian music gamut. 41 equal or 53 equal supports it.


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## millionrainbows

Thank you, BabyGiraffe, that clears everything up! :lol:


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## millionrainbows

Woodduck said:


> A clear case of diamentia.


"The way out is down the toilet; why is it that more people do not use this method?'


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## millionrainbows

The tetrachords which make up the C major diatonic scale, when used as a scale, both have leading tones. The first implies F, the second implies C. Thus, the C major scale has "two tonics" and is "ditonic" in keeping with the original Greek root, which can mean two things. I'm on solid ground.


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## isorhythm

millionrainbows said:


> The tetrachords which make up the C major diatonic scale, when used as a scale, both have leading tones. The first implies F, the second implies C. Thus, the C major scale has "two tonics" and is "ditonic" in keeping with the original Greek root, which can mean two things. I'm on solid ground.


We've all made factual mistakes and admitted them on here. There's really no shame in it!


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## millionrainbows

isorhythm said:


> We've all made factual mistakes and admitted them on here. There's really no shame in it!


That's OK if you are ignorant!


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## Phil loves classical

The prefix dia in Greek means across or through. Diameter (across or through a circle), diatonic (through the tones).

https://pressbooks.bccampus.ca/greeklatinroots2/chapter/§133-exploring-greek-prefixes/

Not 2 of anything. To force the relation of diatonic to 2 tonics is like forcing a relationship between Hitler and Christianity


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## millionrainbows

Phil loves classical said:


> The prefix dia in Greek means across or through. Diameter (across or through a circle), diatonic (through the tones).


Yeah, yeah, we know all that. I also pointed out that the Greek root has 2 meanings.


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## Bwv 1080

millionrainbows said:


> Yeah, yeah, we know all that. I also pointed out that the Greek root has 2 meanings.


Yes, that was quite the virtuosic display of confirmation bias


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## EdwardBast

millionrainbows said:


> The tetrachords which make up the C major diatonic scale, when used as a scale, both have leading tones. The first implies F, the second implies C. Thus, the C major scale has "two tonics" and is "ditonic" in keeping with the original Greek root, which can mean two things. I'm on solid ground.


Once again, this is false. This "original Greek root" to the term diatonic is your fabrication. There is no ground supporting your position. You continue to fill this thread with misinformation. Just admit you were wrong already.


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## jegreenwood

millionrainbows said:


> Thank you, BabyGiraffe, I'll take that into consideration.
> The English word diatonic is ultimately from the Greek διατονικός (diatonikós), itself from διάτονος (diátonos), which may mean (as OEDclaims) "through the tones" (taking τόνος, tónos, to mean interval of a tone), or perhaps stretched out (as recorded in Liddell and Scott's Greek Lexicon). See also Barsky (Chromaticism, Barsky, Vladimir, Routledge, 1996, p. 2): "There are two possible ways of translating the Greek term 'diatonic': (1) 'running through tones', i.e. through the whole tones; or (2) a 'tensed' tetrachord filled up with the widest intervals". The second interpretation would be justified by consideration of the pitches in the diatonic tetrachord, which are more equally distributed ("stretched out") than in the chromatic and enharmonic tetrachords, and are also the result of tighter stretching of the two variable strings. It is perhaps also sounder on linguistic morphological grounds. (See also Merriam-Webster Online.)
> A completely separate explanation of the origins of *the term diatonic appeals to the generation of the diatonic scale from "two tones"*: "Because the musical scale is based entirely on octaves and fifths, that is, two notes, it is called the 'diatonic scale' " (Phillips, Stephen, "Pythagorean aspects of music", in Music and Psyche, Vol. 3, available also online. *But this ignores the fact that it is the element di- that means "two", not the element dia-,* which has "through" among its meanings (see Liddell and Scott). *There is a Greek term δίτονος (dítonos), which is applied to an interval equivalent to two tones. It yields the English words ditone and ditonic (see Pythagorean comma), but it is quite distinct from διάτονος.*
> *Yet another derivation assumes the sense "through the tones" for διάτονος, but interprets tone as meaning individual note of the scale: "The word diatonic means 'through the tones' (i.e., through the tones of the key)" (Gehrkens, 1914, see below; see also the Prout citation, at the same location). This is not in accord with any accepted Greek meaning, and in Greek theory it would fail to exclude the other tetrachords.*
> *The fact that τόνος itself has at least four distinct meanings in Greek theory of music contributes to the uncertainty of the exact meaning and derivation of διατονικός, even among ancient writers. *(See Solon Michaelides, The Music of Ancient Greece: An Encyclopaedia (London; Faber and Faber, 1978), pp. 335-40: "Tonos".
> Τόνος may refer to a pitch, an interval, a *"key"* or register of the voice, or a mode.) For more information, especially concerning the various exact tunings of the diatonic tetrachord, see Diatonic genus.
> 
> Hmm, two tones, two tetrachords, two semitones, two keys...


I was impressed with your research and knowledge here, until I discovered you simply copied and pasted a Wikipedia footnote.

https://en.wikipedia.org/wiki/Diatonic_and_chromatic (footnote 8)

You did add lots of boldface, large fonts and red coloring, though.

Reading it in Wikipedia, I was drawn to this sentence:

But this ignores the fact that it is the element di- that means "two", not the element dia-, which has "through" among its meanings (see Liddell and Scott). There is a Greek term δίτονος (dítonos), which is applied to an interval equivalent to two tones. It yields the English words ditone and ditonic (see Pythagorean comma), but it is quite distinct from διάτονος.


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## millionrainbows

EdwardBast said:


> Once again, this is false. This "original Greek root" to the term diatonic is your fabrication. There is no ground supporting your position. You continue to fill this thread with misinformation. Just admit you were wrong already.


The English word diatonic is ultimately from the Greek διατονικός (diatonikós), itself from διάτονος (diátonos), which may mean (as OEDclaims) "through the tones" (taking τόνος, tónos, to mean interval of a tone), or perhaps stretched out (as recorded in Liddell and Scott's Greek Lexicon). See also Barsky (Chromaticism, Barsky, Vladimir, Routledge, 1996, p. 2): "There are two possible ways of translating the Greek term 'diatonic': (1) 'running through tones', i.e. through the whole tones; or (2) a 'tensed' tetrachord filled up with the widest intervals". The second interpretation would be justified by consideration of the pitches in the diatonic tetrachord, which are more equally distributed ("stretched out") than in the chromatic and enharmonic tetrachords, and are also the result of tighter stretching of the two variable strings. It is perhaps also sounder on linguistic morphological grounds. (See also Merriam-Webster Online.)
A completely separate explanation of the origins of *the term diatonic appeals to the generation of the diatonic scale from "two tones"*: "Because the musical scale is based entirely on octaves and fifths, that is, two notes, it is called the 'diatonic scale' " (Phillips, Stephen, "Pythagorean aspects of music", in Music and Psyche, Vol. 3, available also online. *But this ignores the fact that it is the element di- that means "two", not the element dia-,* which has "through" among its meanings (see Liddell and Scott). *There is a Greek term δίτονος (dítonos), which is applied to an interval equivalent to two tones. It yields the English words ditone and ditonic (see Pythagorean comma), but it is quite distinct from διάτονος.*
*Yet another derivation assumes the sense "through the tones" for διάτονος, but interprets tone as meaning individual note of the scale: "The word diatonic means 'through the tones' (i.e., through the tones of the key)" (Gehrkens, 1914, see below; see also the Prout citation, at the same location). This is not in accord with any accepted Greek meaning, and in Greek theory it would fail to exclude the other tetrachords.*
*The fact that τόνος itself has at least four distinct meanings in Greek theory of music contributes to the uncertainty of the exact meaning and derivation of διατονικός, even among ancient writers. *(See Solon Michaelides, The Music of Ancient Greece: An Encyclopaedia (London; Faber and Faber, 1978), pp. 335-40: "Tonos".
Τόνος may refer to a pitch, an interval, a *"key"* or register of the voice, or a mode.) For more information, especially concerning the various exact tunings of the diatonic tetrachord, see Diatonic genus.


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## AeolianStrains

I have no idea how you can't read that and not immediately recognize how wrong you are. The note quite clearly says that whatever ignorant writer proposed that "diatonic" means "two tones" ignores the basic and indisputable fact that dia- comes from the Greek preposition meaning "through" or "across."

An ancient Greek writer would not have confused the two. The _precise_ meaning διατονικός is up for debate, but at no point is the number "two" a part of that.

How many Classics PhDs will it take for you to just admit you, having no Greek, are just wrong here?


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## ECraigR

No PhD in classics, but as a reader of Ancient Greek and Latin, I fully support AeolianStrains, and Millionrainbows, you’re rather off the mark.


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## millionrainbows

ECraigR said:


> No PhD in classics, but as a reader of Ancient Greek and Latin, I fully support AeolianStrains, and Millionrainbows, you're rather off the mark.


Well, that's charming! I'll buy you a cake so you can have a little party!

Meanwhile, jegreenwood and I will have a drink out in the garden.


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## ECraigR

Thanks I prefer chocolate


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## Merl

Is this diatonic?


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## jegreenwood

Merl said:


> Is this diatonic?
> 
> View attachment 122197


No, no no!! If the word is "di-atonic" it means in the style of Schoenberg AND Webern.


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## Merl

jegreenwood said:


> No, no no!! If the word is "di-atonic" it means in the style of Schoenberg AND Webern.


Does that mean that Schoenberg and Webern drank gin and tonic? This is why I love TC. You learn so much about CM.


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## mikeh375

jegreenwood said:


> No, no no!! If the word is "di-atonic" it means in the style of Schoenberg AND Webern.


no, no no jegreenwood and Merl. Di-atonic refers to an obsession with Princess Diana that results in a paralysis of the left leg...(?)


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## jegreenwood

On reflection maybe Merl was the closest, and it means this:


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## millionrainbows

At least drinking tonic water prevents malaria, which is more than I can say for the academics around theses parts!


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## AeolianStrains

millionrainbows said:


> At least drinking tonic water prevents malaria, which is more than I can say for the academics around theses parts!


Oh, yes, I'm sure you're very active dedicating your time to preventing malaria. 

Is your ego really that big you can't admit a simple mistake?


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## Woodduck

millionrainbows said:


> At least drinking tonic water prevents malaria, which is more than I can say for the academics around theses parts!


Posts #4 and #42, of course, have not a whiff of academicism about them.


----------



## ECraigR

I don’t care much for academics either. I do, however, care quite strongly about facts. Call me kooky


----------



## isorhythm

One time I wrote on here that Schubert didn't write any operas, which was embarrassing, but not as embarrassing as if I'd bizarrely continued arguing that his operas were not authentic or something.

Also worth noting that the stakes are particularly low since we're all writing under pseudonyms.


----------



## Becca

ECraigR said:


> I don't care much for academics either. *I do, however, care quite strongly about facts*. Call me kooky


But, but ... this is TC, often a fact-free zone.


----------



## mikeh375

isorhythm said:


> ..
> ......Also worth noting that the stakes are particularly low since we're all writing under pseudonyms.


Not _all_ IsoR.... I try hard to be careful, doesn't always work though.


----------



## millionrainbows

Regardless, the C major scale has two leading tones, E-F and B-C, one of which supports F and one which supports C. 

The C Lydian Scale has two leading tones, one of which supports C (B-C) and the other supporting G (F#-G), a more closely related key. 
The Lydian scale is therefore more consonant with the key of C, which a scale on C is supposed to do.

You can view this as a deficiency of the C major scale (as it is in Jazz), or see it as an inherent "restless" quality which encourages travel away from the key. 
The choice is yours, but don't play an F over a C major seventh chord, and always resolve the F if it's over a C.


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## Bwv 1080

Yes but in Jazz its ii- V7 I△ not II7 V△ I△, so maybe major is more harmonically stable than Lydian


----------



## EdwardBast

millionrainbows said:


> Regardless, the C major scale has two leading tones, E-F and B-C, one of which supports F and one which supports C.
> 
> The C Lydian Scale has two leading tones, one of which supports C (B-C) and the other supporting G (F#-G), a more closely related key.
> The Lydian scale is therefore more consonant with the key of C, which a scale on C is supposed to do.
> 
> You can view this as a deficiency of the C major scale (as it is in Jazz), or see it as an inherent "restless" quality which encourages travel away from the key.
> The choice is yours, but don't play an F over a C major seventh chord, and always resolve the F if it's over a C.


1. Not all half steps involve leading tones. 
2. G major is not more closely related to C major than F major. 
3. The Lydian mode is, quite obviously, not "more consonant with the key of C major" than a C major scale (whatever that's supposed to mean.)
4. Major scales aren't deficient. 
5. Major scales aren't inherently more restless than other modes.

Calling this theory half-baked would be an insult to bakers.


----------



## millionrainbows

EdwardBast said:


> 1. Not all half steps involve leading tones.


So? That's just a meaningless exception, which doesn't disprove what I said.



> 2. G major is not more closely related to C major than F major.


As a tone, yes it is, because G is more prominent in the overtone series. Were you thinking in keys exclusively? I'm not an exclusive kind of thinker.



> 3. The Lydian mode is, quite obviously, not "more consonant with the key of C major" than a C major scale (whatever that's supposed to mean.)


Yes it is; a C major scale clashes with a C major seventh chord, because "F" is an "avoid" note. Everyone knows that. What are you trying to say?



> 4. Major scales aren't deficient.


Again, you don't have to view this as a deficiency, but it's not as harmonically congruent as a scale as C Lydian is.



> 5. Major scales aren't inherently more restless than other modes.


As a "C" scale which reinforces the key of C, the Lydian scale reinforces the key of C better. The C major scale's E-F leading tone creates a movement out of C, into F. That's restless.



> Calling this theory half-baked would be an insult to bakers.


I think this argument works very well, and you can't seem to find any weaknesses in it which are really credible; all you've done is try to negate what I've said, with no real ideas to the contrary. That's merely an attempt at invalidation, not counter-argument.


----------



## isorhythm

millionrainbows said:


> I'm not an exclusive kind of thinker.


No?

It seems to me that you get in trouble by wanting to understand music exclusively in terms of rigid, black-and-white rules and abstractions.

It doesn't work that way.


----------



## Woodduck

millionrainbows said:


> Regardless, the C major scale has two leading tones, E-F and B-C, one of which supports F and one which supports C.


In the C Major scale, E is not a leading tone. But neither is B. In scales _as such,_ there are no leading tones.

"Leading" is a subjective sensation; that term wouldn't exist but for the feeling that a tone needs to move to the adjacent one. Outside of some specific musical context which would frame the E as needing to resolve to the F above - typically, a modulation into the subdominant - the E doesn't function as a leading tone. It doesn't "lead" anywhere; it just sits there. But more than this: even the B in a C Major scale depends upon its being heard as a component in a particular tonal system in order to be heard as "leading." As we know from much 20th-century music, particularly jazz, the B can be heard as a stable component of a C7, and as such doesn't need to be resolved. The tonality, no longer common practice, removes from B its "leading" function, and makes referring to it as a leading tone meaningless.

To speak of the components of scales as having specific tendencies is to confuse a potential with an actuality. Scales are not tonal systems but are merely collections of pitches, materials from which tonalities are formed. The laws of a tonal system determine the potential activity of the tones which compose it. What we know as the C Major scale can provide the material for more than one tonal system, and in a system which lacks modulation into the subdominant, the E never becomes - i.e., never _feels like_ - a leading tone. A piece of music exhibiting this would be easy to write - and, in fact, in such a piece it would be the F, not the E, which would feel like a "leading tone": the F would be heard as having a "downward leading" function, wanting resolution to the E because of its dissonant status against the chord of C Major, and specifically against the adjacent E. Far from implying "travel" to another key, the occurrence of the note F would then only reinforce the strength of C as the tonal center.


----------



## Bwv 1080

Yes - half steps resolve either up or down -the resolution of F-E in C Major is at least as strong as F# to G in the C Lydian scale. Put the two half step resolutions together and the Tritone resolution by contraction to a major third is stronger than by expanding to a 5th. Then you get the phyrigian mode where the half steps both resolve down.


----------



## Bwv 1080

If you think about it, the primary reason the #11 is played on tonic major chords is that the need to resolve the natural 4th is so strong - if you play the natural 11 and the 7th you are outlining the dominant when you are supposed to resolve it. You play the #11 because it’s not important - it’s just color and does not imply any tonal function


----------



## Woodduck

Bwv 1080 said:


> If you think about it, the primary reason the #11 is played on tonic major chords is that the need to resolve the natural 4th is so strong - if you play the natural 11 and the 7th you are playing outlining the dominant when you are supposed to resolve it.


And thinking about it further, the need of the natural 4th to "lead" downward is stronger than the need of the 7th to "lead" upward. By extension, above a C tonic chord (whether or not it includes the added 7th) we can superimpose a G major triad with no need to resolve it (see _Appalachian Spring_), but not an F major triad. Moreover, a plagal cadence, IV-I, can sound more decisive and final than an authentic cadence, V-I, presumably because IV has greater tension with I than V does, and thus a greater need to resolve into it.

All this argues against the idea that the 3rd note of a major scale is a "leading tone" and that the 4th somehow wants to become a tonic.


----------



## Bwv 1080

(Deleted duplicate post)


----------



## millionrainbows

Woodduck said:


> In the C Major scale, E is not a leading tone. But neither is B. In scales _as such,_ there are no leading tones.


More irrelevant technical clutter, demonstrating a resistance to consider the idea.



> "Leading" is a subjective sensation; that term wouldn't exist but for the feeling that a tone needs to move to the adjacent one. Outside of some specific musical context which would frame the E as needing to resolve to the F above - typically, a modulation into the subdominant - the E doesn't function as a leading tone. It doesn't "lead" anywhere; it just sits there.


In a scale, without context, true; but this is more technicality, more clutter.



> But more than this: even the B in a C Major scale depends upon its being heard as a component in a particular tonal system in order to be heard as "leading." As we know from much 20th-century music, particularly jazz, the B can be heard as a stable component of a C7, and as such doesn't need to be resolved. The tonality, no longer common practice, removes from B its "leading" function, and makes referring to it as a leading tone meaningless.


Irrelevant. If this is all you can "get me" on, it's not sufficient to disprove anything I've said. It's just counter-argument.



> To speak of the components of scales as having specific tendencies is to confuse a potential with an actuality.


No, I disagree. I like to consider things like this as "underlying principles."



> Scales are not tonal systems but are merely collections of pitches, materials from which tonalities are formed.


In some rigid, technical sense this may be true, but it is misleading clutter in the discussion at hand.



> The laws of a tonal system determine the potential activity of the tones which compose it.


Not exclusively. The mere content of a scale can also determine its tonal potential, in a more basic way. Your stuff comes later.



> What we know as the C Major scale can provide the material for more than one tonal system, and in a system which lacks modulation into the subdominant, the E never becomes - i.e., never _feels like_ - a leading tone.


"...in a system which lacks modulation into the subdominant"? What kind of super-specific exception have you concocted now? :lol:



> A piece of music exhibiting this would be easy to write - and, in fact, in such a piece it would be the F, not the E, which would feel like a "leading tone": the F would be heard as having a "downward leading" function, wanting resolution to the E because of its dissonant status against the chord of C Major, and specifically against the adjacent E. Far from implying "travel" to another key, the occurrence of the note F would then only reinforce the strength of C as the tonal center.


Sounds like your everyday suspension.


----------



## millionrainbows

isorhythm said:


> No?
> 
> It seems to me that you get in trouble by wanting to understand music exclusively in terms of rigid, black-and-white rules and abstractions.
> 
> It doesn't work that way.


I try to understand the underlying principles. I'm also more of a "vertical" thinker that you & Woooduck.


----------



## millionrainbows

Woodduck said:


> And thinking about it further, the need of the natural 4th to "lead" downward is stronger than the need of the 7th to "lead" upward. By extension, above a C tonic chord (whether or not it includes the added 7th) we can superimpose a G major triad with no need to resolve it (see _Appalachian Spring_), but not an F major triad.


That proves my earlier assertion that G major is a more closely related key to C major.



> Moreover, a plagal cadence, IV-I, can sound more decisive and final than an authentic cadence, V-I, presumably because IV has greater tension with I than V does, and thus a greater need to resolve into it.


You're supporting my idea that "F" produces tension in the C major scale. Of course it would sound more "final" if it resolves to C (duh). This neatly bypasses the tendency of "F" to reinforce the key of F.



> All this argues against the idea that the 3rd note of a major scale is a "leading tone" and that the 4th somehow wants to become a tonic.


This is a self-justifying answer. Of course the third is not acting as a leading tone in the context of C. But if the fourth "somehow wants to become a tonic" the E is a leading tone. None of this contradicts anything I have said.


----------



## isorhythm

What if Ionian and Lydian modes can both give rise to feelings of stability or instability in different situations, depending on context and cultural expectations??


----------



## Bwv 1080

isorhythm said:


> What if Ionian and Lydian modes can both give rise to feelings of stability or instability in different situations, depending on context and cultural expectations??


What? you mean to imply that music is an art that exists within a cultural context, and not a set of universal laws? Heresy!


----------



## Woodduck

millionrainbows said:


> *More irrelevant technical clutter, demonstrating a resistance to consider the idea.*
> 
> In a scale, without context, true; but this is more technicality, *more clutter.*
> 
> *Irrelevant. If this is all you can "get me" on,* it's not sufficient to disprove anything I've said. It's just counter-argument.
> 
> No, I disagree. *I like to consider things like this* as "underlying principles."
> 
> *In some rigid, technical sense* this may be true, but* it is misleading clutter* in the discussion at hand.
> 
> "...in a system which lacks modulation into the subdominant"? *What kind of super-specific exception have you concocted now?* :lol:


Arrogant posturings and putdowns are no substitute for argument. Cut it out.

You speak of scales _as such_ having tendencies and instabilities. I say that these are properties not of scales but of tonal systems. Isorhythm supports this: "What if Ionian and Lydian modes can both give rise to feelings of stability or instability in different situations, depending on context and cultural expectations??" The point of this is that we attribute "tendencies" to the tones in certain scales only by extension and retrospectively, because the tonal systems in which the scales have been used (the "context") lead us to expect the tones in question to have particular functions (the "cultural expectations"). There is no basis for attributing these functions or "tendencies" to scales as such.


----------



## millionrainbows

Woodduck said:


> You speak of scales _as such_ having tendencies and instabilities. I say that these are properties not of scales but of tonal systems. Isorhythm supports this: "What if Ionian and Lydian modes can both give rise to feelings of stability or instability in different situations, depending on context and cultural expectations??" The point of this is that we attribute "tendencies" to the tones in certain scales *only by extension and retrospectively,* because the tonal systems in which the scales have been used (the "context") lead us to expect the tones in question to have particular functions (the "cultural expectations").


I disagree. I frequently attribute tendencies and qualities of tonality to static "vertical" aspects of scales (interval vectors), the harmonic series, and harmonic "models" which you do not; you tend to want to derive all tendencies from horizontal, narrative aspects of "events."



> There is no basis for attributing these functions or "tendencies" to scales as such.


 I couldn't disagree more.


----------



## isorhythm

millionrainbows said:


> I try to understand the underlying principles. I'm also more of a "vertical" thinker that you & Woooduck.


Do you mean "vertical" as in chords, or in some more esoteric sense that you haven't defined?


----------



## millionrainbows

Bwv 1080 said:


> What? you mean to imply that music is an art that exists within a cultural context, and not a set of universal laws? Heresy!


You make art sound like style. Viva quadrivium!

These "cultural expectations" are just mannerisms & procedures. When you enter into "uncharted" territory such as serialism, procedures & assumptions are gone, and you have to start dealing with the nuts & bolts. You start questioning everything instead of taking everything for granted.


----------



## millionrainbows

isorhythm said:


> Do you mean "vertical" as in chords, or in some more esoteric sense that you haven't defined?


As in chords, and as in potentialities which exist in the instant, before time becomes a factor. For instance, the interval vector of a scale or set exists as an "index of possibilities" before it is put onto a time line.


----------



## isorhythm

Sincere question: how do you account for the fact that different musical traditions treat melody and harmony so differently, if they're supposed to be governed by universal laws?


----------



## millionrainbows

isorhythm said:


> Sincere question: how do you account for the fact that different musical traditions treat melody and harmony so differently, if they're supposed to be governed by universal laws?


\

I'm not a rigid thinker, so I can't answer that. I tend to see how different musical traditions treat melody and harmony similarly; I look for commonalities. What separates things is the tendency to think academically.

We all have ears, and the harmonic series is a universal, so if I see things as "governed" by vertical harmonic models, then I will see similarities, not differences. All of these "exceptions" posed by Woodduck are just argumentation; they don't prove or disprove anything I've said.

Additionally, all great musical thinkers are aware of this. They tend to see beyond the surface, into the "underlying principles" of music. To do this, you must think vertically and stop depending on narrative thinking. Most of their great ideas came in instantaneous "flashes" of inspiration, not drudgery and re-writes.


----------



## Woodduck

millionrainbows said:


> I frequently attribute tendencies and qualities of tonality to static "vertical" aspects of scales (interval vectors), the harmonic series, and harmonic "models" which you do not; you tend to want to derive all tendencies from horizontal, narrative aspects of "events."


What you appear to do is give metaphoric life and agency to inanimate things, as in your statement: "The C major scale's E-F leading tone *creates a movement* out of C, into F. That's restless." No, the E in a C major scale doesn't create any movement. It just sits there, being the third note of a scale with no need to become or do anything. When I play a major scale I feel no restlessness at all.


----------



## KenOC

millionrainbows said:


> \
> 
> I'm not a rigid thinker...


It is possible - barely possible but possible nonetheless - that _some _- a scant few out of the very many existing - may find this an understatement. :angel:


----------



## Woodduck

millionrainbows said:


> *I'm not a rigid thinker, so I can't answer that.*


That's priceless. I must remember to use it next time I'm in a jam.



> I tend to see how different musical traditions treat melody and harmony similarly; *I look for commonalities.* *What separates things is the tendency to think academically.*


What "separates things" is elementary perception and thinking. You can't be sure about your "commonalities" until you've defined the differences between things that may, or may not, possess commonalities. Until you do that, it's all mush. I'm afraid your identifying the dynamics of tonal systems with supposed "tendencies" of scales is an example of mush.



> We all have ears, and *the harmonic series is a universal,*


The harmonic series is not a "universal." It's merely a phenomenon.



> if I see things as "governed" by vertical harmonic models, then *I will see similarities, not differences.*


Or maybe, because you see "similarities" between scales and tonal systems, you imagine that both are "governed," and in the same way, by the harmonic series. In any case, when your only tool is a hammer, everything looks like a nail.



> All of these *"exceptions" posed by Woodduck are just argumentation; they don't prove or disprove anything I've said.*


Exceptions, when acknowledged, rein us in and protect the world from our delusions of grandeur.



> Additionally, *all great musical thinkers* are aware of this.


Including your humble self, no doubt.



> They tend to see beyond the surface, into *the "underlying principles"* of music.


Yeah, we're all doing this. But we don't all agree on what principles underlie what.



> To do this, *you must think vertically and stop depending on narrative thinking.* Most of their great ideas came in instantaneous "flashes" of inspiration, not drudgery and re-writes.


If you can't put your vertical flashes of inspiration into a narrative that holds up to analysis - _and explains the exceptions_ - it doesn't matter how "great" your mind is.


----------



## isorhythm

millionrainbows said:


> I'm not a rigid thinker


At least in this discussion, your thinking seems to be extremely rigid in some respects and totally anarchic in others, which makes productive engagement challenging.

Here's an underlying principle for you: music theory comes after music practice. If your theory doesn't describe the music people actually make, then the theory is bad. You can't force music to conform to it.


----------



## Minor Sixthist

Someone already mentioned that taking "di" to mean "two" would be incorrect..."dia" means "through," Like "diagonal" means "through two angles", and yeah, diarrhea comes from "dia" for through and "rhein" for flow, like in Das Diarrheingold from the Runs of the Nibelung. The original etymology references the three standard tetrachords, but all the etymology I just read supports that the word either comes from "through tones" or possibly from "through stretching," which makes a little less sense.

As far as I know, using the 'diatonic scale' involves using the notes from a parent scale only, no other notes from the chromatic scale. https://www.guitarmusictheory.com/what-does-diatonic-mean/ I've usually only taken it to be used around major scales, but I could be off.

What's so interesting about it? I would generally just use the more specific, less ambiguous words for scales, since they're at our disposal.

Edit; deleted what's already been covered


----------



## millionrainbows

isorhythm said:


> At least in this discussion, your thinking seems to be extremely rigid in some respects and totally anarchic in others, which makes productive engagement challenging.
> 
> Here's an underlying principle for you: music theory comes after music practice. If your theory doesn't describe the music people actually make, then the theory is bad. You can't force music to conform to it.


Your thinking seems externally focussed, a sure sigh of an invalidator. Ugly, ugly.


----------



## millionrainbows

Woodduck said:


> That's priceless. I must remember to use it next time I'm in a jam...What "separates things" is elementary perception and thinking. You can't be sure about your "commonalities" until you've defined the differences between things that may, or may not, possess commonalities. Until you do that, it's all mush. I'm afraid your identifying the dynamics of tonal systems with supposed "tendencies" of scales is an example of mush...The harmonic series is not a "universal." It's merely a phenomenon...Or maybe, because you see "similarities" between scales and tonal systems, you imagine that both are "governed," and in the same way, by the harmonic series. In any case, when your only tool is a hammer, everything looks like a nail...Exceptions, when acknowledged, rein us in and protect the world from our delusions of grandeur. ..Including your humble self, no doubt...Yeah, we're all doing this. But we don't all agree on what principles underlie what...If you can't put your vertical flashes of inspiration into a narrative that holds up to analysis - _and explains the exceptions_ - it doesn't matter how "great" your mind is.


Empty argumentation. My advantage over you is that I'm here to _advance_ an idea, not argue or try to invalidate others' ideas.


----------



## millionrainbows

I don't need to have a theory which "covers all exceptions" because the exceptions you give are not universal in nature; they are procedural mundanities.


----------



## millionrainbows

isorhythm said:


> At least in this discussion, your thinking seems to be extremely rigid in some respects and totally anarchic in others, which makes productive engagement challenging.


you're not talking about ideas; you're talking about "my thinking" in an attempt at an ad-hominem put-down.



> Here's an underlying principle for you: music theory comes after music practice. If your theory doesn't describe the music people actually make, then the theory is bad. You can't force music to conform to it.


When soloing over a C major 7th chord, avoid the "F" because it sounds dissonant. How's that for practical advice, Einstein?


----------



## mikeh375

millionrainbows said:


> When soloing over a C major 7th chord, avoid the "F" because it sounds dissonant. How's that for practical advice, Einstein?


Not necessarily true MR, it depends on the style of music. F natural over cmaj 7 is fine as a note to use in a solo rather than a lydian f sharp. Admittedly, the f natural wants to resolve to the third more readily than the f sharp, and it is best used in passing, but it is still useable and is more appropriate for certain styles of improvising.


----------



## BabyGiraffe

millionrainbows said:


> When soloing over a C major 7th chord, avoid the "F" because it sounds dissonant.


"F" will clash way more with the "E" of your chord than with the "B".
And "F#" will clash with "G" over the major 7th, so lydian is not better.

If you are after tritone-like sonorities, scales where 11th harmonic or 7/5 septimal tritone are more in tune are preferable over whatever we have in 12 equal.

Diatonic tritone in Lydian in just tuning is 45/32 - 8 cents sharper than 7/5.


----------



## EdwardBast

Minor Sixthist said:


> As far as I know, using the 'diatonic scale' involves using the notes from a parent scale only, no other notes from the chromatic scale. https://www.guitarmusictheory.com/what-does-diatonic-mean/ *I've usually only taken it to be used around major scales, but I could be off.*


It applies to any standard mode using seven notes and only whole steps and half steps. This meaning is a direct extrapolation from Ancient Greek tetrachord theory.



isorhythm said:


> Here's an underlying principle for you: music theory comes after music practice. If your theory doesn't describe the music people actually make, then the theory is bad. You can't force music to conform to it.


Precisely! Million's advocacy for the superior stability of Lydian mode is contradicted by the whole history of both Western art music and folk music. It is a non-starter with no connection to musical reality.


----------



## millionrainbows

EdwardBast said:


> It applies to any standard mode using seven notes and only whole steps and half steps. This meaning is a direct extrapolation from Ancient Greek tetrachord theory.


The Greek root which this is derived from has more than one meaning. It could mean "two tonics."


----------



## Bwv 1080

So what if it did, what would that prove - that Russell had rediscovered lost Ancient Greek wisdom?


----------



## Bwv 1080

BabyGiraffe said:


> "F" will clash way more with the "E" of your chord than with the "B".
> And "F#" will clash with "G" over the major 7th, so lydian is not better.
> 
> If you are after tritone-like sonorities, scales where 11th harmonic or 7/5 septimal tritone are more in tune are preferable over whatever we have in 12 equal.
> 
> Diatonic tritone in Lydian in just tuning is 45/32 - 8 cents sharper than 7/5.


The point is jazz musicians play the #11 not the natural one, that part is not disputable. In common practice music harmonic major 7ths are more common and perceived as less dissonant than flat 9ths


----------



## KenOC

millionrainbows said:


> The Greek root which this is derived from has more than one meaning. It could mean "two tonics."


Sorry, no. "ORIGIN: …via late Latin from Greek _diatonikos _'at intervals of a tone', from _dia _'through' + _tonos _'tone'."


----------



## jegreenwood

millionrainbows said:


> The Greek root which this is derived from has more than one meaning. It could mean "two tonics."


You are apparently referring to a portion of your Wikipedia quote citing the work of Stephen M. Philips, the author of Sacred Geometries and Their Scientific Meaning as well as "ESP of Quarks and Superstrings."

The article cited in the footnote begins:

I shall explore in this article how the 'harmonies of heaven' manifest here on earth in our acoustic responses to different tunings. We are aware that Pythagoras was supposed to have discovered the mathematical basis of music, although the various legends surrounding his discovery of its laws probably contain little truth. But we are, perhaps, not aware that the Pythagorean theory of music was but one application of the principles of his holistic philosophy, which was not only a modus vivendi but a system of understanding the immanence of God in nature through the study of number. As part of a continuing programme of research into the connection between Pythagorean number philosophy and contemporary particle physics, I would like to set out here what I believe are some fruits of this work.


----------



## Bwv 1080

LOL, any time quantum mechanics comes into a conversation you know we are well into the land of ********


----------



## BabyGiraffe

Bwv 1080 said:


> LOL, any time quantum mechanics comes into a conversation you know we are well into the land of ********


Check this:
"Modelling tonal attraction: tonal hierarchies, interval cycles, and quantum probabilities"

https://link.springer.com/article/10.1007/s00500-015-1801-7

Still nothing about Lydian's superiority even in quantum music theories, I guess academics aren't ready about Russel's theories...


----------



## Bwv 1080

BabyGiraffe said:


> Check this:
> "Modelling tonal attraction: tonal hierarchies, interval cycles, and quantum probabilities"
> 
> https://link.springer.com/article/10.1007/s00500-015-1801-7
> 
> Still nothing about Lydian's superiority even in quantum music theories, I guess academics aren't ready about Russel's theories...


Well that is another realm of BS, there is invoking quantum mechanics to give a veneer of science to mystical mumbo jumbo, and this, which (as far as I can tell), uses some QM mathematical formalism correctly to describe something that does not need Hilbert spaces to describe.


----------



## millionrainbows

KenOC said:


> Sorry, no. "ORIGIN: …via late Latin from Greek _diatonikos _'at intervals of a tone', from _dia _'through' + _tonos _'tone'."


Sorry, back atcha: The fact that τόνος itself has at least four distinct meanings in Greek theory of music contributes to the uncertainty of the exact meaning and derivation of διατονικός, even among ancient writers.


----------



## millionrainbows

Bwv 1080 said:


> LOL, any time quantum mechanics comes into a conversation you know we are well into the land of ********


How typically unimaginative.


----------



## millionrainbows

some obscure guy on the internet said:


> Well that is another realm of BS, there is invoking quantum mechanics to give a veneer of science to mystical mumbo jumbo, and this, which (as far as I can tell), uses some QM mathematical formalism correctly to describe something that does not need Hilbert spaces to describe.


Yeah, and they wrote a book about it! 
OK, then go back to your college theory text...


----------



## jegreenwood

millionrainbows said:


> Sorry, back atcha: The fact that τόνος itself has at least four distinct meanings in Greek theory of music contributes to the uncertainty of the exact meaning and derivation of διατονικός, even among ancient writers.


Yes, τόνος may have multiple meanings. But as I read your beloved footnote, τόνος is not the issue; *δί*τονος/*di*tonic vs *διά*τονος/*dia*tonic is the issue. You wish the word would be ditonic. However, it is diatonic.

Edit - it does make me wonder what Scotty might have done if he only had dialithium crystals. . .


----------



## millionrainbows

jegreenwood said:


> Yes, τόνος may have multiple meanings. But as I read your beloved footnote, τόνος is not the issue; *δί*τονος/*di*tonic vs *διά*τονος/*dia*tonic is the issue. You wish the word would be ditonic. However, it is diatonic.
> 
> Edit - it does make me wonder what Scotty might have done if he only had dialithium crystals. . .


You're still not getting it: those words are after the fact. The root is tovoc.

Read post #101 carefully!


----------



## jegreenwood

millionrainbows said:


> You're still not getting it: those words are after the fact. The root is tovoc.
> 
> Read post #101 carefully!


I have read it carefully. From your Wikipedia footnote: "Τόνος may refer to a pitch, an interval, a "key" or register of the voice, or a mode.)"

Which of those has anything to do with '2'? What does dia have to do with '2'? What does any part of διάτονος/diatonic have to do with '2'?


----------



## ECraigR

Alright Millionrainbows, you’re right. Now what?


----------



## AeolianStrains

millionrainbows said:


> You're still not getting it: those words are after the fact. The root is tovoc.
> 
> Read post #101 carefully!


What's your point? You haven't even made a point except to say falsely that dia = two.


----------



## Woodduck

You people are just thinking too horizontally. Here are the true definitions of words containing the prefix "dia-" (we don't countenance fake definitions around here), arrived at through vertiginously vertical insight uninhibited by dry academicism, or by anything similar to that. 

1. Diametric: two meters in extent.
2. Diagrammatical: weighing two grams. 
3. Diamond: Modified Newtonian Dynamics, further modified. 
4. Diacritical mark: a mark twice as critical as a unicritical mark. 
5. Diagnostic: someone twice as uncertain of the existence of God as a regular agnostic. 
6. Diagonal: having two reproductive glands. 
7. Diagenesis: the conception of twins.
8. Diarrhea: a flightless, diagonal, diagenetic bird that lays two eggs which hatch into twins. 
9. Diakinesis: the state of having two relatives. 
10. Diatessaron: two of the Gospels combined into a single narrative. 
11. Dialect: a public official who has served two terms.
12. Diarist: someone who keeps two journals, one honest but unflattering, the other to be published as an autobiography.
13. Diaper: a loincloth designed to catch number two.
14. Dialogue: one who speaks with forked tongue.

From all of this it should be clear to all but those hopelessly bound to a pedantic correctness that when I assert that "diatonic" is a fizzy beverage with zero calories I'm probably just whistling Twoxie.

Cross my heart and hope to two.


----------



## Larkenfield

Diagraham Crackers means you get two.


----------



## Bwv 1080

And L Ron Hubbard gave us two netics


----------



## KenOC

I've been trying to figure out what to do with dialysis, but my creativity fails.


----------



## Woodduck

KenOC said:


> I've been trying to figure out what to do with dialysis, but my creativity fails.


It's an alysis of an alysis, thus making for a double alysis of a subject. Whenever million offers an alysis, we do an alysis of his alysis, usually beginning by saying "You have got to be kidney!"


----------



## mikeh375

Woodduck, what have you started...

Diaspora: Having to move home twice.
Diabolical: The default physique for the male of our species.
Chlamydia: An affliction causing one to order two starters in a fish restaurant instead of one.
Multimedia: A clear tautology pertaining to the self.


----------



## Woodduck

mikeh375 said:


> Woodduck, what have you started...
> 
> Diaspora: Having to move home twice.
> Diabolical: The default physique for the male of our species.
> Chlamydia: An affliction causing one to order two starters in a fish restaurant instead of one.
> Multimedia: A clear tautology pertaining to the self.


"-dia" as a suffix? This spells double trouble!


----------



## millionrainbows

Please spare us the feeble attempts at humor, and demonstrate your cleverness with the subject at hand.

Diatonic: "Two tonics": E-F, B-C.

The diatonic C major scale implies two tonics: F and C.

I know that's really hard to live with...

*dia- (prefix)*


through, across, *between*

Between: In the position or interval that separates (two things), or intermediate in quantity or degree.

Like two tonics?

Done together or reciprocally

In transit from (one to the other, or connecting places).

Between two tonics?

Combined (by effort or ownership).

Two tonics?

One of (representing a choice).You must choose between him and me.

Or between two tonics?

*So there is a definite sense of "two-ness" inherent in, and conveyed by the prefix "dia".

*Beethoven's tonal ambiguity, as discussed in that other thread, is also evidence that the "Ionian Scalar Instability" theory is not just an idea, but an underlying principle of Western diatonic tonality.


----------



## mikeh375

Is it also bi-scalic (diascalic) then...c major and f lydian? ......:devil:

Seriously though, whilst it's not difficult to imagine what you say has some theoretical credence MR, especially if one looks at the symmetry in the tetrachords, in reality, there is no parity between f and c as tonics within the one scale in CP. Functionally, the note f is under the influence of the tonic of C in normal CP practice until the notes and or harmony around it suggest otherwise in say a modulation. It is more likely subservient to the mediant and dominant ( especially melodically, but harmonically too). The mediant itself surely has no obligation to become a leading note, unless as before, the surrounding environment compels it to act as such. It's all about the context and in a CP context, I can't agree with you on this.


That said, I for one, don't object too much to your way of thinking, because I like to find pattern and association in scalic material, especially when searching for new ideas via technical means -making up scales, modes and harmony based on them. Doing so encourages further compositional exploration albeit under a shaky justification borne out of the most tenuous of connections sometimes. If you don't seek however, you don't find.

(btw, If I was you, I'd give up on the definition of 'dia' ...

edit...Just read through a lot of the posts here, realising I'm not adding much, but was intrigued by MR's post 78 as it resonated with me. I think primarily in the vertical too in the initial flush of composing and much of the scalic invention I use is then used to generate harmony based on differing intervals. The scale used for this purpose is not bound by any particular dominating note, nor is there actual function within the scale unless it is manipulated as such on the manuscript. I do not rule out or ignore gravitational leanings because they will become apparent to my aesthetic sense and CP techniques can still apply because of the fundamentally scale-like nature of any material. I put all this down to a guitar background in my formative years.

I wonder if you MR have similar leanings..


----------



## jegreenwood

mikeh375 said:


> Is it also bi-scalic (diascalic) then...c major and f lydian? ......:devil:
> 
> Seriously though, whilst it's not difficult to imagine what you say has some theoretical credence MR, especially if one looks at the symmetry in the tetrachords, in reality, there is no parity between f and c as tonics within the one scale in CP. Functionally, the note f is under the influence of the tonic of C in normal CP practice until the notes and or harmony around it suggest otherwise in say a modulation. It is more likely subservient to the mediant and dominant ( especially melodically, but harmonically too). The mediant itself surely has no obligation to become a leading note, unless as before, the surrounding environment compels it to act as such. It's all about the context and in CP, I can't agree with you on this.
> 
> That said, I for one, don't object too much to your way of thinking, because I like to find pattern and association in scalic material, especially when searching for new ideas via technical means -making up scales, modes and harmony based on them. Doing so encourages further compositional exploration albeit under a shaky justification borne out of the most tenuous of connections sometimes. If you don't seek however, you don't find.
> 
> *(btw, If I was you, I'd give up on the definition of 'dia' ...*


Never gonna happen. Let's just leave it as one person's interpretation.

Edit - make it two people (or a diaperson). That fellow explaining ESP amongst sub-atomic particles would agree.


----------



## isorhythm

What's the point of all this stuff about the word "diatonic" anyway? It seems like you're arguing it tells us something about the major scale as opposed to the Lydian, but the Lydian is also diatonic.


----------



## Minor Sixthist

So what if there is an "inherent two-ness" in diatonic scales? There's an "inherent two-ness" in a lot of things if you're willing to make enough of a stretch. I don't think anyone remembers what the original point of the thread was anymore.


----------



## Woodduck

Exactly. In non-ancient-Greek usage, "diatonic" simply means "without chromatic alteration of the notes of a scale." The term can apply to any scale utilizing (for example) only the white keys of the piano. Everything necessary to an understanding of the subject appears to have been said in the first few posts of the thread. 

I think I need to get outside for a breath of fresh air and an experience of twoness with nature.


----------



## BabyGiraffe

Minor Sixthist said:


> So what if there is an "inherent two-ness" in diatonic scales? There's an "inherent two-ness" in a lot of things if you're willing to make enough of a stretch. I don't think anyone remembers what the original point of the thread was anymore.


That's a nonsense; there is no "two-ness" in diatonic scale; any of the diatonic modes aside from Locrian can serve as a harmonic tonic with proper voice leading and chord progressions; and you can modulate to any chromatic pitch in any equal temperament that supports diatonic-sounding scales.

I still can't get why this guys thinks that diatonic scale generated as a linear temperament means anything special (and promoting lydian so much). 
You can generate it also as a rank-2 (major or minor triad) or even rank-3 temperament (and here we go into quantum and dynamic systems "nonsense", check the last edition of "Mathematics and computation in music" journal from this year). Or projective geometry; or statistical physics or even from common overtones and sum tones.

20 + people telling him that his Greek language interpretation is also wrong is still not enough for him.

"Russel's book is da bestest, cuz he invented modal jazz" , so Million cannot use his brain to see why his (or more correctly: Russel's) arguments make 0 sense; he must follow his "jedi" master and continue to ignore any criticism.


----------



## mikeh375

I think MR believes the lydian expression more closely equates with the 3rd partial of which the raised 4th is the leading note (you know that of course). The reason the F natural is disruptive is because it plays against this natural hierarchy (tendency even)...I think!!! The fact that the e natural is in the scale seems to have exacerbated this line of thinking. 
None of which matters for the reality of music composition in the last few hundred years, unless we include John Williams... My bets on the art and not any theory strained or not.


----------



## jegreenwood

Minor Sixthist said:


> So what if there is an "inherent two-ness" in diatonic scales? There's an "inherent two-ness" in a lot of things if you're willing to make enough of a stretch. I don't think anyone remembers what the original point of the thread was anymore.


Careful there. I've already gotten into another debate with MR over the meaning of twoness.


----------



## KenOC

jegreenwood said:


> Careful there. I've already gotten into another debate with MR over the meaning of twoness.


In fact, two-ness permeates the universe. As an example: There are two kinds of people, people who believe two-ness permeates the universe and people who don't. That should be sufficient to prove my thesis and, additionally, provide support to the always well-considered and logical musings of MR.


----------



## Minor Sixthist

jegreenwood said:


> Careful there. I've already gotten into another debate with MR over the meaning of twoness.


I didn't know it was that deep. All I know is I like my twoness salad without too much mayo.


----------



## millionrainbows

BabyGiraffe said:


> That's a nonsense; there is no "two-ness" in diatonic scale; I still can't get why this guys thinks that diatonic scale generated as a linear temperament means anything special (and promoting lydian so much). 20 + people telling him that his Greek language interpretation is also wrong is still not enough for him. "Russel's book is da bestest, cuz he invented modal jazz" , so Million cannot use his brain to see why his (or more correctly: Russel's) arguments make 0 sense; he must follow his "jedi" master and continue to ignore any criticism.


Irrelevant; this thread is not about me.

Diametric: *two* opposing sides, as in "diametrically opposed."

Diameter: A line which divides a circle into *two *parts.

Etc., etc...


----------



## Phil loves classical

I suppose rather than through-flowing, diarrhea could also mean 2 states of the person experiencing it: calm, and then sudden panic to get to the washroom.


----------



## millionrainbows

Phil loves classical said:


> I suppose rather than through-flowing, diarrhea could also mean 2 states of the person experiencing it: calm, and then sudden panic to get to the washroom.


No, in this case it means "through." I'm not saying that "dia" has only one meaning, like you are. It can mean "two," however.


----------



## Bwv 1080

millionrainbows said:


> Irrelevant; this thread is not about me.
> 
> Diametric: *two* opposing sides, as in "diametrically opposed."
> 
> Diameter: A line which divides a circle into *two *parts.
> 
> Etc., etc...


Sorry, no. You are becoming quite pathetic here, dont know why I bother - Diameter means measure through or across, not divide in two parts



> late Middle English: from Old French diametre, via Latin from Greek diametros (grammē) '(line) measuring across', from dia 'across' + metron 'measure'.


----------



## jegreenwood

https://virtualsalt.com/roots2.htm

https://membean.com/wrotds/dia-through

https://www.etymonline.com/word/diameter

https://www.oakton.edu/user/3/gherrera/Greek and Latin Roots in English/greek_and_latin_roots.pdf

https://www.cdl.org/wp-content/uploads/2013/12/Common-Prefixes-Suffixes-and-Roots-8.5.13.pdf

I could go on.


----------



## jegreenwood

Phil loves classical said:


> I suppose rather than through-flowing, diarrhea could also mean 2 states of the person experiencing it: calm, and then sudden panic to get to the washroom.


Thinking further about this. If dia means two, then shouldn't a baseball diamond be the same as a cricket pitch?


----------



## millionrainbows

Bwv 1080 said:


> Sorry, no. You are becoming quite pathetic here, dont know why I bother - Diameter means measure through or across, not divide in two parts


Same net result. Arguing for the sake of arguing? Obstinate brat.


----------



## millionrainbows

jegreenwood said:


> Thinking further about this. If dia means two, then shouldn't a baseball diamond be the same as a cricket pitch?


I'm not saying that "dia" has only one meaning, like you are. It can mean "two," however. This line of argument should be abandoned.


----------



## Minor Sixthist

millionrainbows said:


> Irrelevant; this thread is not about me.
> 
> Diametric: *two* opposing sides, as in "diametrically opposed."
> 
> Diameter: A line which divides a circle into *two *parts.
> 
> Etc., etc...


Purely wrong. Diameter, meaning "across measurement", from "dia" (*across, through*) and "metros" (measure).

Diametric comes from diameter, and so has the exact same roots.

Are you trying to suggest the word is built from the distinct roots "di" and "ameter?" Honestly? Or is the 'a' just supposed to be floating around in the world for no reason?

Please tell us you weren't trying to prove the etymology of a word by bolding the word 'two' in its plain definition.

Also, the plain functional mathematical definition of diameter isn't even "line that cuts a circle in two." It's "line drawn from one side of a circle to another which passes through its center." Just like the definition of dog is not "animal that likes chasing squirrels," even if that's happens to be true.

You are grasping at straws, and have the gall to try rewriting etymology before our eyes to do that.


----------



## Minor Sixthist

millionrainbows said:


> Same net result. Arguing for the sake of arguing? Obstinate brat.


"Same net result" he says. Seriously? So you subtracted the correct root and added a fake one to balance the equation, right?


----------



## Woodduck

millionrainbows said:


> I'm not saying that "dia" has only one meaning, like you are. It can mean "two," however.


It's also rarely appreciated that "bio" can mean "two." Examples:

Biography: the act of writing with two hands simultaneously
Biology: twice as sluggish
Biomass: the mass presented by both a priest speaking in Latin and a translator speaking in the vernacular
Biorhythm: duple time, such as 2/4, 4/4 or cut time
Biochemistry: erotic attraction to both men and women
Bioethics: hypocrisy


----------



## jegreenwood

millionrainbows said:


> I'm not saying that "dia" has only one meaning, like you are. It can mean "two," however. This line of argument should be abandoned.


So other than you and and the guy whose home page looks like this:









where do you find academic support for your statement that it can mean 2? Remember just repeating that it could have that meaning doesn't cut it for anyone but yourself (and maybe Mr. Phillips).


----------



## KenOC

Diabolical ... having two testicles (a common condition)


----------



## Woodduck

KenOC said:


> Diabolical ... having two testicles (a common condition)


When did you become a radical feminist?


----------



## mikeh375

KenOC said:


> Diabolical ... having two testicles (a common condition)


Well Ken, that's just rude, stealing my joke......post 114 in this thread....


----------



## mikeh375

Woodduck said:


> "-dia" as a suffix? This spells double trouble!


You know composers WD, always angling to develop things...


----------



## KenOC

mikeh375 said:


> Well Ken, that's just rude, stealing my joke......post 114 in this thread....


Yes, now I see your post. Plagiarism in advance, the worst kind!


----------



## jegreenwood

mikeh375 said:


> Well Ken, that's just rude, stealing my joke......post 114 in this thread....





KenOC said:


> Yes, now I see your post. Plagiarism in advance, the worst kind!


Now don't you two get diacritical of one another.


----------



## Woodduck

jegreenwood said:


> Now don't you two get diacritical of one another.


Would it be petty and egotistical to draw your attention to example #4 in post 109?

My urge to bring suit could be blunted if you could convince me that this is merely a convergence of great intellects attuned to the zeitgeist.


----------



## millionrainbows

jegreenwood said:


> ...where do you find academic support for your statement that it can mean 2? Remember just repeating that it could have that meaning doesn't cut it for anyone but yourself (and maybe Mr. Phillips).


It's obvious, if you think about it rather than merely accepting an academic meaning. Why does it matter? A C major 'diatonic' scale still has two conflicting tonics; the whole Western music system is based on this ambiguity.


----------



## jegreenwood

jegreenwood said:


> where do you find academic support for your statement that it can mean 2? *Remember just repeating that it could have that meaning doesn't cut it for anyone but yourself *(and maybe Mr. Phillips).





millionrainbows said:


> *It's obvious, if you think about it rather than merely accepting an academic meaning. Why does it matter? *A C major 'diatonic' scale still has two conflicting tonics; the whole Western music system is based on this ambiguity.


I rest my case.


----------



## Phil loves classical

millionrainbows said:


> No, in this case it means "through." I'm not saying that "dia" has only one meaning, like you are. It can mean "two," however.


"dia" (δια) cannot mean two, while "di" (δίς) does. In the original Greek, the dia prefix used in diatonic is the former (δια). In English they use dia instead of di for through. Dia-meter means through a circle, while Di-meter means a line of verse with 2 feet.


----------



## mikeh375

KenOC said:


> Yes, now I see your post. *Plagiarism in advance,* the worst kind!


I'm still trying to sue that Beethoven fella for copying my 5th note for note..tsch, media composers.


----------



## BabyGiraffe

millionrainbows said:


> It's obvious, if you think about it rather than merely accepting an academic meaning. Why does it matter? A C major 'diatonic' scale still has two conflicting tonics; the whole Western music system is based on this ambiguity.


C major doesn't have two "conflicting" tonics and none of Western music is based on this, wow.
Diatonic scale as constructed by a pythagorean fifth has 6 potential tonics (and is out of tune with no good major or minor thirds and sixths);... by 12 equal P5 - again 6 potential tonics; ... by using major and minor triadic chains - only 2 tonics - Ionian and Aeolian (see Riemann's book, good luck arguing with the father of functional theory).

Let's try division of string lengths and see what modes we get:
First try- divide into two most even linear parts and then divide the first of these parts by the second, then divide these two "tetrachords", separated by a major whole tone into most even 5-limit ratios. If we don't use 5-limit ratios we get the "Rast" oriental tetrachord (Ptolemy has another name for it, but I have to check his book for it).

Another method - divide the octave into 3 equal parts. The first one of these is divided into 3, the other two - into 2 5-limit parts. Again Ionian. That's intense diatonic of Ptolemy.

Here are all divisions of tetrachord into superparticular ratios, from most uneven to most even, permutations of these were used by Greeks and Arabs into construction of their (chromatic, diatonic, enharmonic) scales :

5/4 17/16 256/255 17-limit
5/4 18/17 136/135 17-limit
5/4 19/18 96/95 19-limit
5/4 20/19 76/75 19-limit
5/4 21/20 64/63 7-limit
5/4 22/21 56/55 11-limit
5/4 24/23 46/45 23-limit
5/4 26/25 40/39 13-limit
5/4 28/27 36/35 7-limit
5/4 31/30 32/31 31-limit
6/5 11/10 100/99 11-limit
6/5 12/11 55/54 11-limit
6/5 13/12 40/39 13-limit
6/5 15/14 28/27 7-limit
6/5 16/15 25/24 5-limit
6/5 19/18 20/19 19-limit
7/6 9/8 64/63 7-limit
7/6 10/9 36/35 7-limit
7/6 12/11 22/21 11-limit
7/6 15/14 16/15 7-limit
8/7 8/7 49/48 7-limit
8/7 9/8 28/27 7-limit
8/7 10/9 21/20 7-limit
8/7 13/12 14/13 13-limit
9/8 10/9 16/15 5-limit (diatonic tetrachord)
10/9 11/10 12/11 11-limit (oriental tetrachord)
Count is 26

Superparticular ratios have interesting connection with dynamical systems, chaos and fractals (read on mode locking). 
Ionian scale in Intense diatonic tuning is the optimal tuning for 7 note 5-limit in terms of harmony against the root. Still, syntonic comma ruins at least one of the modes, this leads us to the meantone temperament, which is optimal in 43 or 55 equal (this one is recommended in the Leopold Mozart's letter), if we want everything to sound nice. If we are after minor tonality - 19 equal; if we are after major tonality - 31 equal (that's the popular 1/4 comma meantone).

4/3|| 5/4 || 6/5 - most even 3 part division
9/8 10/9 16/15 || 9/8 10/9 || 9/8 16/15 - subdivision of each of these parts = Ptolemy/ Zarlino scale = 1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8, 2 - D-A is a wolf; D-F is a syntonic comma lower, another false relation.

Subdivision of octave into two parts - the first one is the arithmetic mean, the second is the harmonic mean.
3/2 4/3
Then u divide 3/2:4/3 to get 9/8, then subdivide 4/3 to get Ionian in another tuning.
Subdividing 3/2 and 4/3 can get us lydian, but it's out of tune - it will have more false relations than what we have in Intense diatonic or the other alternative Ionian tuning and 45/32 is not superparticular, so it is more complex than other good tunings of rest of the diatonic modes (except Locrian, which is totally useless) and has nothing to do with optimal harmonious tuning (and physics of dynamical systems).


----------



## millionrainbows

BabyGiraffe said:


> C major doesn't have two "conflicting" tonics and none of Western music is based on this, wow.
> Diatonic scale as constructed by a pythagorean fifth has 6 potential tonics (and is out of tune with no good major or minor thirds and sixths);... by 12 equal P5 - again 6 potential tonics; ... by using major and minor triadic chains - only 2 tonics - Ionian and Aeolian (see Riemann's book, good luck arguing with the father of functional theory).
> 
> Let's try division of string lengths and see what modes we get:
> First try- divide into two most even linear parts and then divide the first of these parts by the second, then divide these two "tetrachords", separated by a major whole tone into most even 5-limit ratios. If we don't use 5-limit ratios we get the "Rast" oriental tetrachord (Ptolemy has another name for it, but I have to check his book for it).
> 
> Another method - divide the octave into 3 equal parts. The first one of these is divided into 3, the other two - into 2 5-limit parts. Again Ionian. That's intense diatonic of Ptolemy.
> 
> Here are all divisions of tetrachord into superparticular ratios, from most uneven to most even, permutations of these were used by Greeks and Arabs into construction of their (chromatic, diatonic, enharmonic) scales :
> 
> 5/4 17/16 256/255 17-limit
> 5/4 18/17 136/135 17-limit
> 5/4 19/18 96/95 19-limit
> 5/4 20/19 76/75 19-limit
> 5/4 21/20 64/63 7-limit
> 5/4 22/21 56/55 11-limit
> 5/4 24/23 46/45 23-limit
> 5/4 26/25 40/39 13-limit
> 5/4 28/27 36/35 7-limit
> 5/4 31/30 32/31 31-limit
> 6/5 11/10 100/99 11-limit
> 6/5 12/11 55/54 11-limit
> 6/5 13/12 40/39 13-limit
> 6/5 15/14 28/27 7-limit
> 6/5 16/15 25/24 5-limit
> 6/5 19/18 20/19 19-limit
> 7/6 9/8 64/63 7-limit
> 7/6 10/9 36/35 7-limit
> 7/6 12/11 22/21 11-limit
> 7/6 15/14 16/15 7-limit
> 8/7 8/7 49/48 7-limit
> 8/7 9/8 28/27 7-limit
> 8/7 10/9 21/20 7-limit
> 8/7 13/12 14/13 13-limit
> 9/8 10/9 16/15 5-limit (diatonic tetrachord)
> 10/9 11/10 12/11 11-limit (oriental tetrachord)
> Count is 26
> 
> Superparticular ratios have interesting connection with dynamical systems, chaos and fractals (read on mode locking).
> Ionian scale in Intense diatonic tuning is the optimal tuning for 7 note 5-limit in terms of harmony against the root. Still, syntonic comma ruins at least one of the modes, this leads us to the meantone temperament, which is optimal in 43 or 55 equal (this one is recommended in the Leopold Mozart's letter), if we want everything to sound nice. If we are after minor tonality - 19 equal; if we are after major tonality - 31 equal (that's the popular 1/4 comma meantone).
> 
> 4/3|| 5/4 || 6/5 - most even 3 part division
> 9/8 10/9 16/15 || 9/8 10/9 || 9/8 16/15 - subdivision of each of these parts = Ptolemy/ Zarlino scale = 1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8, 2 - D-A is a wolf; D-F is a syntonic comma lower, another false relation.
> 
> Subdivision of octave into two parts - the first one is the arithmetic mean, the second is the harmonic mean.
> 3/2 4/3
> Then u divide 3/2:4/3 to get 9/8, then subdivide 4/3 to get Ionian in another tuning.
> Subdividing 3/2 and 4/3 can get us lydian, but it's out of tune - it will have more false relations than what we have in Intense diatonic or the other alternative Ionian tuning and 45/32 is not superparticular, so it is more complex than other good tunings of rest of the diatonic modes (except Locrian, which is totally useless) and has nothing to do with optimal harmonious tuning (and physics of dynamical systems).


What's the short answer? Your replies are hopelessly complicated and unclear.

Yes, the C major scale is harmonically ambiguous, because its leading tones (half-steps) imply C major and F major; and F major is not the most closely related key to C, because G is.

Yes, any note in the scale can be a tonic (that's where modes come from), but you have to look at the _internal relations_ of the scale, and see how it either reinforces a tonic, or not.

D dorian, for example: D-E-F-G-A-B-C, has no such problems: the A-B half-step is not internally positioned to suggest another tonic.

You _must_ consider the internal relations of the scale.

Diatribe: a group of primitive thinkers who all think the same way.


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## isorhythm

If I'm writing a piece in C major, and I introduce an F sharp, what happens, subjectively, for the listener? Where does it feel like it wants to go? What if I introduce a B flat?


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## Woodduck

isorhythm said:


> If I'm writing a piece in C major, and I introduce an F sharp, what happens, subjectively, for the listener? Where does it feel like it wants to go? What if I introduce a B flat?


Where does _what_ want to go? The melody containing the altered note, or the tonality of the piece? An F# will usually suggest resolution to the G above it, and a Bb to the A below, in order to affirm the tonality we know as C Major. It depends on context - on how those altered tones are used. They may be heard merely as melodic embellishment tones or as harmonic color and so not make the music want to go anywhere (modulate) at all. An example of this is the opening melody of Korngold's Violin Concerto, which features prominently the raised fourth scale degree:

https://www.youtube.com/results?search_query=korngold+violin+concerto

When we hear that note, we may have some semiconscious sense that the melody could continue upward a half-step, but its drop down to the third of the tonic chord feels no less natural, perhaps due to the fact that the melody has ascended two octaves but thus far "skipped over" the third of the tonic triad, which makes its arrival here satisfying.

The principle of tonal gravitation dictates that in most contexts the F# and the Bb (in C Major) create instability and want to resolve into the nearest tones that define the mode we're in, the major mode. _But this depends on contextual factors, including our perception that we are actually in that mode._ It's possible to mix modes, giving tones different functions in different contexts, and thus removing from them the "desire" to resolve in specific ways. I'm thinking of certain piano pieces by Grieg that utilize the Lydian mode found in Norwegian folk music; a piece may not be Lydian throughout - it may be basically in a major key with Lydian "coloration" - and by the harmonic context we know when the raised fourth degree suggests a "dominant" function and when it doesn't.


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## BabyGiraffe

millionrainbows said:


> What's the short answer? Your replies are hopelessly complicated and unclear.
> 
> Yes, the C major scale is harmonically ambiguous, because its leading tones (half-steps) imply C major and F major; and F major is not the most closely related key to C, because G is.
> 
> Yes, any note in the scale can be a tonic (that's where modes come from), but you have to look at the _internal relations_ of the scale, and see how it either reinforces a tonic, or not.
> 
> D dorian, for example: D-E-F-G-A-B-C, has no such problems: the A-B half-step is not internally positioned to suggest another tonic.
> 
> You _must_ consider the internal relations of the scale.


Dorian is the most problematic mode to tune and play chords in it in non-meantone temperaments, so your example is very bad. (10/9 and 9/8 are equalized in meantone.)

About C major, F major and G major. You can go from C to F or C to G with 1 change of a chroma and the voice leading is smooth and parsimonious in any meantone tuning. In non-meantone you will need additional chroma(s - depending on what you want to play).

"
If I'm writing a piece in C major, and I introduce an F sharp, what happens, subjectively, for the listener? Where does it feel like it wants to go? What if I introduce a B flat? 
"

Just a change of chroma in one of the scale steps (shifting one of the notes by a chromatic semitone; there is a difference between chromatic and diatonic semitone in any equal division where major thirds are somewhat more "in tune").
You need big preparations and changes in rhythm, harmony and melody to make a convincing impression for modulation to another tonal centre, if that is the point.

Tymoczko has a whole book on such topics like scale modulations and smooth voice leading.

(All these big + small steps generated scales that have step ratios 2:1 or 1:2 are "diatonic" in some equal temperament and translate/modulate the same way 7 note heptatonic does in 12 equal. So, 7-note diatonic lives only in 12 notes "world". In 31 equal the "diatonic" meantone scale has 19 steps, because it's basically a finer tuning of 19 equal just like diatonic is a finer tuning of 7 equal in 12.)

To million:
What is "diaschisma" in music/tuning theory? (Hint: It has nothing to do with "duality"). Tempering this comma actually gives better tuning than any meantone and is probably optimal for stuff like double harmonic and other "harmonic" scales like major/minor or some "gypsy"/indian scales and all these live in a 10 tones world.
Of course, it is bad for diatonic music, because you need to deal with the syntonic comma there.
12 equal is the only tuning where this diaschismic and syntonic worlds meet (both are badly tuned, of course).


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## millionrainbows

I think Woodduck and Baby Giraffe in particular are needlessly complicating what is basically a simple idea.

Thinking specifically in terms of scales, and their harmonic implications, the C major scale is harmonically ambiguous, in terms of reinforcing its "key" starting note, C. The C lydian scale is better at reinforcing C.

What can be revealed by doing a vector analysis? 
The ntervals are reduced to smallest values, inversions ignored, giving us six intervals: m2, M2, m3, M3, 4th, tritone.

C-D....M2
C-E....M3
C-F....4th
C-G....5th (inversion of 4th)
C-A....m3
C-B....m2
D-E....M2
D-F....m3
D-G....4th
D-A....5th (inversion of 4th)
D-B....m3
D-C (redundant)
E-F....m2
E-G....m3
E-A....4th
E-B....5th (inversion of 4th)
E-C (redundant)
F-G....M2
F-A....M3
F-B....tritone
F-C (redundant)
G-A....M2
G-B....M3
G-C (redundant)
A-B....M2
A-C (redundant)
B-C (redundant)

The total interval content is:

m2: 2
M2: 5
m3: 4
M3: 3
4th: 3
Tritone: 1

Vector analysis of Lydian scale:

C-D....M2
C-E....M3
C-F#...tritone
C-G....5th (inversion of 4th)
C-A....m3
C-B....m2
D-E....M2
D-F#....M3
D-G....4th
D-A....5th (inversion of 4th)
D-B....m3
D-C (redundant)
E-F#....M2
E-G....m3
E-A....4th
E-B....5th (inversion of 4th)
E-C (redundant)
F#-G....m2
F#-A....m3
F#-B....4th
F#-C (redundant)
G-A....M2
G-B....M3
G-C (redundant)
A-B....M2
A-C (redundant)
B-C (redundant)

The total interval content is:

m2: 2
M2: 5
m3: 4
M3: 3
4th: 3
Tritone: 1

As you can see, the interval vector is the same; in other words, both scales have the identical harmonic content. Therefore, the factors which distinguish them are:
(1) the _internal relations_ of the scale, and _where_ these intervals are located _within _the scale;
(2) and _melodic_ factors, such as _leading tones.

all of these other "contextual" harmonic justifications are irrelevant to my point._


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## millionrainbows

The interval vector is the same in both major and lydian scales; in other words, both scales have the identical harmonic content. Therefore, the factors which distinguish them are:

(1) the _internal _relations of the scale, and _where _these intervals are located _within _the scale;
(2) and _melodic factors, _such as_ leading tones.

_Most of the harmonic justifications cited are irrelevant, because they are not reflections of the scale, the _location_ of its internal intervallic relations, and melodic implications.

So all of BabyGiraffe's talk of "tuning" is irrelevant to the point; the location within the scale of _internal relations _and_ melodic tendencies_ are what matter.



Woodduck said:


> Where does _what_ want to go? The melody containing the altered note, or the tonality of the piece? An F# will usually suggest resolution to the G above it, and a Bb to the A below, in order to affirm the tonality we know as C Major.


"Resolution" is harmonic. Harmonic factors like this are extraneous to considerations of the internal scale structure with its melodic implications, which is essentially a melodic way of suggesting root movement, and "resolution" to a new key.



> It depends on context - on how those altered tones are used. They may be heard merely as melodic embellishment tones or as harmonic color and so not make the music want to go anywhere (modulate) at all.


These are extraneous digressions, which distract from my original point of scale structure.



> When we hear that note, we may have some semiconscious sense that the melody could continue upward a half-step, but its drop down to the third of the tonic chord feels no less natural, perhaps due to the fact that the melody has ascended two octaves but thus far "skipped over" the third of the tonic triad, which makes its arrival here satisfying.


That is true, but is not based on scale structure.



> The principle of tonal gravitation dictates that in most contexts the F# and the Bb (in C Major) create instability and want to resolve into the nearest tones that define the mode we're in, the major mode. _But this depends on contextual factors, including our perception that we are actually in that mode._


But that's not the point I'm making; my assertions that the C major scale is ambiguous are based solely on scale structure, abstracted from context, as a working principle.



> It's possible to mix modes, giving tones different functions in different contexts, and thus removing from them the "desire" to resolve in specific ways. I'm thinking of certain piano pieces by Grieg that utilize the Lydian mode found in Norwegian folk music; a piece may not be Lydian throughout - it may be basically in a major key with Lydian "coloration" - and by the harmonic context we know when the raised fourth degree suggests a "dominant" function and when it doesn't.


The Grieg example is purely harmonic, then; it has nothing to do with the idea of a lydian scale being more "reinforcing" of its starting root note due to internal structure locations within the scale itself, which is what the point of my assertions are.


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## BabyGiraffe

Damn, I wrote a long post that managed to get deleted... Anyway, we have diminished fifth and augmented fourth in any other meantone tuning (including all historical variants), nothing is ambiguous (diaschisma - the difference between the two JI 5-limit tritones is tempered in 12 equal and is identical to diminished/augmented fifth/fourth in any meantone - so in diaschismic tuning we will still have wolf intervals, differing by a syntonic comma along with real tritones. In 12 edo all this is messed up, because it not accurate system.)



http://imgur.com/ZLESUxC

 (Sorry, forum's image upload is broken on my browser; and broke my unpiblished post). Not very hard to see that in octave the best intervals are 3/2, _4/3_, 5/3, 5/4...

https://www.amazon.com/Beyond-Measure-Jay-Kappraff/dp/9810247028#reader_9810247028 - Read chapter 25 on dynamical systems, if you want to understand why harmonic musical instruments and scales work the best with "F", no lydian nonsense. It's a good introduction to this topic.

I don't know why continue - it is not hard to create lattices or graphs that show that even the whole 12 equal is a consonant TONAL scale in just intonation (needs slight retuning). With a little more retuning we can tune it even to African (septimal blues) ratios or even oriental scales (check 17 equal for tempered version, of course, it won't support triadic major-minor harmony, but pitch classes are the same as in 12 equal).

Until you learn more about physics of vibration and tuning theory, you will remain ignorant.

Of course, Lydian scale is excellent for melody and underutilized, but you are overrating it. It has no importance. (We can start from medieval music practices and pythagorean tuning, doing the same logical mistakes as you and your jazz master and somehow decide that Locrian is "da best", right...)


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## millionrainbows

BabyGiraffe said:


> Damn, I wrote a long post that managed to get deleted...


I wonder why that was?...



> Until you learn more about physics of vibration and tuning theory, you will remain ignorant.


Yeah, right, BabyGirraffe...whatever you say. :lol:


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## Woodduck

millionrainbows said:


> The *interval vector* is the same in *both major and lydian scales*; in other words, *both scales have the identical harmonic content.*


1.) No they don't. Every scale offers a different set of harmonic possibilities. 2.) "Interval vector," applied to musical scales, is pseudo-scientific gobbledegook. You don't help your argument with such opaque jargon.



> Therefore, the factors which distinguish them are:
> 
> (1) the _internal _relations of the scale, and _where _these intervals are located _within _the scale;
> (2) and _melodic factors, _such as_ leading tones._


_

What's the difference between "1" and "2"? The "internal relations" of the scale (the distribution of its intervals, of which a leading tone is an instance) are its "melodic factors," the only "melodic factors" a scale has.




"Resolution" is harmonic. Harmonic factors like this are extraneous to considerations of the internal scale structure with its melodic implications, which is essentially a melodic way of suggesting root movement, and "resolution" to a new key.

Click to expand...

So resolution is harmonic, harmonic factors are extraneous to considerations of scale structure, but scale structure is essentially a way of suggesting resolution...

How's that again??? 

Your statement that the internal structure of a scale is "a melodic way of suggesting root movement, and 'resolution' to a new key" is the thing you keep repeating but have not demonstrated. The melodic tendencies of scale tones depend on a number of factors; there is no suggestion of new roots or keys unless the harmonic system of the music utilizing the scale imparts that suggestion to the tones in question. You only feel (imagine) those suggestions retrospectively, based on association with familiar Western musical practice. There is no intrinsic tendency of any note of a scale to become the root of a new key. The world is full of music, utilizing various scales, which never modulates and has no tendency or "desire" to, regardless of the intervallic structure of those scales.




my assertions that the C major scale is ambiguous are based solely on scale structure, abstracted from context, as a working principle.

Click to expand...

And they remain mere assertions._


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## millionrainbows

Woodduck said:


> 1.) No they don't. Every scale offers a different set of harmonic possibilities. 2.) "Interval vector," applied to musical scales, is pseudo-scientific gobbledegook. You don't help your argument with such opaque jargon.


It's not gobbledegook. It's an idea from Howard Hanson's book. If you see that "every scale offers a different set of harmonic possibilities," then you are thinking vertically and abstractly, without the baggage of all your 'narrative' and horizontal notions of tonality and resolution. That's not like you, Woodduck, but since you are trying to invalidate my ideas, I guess you've made an exception. :lol:



> What's the difference between "1" and "2"? The "internal relations" of the scale (the distribution of its intervals, of which a leading tone is an instance) _are_ its "melodic factors," the only "melodic factors" a scale has.


Yes, but _where (in the scale) those melodic factors exist matters greatly._ The Dorian scale has no such tendencies, even though it has the same notes as C major. In fact, these "internal differences" are what give us our modes! You are ignoring basic facts in your haste to invalidate.

This is easily demonstrated at an organ. Playing C-G-D-A-E-F-B as a stack of fifths is dissonant when we hit F-B, the tritone.

By contrast, playing those same notes F-C-G-D-A-E-B is _much more consonant,_ because the tritone F-B is positioned differently. This is a "harmonic" way of testing a scale which is vertical, and involves none of your "horizontal" academic thinking.



> So resolution is harmonic, harmonic factors are extraneous to considerations of scale structure, but scale structure is essentially a way of suggesting resolution...
> 
> How's that again???
> 
> Your statement that the internal structure of a scale is "a melodic way of suggesting root movement, and 'resolution' to a new key" is the thing you keep repeating but have not demonstrated.


I shouldn't have to, the leading tones E-F and B-C suggest this in a most obvious way.



> The melodic tendencies of scale tones depend on a number of factors; there is no suggestion of new roots or keys unless the harmonic system of the music utilizing the scale imparts that suggestion to the tones in question. You only feel (imagine) those suggestions retrospectively, based on association with familiar Western musical practice.


Once again, you are thinking horizontally. My assertions are all based on vertical factors of scale construction and leading-tone tendencies.



> There is no intrinsic tendency of any note of a scale to become the root of a new key. The world is full of music, utilizing various scales, which never modulates and has no tendency or "desire" to, regardless of the intervallic structure of those scales.


In Western music, the C major scale is used for that precise reason; it suggests a new key, F.


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## Woodduck

millionrainbows said:


> If you see that "every scale offers a different set of harmonic possibilities," then you are thinking vertically and abstractly, without the baggage of all your 'narrative' and horizontal notions of tonality and resolution. That's not like you, Woodduck, but since you are trying to invalidate my ideas, I guess you've made an exception. :lol:


"Possibilities" are not the same as "tendencies." Scale tones have possibilities. They do not have tendencies until we establish a syntactical context in which they are expected to behave and function in certain ways. In a common practice tonal context, against a C major chord, an F wants to "resolve" to E, and a B to C. But I've already cited the fact that in jazz the B - the so-called "leading tone - no longer has any tendency to "lead." The context has changed.

Outside any syntactic context, tones don't "want" to do anything.

You said "both scales [Ionian and Lydian] have identical harmonic content." You must be defining "content" in some way the rest of us are not.



> Yes, but _where (in the scale) those melodic factors exist matters greatly._


Jeez, everybody knows that.



> In fact, these "internal differences" are what give us our modes!


Everybody knows that too.



> Playing C-G-D-A-E-F-B as a stack of fifths is dissonant when we hit F-B, the tritone.


Yeah, everybody knows that a tritone is more dissonant than a perfect fifth.



> By contrast, playing those same notes F-C-G-D-A-E-B is _much more consonant,_ because the tritone F-B is positioned differently. This is a "harmonic" way of testing a scale which is vertical, and involves none of your "horizontal" academic thinking.


To describe "playing" as "consonant" or "dissonant" is linguistically confused. Imprecise language is generally a sign of imprecise thinking.



> Once again, you are thinking horizontally. My assertions are all based on vertical factors of scale construction and leading-tone tendencies.


It doesn't matter what assertions are "based on."



> In Western music, the C major scale is used for that precise reason; it suggests a new key, F.


Ah! Now we're getting somewhere. When you say,_"in Western music,"_ what you should say is, "In the minds of people conditioned by Western music." In non-Western music - let's say, the music of India - the scale we call "major" occurs frequently, yet in hundreds and thousands of years has never "suggested a new key." Why do you suppose that is? Are Indians genetically insensitive to the "instability" of the major scale? Are they unable to perceive this "tendency" to modulate to our "subdominant" which you consider so obvious?

That the two tetrachords of our major scale have an identical sequence of intervals (in equal temperament), and that the third and seventh notes of our major scale can function as "leading tones" (to the tonic and subdominant keys, respectively), is not a reason to project a "tendency" to modulate onto the scale itself. People whose music doesn't modulate between keys appear not to hear any such tendency.


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## Guest

I'm tired of reading through all this endless blah-blah.
If you want a solid C-major scale (and the usual related keys) in a real musical context, check out this 3rd movement from Haydn's cello concerto in C (and no fargin' E-F slip to the subdominant; please, spare me this crap, MR):


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## millionrainbows

Woodduck said:


> "Possibilities" are not the same as "tendencies." Scale tones have possibilities. They do not have tendencies until we establish a syntactical context in which they are expected to behave and function in certain ways. In a common practice tonal context, against a C major chord, an F wants to "resolve" to E, and a B to C. But I've already cited the fact that in jazz the B - the so-called "leading tone - no longer has any tendency to "lead." The context has changed.


Once again, your hair-splitting distinction between "possibilities" and "tendencies" is based on your reliance on horizontal, narrative procedures. So what if "in a common practice tonal context, against a C major chord, an F wants to "resolve" to E"? That's common practice procedure, and has little to do with an abstract vertical view of "tendencies" and "underlying principles" that I speak of.



> Outside any syntactic context, tones don't "want" to do anything.


You just defined "horizontal thinking." I'm not a horizontal thinker like you.



> You said "both scales [Ionian and Lydian] have identical harmonic content." You must be defining "content" in some way the rest of us are not.


Yes, I used an interval vector chart. It includes every possible interval relation in any scale.

I've declined replies to your responses which are merely argumentative, without content.



> Ah! Now we're getting somewhere. When you say,_"in Western music,"_ what you should say is, "In the minds of people conditioned by Western music." In non-Western music - let's say, the music of India - the scale we call "major" occurs frequently, yet in hundreds and thousands of years has never "suggested a new key." Why do you suppose that is? Are Indians genetically insensitive to the "instability" of the major scale? Are they unable to perceive this "tendency" to modulate to our "subdominant" which you consider so obvious?


This seems obvious. Jeez, everybody knows that Indian music doesn't modulate. Still, I can punch holes in this example by pointing out that Indian music is based on melodic factors & tension between the melodic note and the "tonic" drone. In Indian music, an F against a C drone will create tension, but does not have to resolve to E.



> That the two tetrachords of our major scale have an identical sequence of intervals (in equal temperament), and that ç, is not a reason to project a "tendency" to modulate onto the scale itself.


Again, you are demonstrating "horizontal" thinking, in which tonality depends on sequences of events in a common-practice context.

You do clearly seem to recognize that "...the two tetrachords of our major scale have an identical sequence of intervals (in equal temperament), and that the third and seventh notes of our major scale can function as "leading tones" (to the tonic and subdominant keys, respectively)", but to conclude that "this is not a reason (thou shalt not) to project a 'tendency' to modulate onto the scale itself" is simply a _refusal to engag_e in vertical thinking (heresy), and a total reliance on academic, horizontal procedures of establishing tonality (belief).

I've always disagreed with you on this. To me, tonality is like the "big bang" theory, whereas you believe that "tonality was created in six days".

I see that "tonality and harmonic truth are born in the moment", where you see that tonality and harmonic truth must be "created" by Man, under the exigis of a horizontal sequence of "creation."

Yours is a model, like all Western music, of Christian concepts of creation, while mine is an instantaneous example of "being", of inherent qualities and potentialities, which is more Eastern or "buddhistic."

The C major scale does not reinforce the key of C because of the "F". This is demonstrable either by considering the "leading tone tendency" melodic proof, or by the "stacking fifths C-G-D-A-E-B" harmonic proof. I'm covered on two fronts.


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## Woodduck

^^^The demonstration of any theory of the dynamics of music must be sought in the dynamics at work _in the actual practice of music._ If we're claiming that any element of music - and the elements of music are merely sounds - has an inherent "tendency" to do something, we have to show that it has that tendency regardless of its actual musical use. If we can't show that, we have to conclude that the "tendency" is not inherent but is a function of its use in a musical context.

I've supported my objection to your theory of the inherent instability of the major scale by citing examples of actual musical practice - specifically, examples from tonal, but non-common-practice, music (Indian music and jazz), which show that the dynamic relationships and tendencies you attribute to scalar tones and intervals are not intrinsic to those tones and intervals, but exist only in specific musical styles and contexts. You've been unable to explain away these examples. Your comments above about Indian music don't suggest any answer to the question of why, outside of Western common practice, the major scale is used with no acknowledgement of what you've called its "restless quality which encourages travel away from the key."

My suspicion is that you only imagine that a C major scale is "unstable," that it "encourages" travel to the key of F, because you're projecting onto that scale the dynamics of the Western tonal system, which is distinguished by keys and key relationships. Influenced by the way the tones of the scale function in common practice music, you're projecting relationships and functions of common practice tonality onto a mere scale, and "hearing" musical activity where there is only a sequence of tones - a sequence of tones which will be heard differently by someone from a different musical tradition.

Your singling out of European tonal music as the Music of the Spheres is ethnocentric and parochial. Brahma is annoyed.


----------



## millionrainbows

Woodduck said:


> ^^^The demonstration of any theory of the dynamics of music must be sought in the dynamics at work _in the actual practice of music._ If we're claiming that any element of music - and the elements of music are merely sounds - has an inherent "tendency" to do something, we have to show that it has that tendency regardless of its actual musical use. If we can't show that, we have to conclude that the "tendency" is not inherent but is a function of its use in a musical context.


That's too restricting. Schoenberg's Structural Functions of Harmony is based on "tendencies", and really, no "proof" is required, since the proof is self-evident, i.e., since we hear fourths as "root on top" and fifths as "root on bottom," i.e. these are the result of the way he hear harmonically. One would have to "prove" this by referring to the harmonic series, and the way we hear. I'm sure that somewhere out there, this proof exists, but I can't reference it for you at present.



> I've supported my objection to your theory of the inherent instability of the major scale by citing examples of actual musical practice - specifically, examples from tonal, but non-common-practice, music (Indian music and jazz), which show that the dynamic relationships and tendencies you attribute to scalar tones and intervals are not intrinsic to those tones and intervals, but exist only in specific musical styles and contexts.


You've cited your reasons, based on your thinking, but that is not "proof;" only an assertion of your commitment to horizontal thinking, and an avoidance of "abstraction of underlying principles" which have a firm harmonic basis.



> You've been unable to explain away these examples. Your comments above about Indian music don't suggest any answer to the question of why, outside of Western common practice, the major scale is used with no acknowledgement of what you've called its "restless quality which encourages travel away from the key."


Since Indian ragas do not modulate, the tendencies I stated in application to to Western music must not be taken so literally. However, the ideas can apply to Indian music as well, though not in terms of "modulation" or "leading tones." You're losing track of the idea, or you're doing a "bait and switch" strategy to change the context of my assertions. Since these assertions are based on "harmonic truths" and "harmonic facts," they can apply to Indian music as well, if we discard Western terms such as "modulation" and "leading tone."

I did earlier, in post #163, say that the note F over a drone of C in an Indian raga would produce _harmonic tension,_ which is the same net result: _the sense of key-centeredness (in the case of a raga, the "drone") is weakened, a tension is created, _compared to other scale notes, since_ C (drone) under F has the tendency to be heard as "key note on top," _a simple harmonic truth.

Also the melodic motive E-F over a C drone does the same thing.



> My suspicion is that you only imagine that a C major scale is "unstable," that it "encourages" travel to the key of F, because you're projecting onto that scale the dynamics of the Western tonal system, which is distinguished by keys and key relationships.


No, this is more basic than that, because C-F (a 4th) is heard as "root" on top. Go to any keyboard and pick out melodies in fourths, and this is an obvious "harmonic truth."



> Influenced by the way the tones of the scale function in common practice music, you're projecting relationships and functions of common practice tonality onto a mere scale, and "hearing" musical activity where there is only a sequence of tones - a sequence of tones which will be heard differently by someone from a different musical tradition.


No, this "tack" of yours is not working. My ideas are based on harmonic principles. They can apply to any music.


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## Woodduck

millionrainbows said:


> Schoenberg's Structural Functions of Harmony is based on "tendencies", and really, no "proof" is required, since the proof is self-evident, i.e., since *we hear fourths as "root on top" and fifths as "root on bottom,"* i.e. these are the result of the way he hear harmonically.


If we play just the first half of a C major scale, ascending from C and stopping on F, we have the feeling of establishing the key of F. I understand that the source of that perception is the fact that C is an overtone of F, making F the stronger tone, the fundamental - in musical terms, the keynote or tonic. However, that feeling of moving to the key of F depends on our stopping on F. If we continue up the scale and stop on G, the feeling that F is a keynote doesn't arise: we've established the tonality of C firmly by ending on its fifth, and the F simply settles into place as part of the major scale and causes no disturbance or distraction.

The difference in feeling we get from the F in these two procedures is a difference in _musical context._ This shows that the C major scale is not inherently "unstable" and doesn't "tend," by itself, to modulate to the key of F. We merely use its elements to modulate to F when we arrange them in certain ways.



> Since Indian ragas do not modulate, the tendencies I stated in application to to Western music must not be taken so literally.


How are they to be taken? Figuratively? Metaphorically? Poetically? Advisedly?



> However, the ideas can apply to Indian music as well, though not in terms of "modulation" or "leading tones." Since these assertions are based on "harmonic truths" and "harmonic facts," they can apply to Indian music as well, *if we discard Western terms such as "modulation" and "leading tone."*


Well, that's a Brobdingnagian "if"! _If_ we discard those things, there's nothing left of your claim that major scales are unstable and tend to modulate. The simple fact is that in non-Western music there is no suggestion of movement to another key - and I contend that even in Western music, tendencies to modulate depend on musical context. A major scale by itself, played from C to shining C, doesn't suggest that any modulation is immanent or necessary.



> I did earlier, in post #163, say that the note F over a drone of C in an Indian raga would produce _harmonic tension,_ which is the same net result: _*the sense of key-centeredness (in the case of a raga, the "drone") is weakened,* a tension is created, _compared to other scale notes, since_ C (drone) under F has the tendency to be heard as "key note on top," _a simple harmonic truth.
> 
> Also the melodic motive E-F over a C drone does the same thing.


Well, here's a lovely raag bilawal ("bilawal" indicates the use of the major scale) in which we can hear the use and effect of all the scale tones.






I hear no "weakening" of the tonality, no suggestion, at any point, that the fourth scale degree could be, or become, a keynote.



> No, this "tack" of yours is not working. *My ideas are based on harmonic principles. They can apply to any music.*


My "tack" acknowledges harmonic principles. But it doesn't overlook the way those principles are perceived to different effect in different artistic contexts. The way they're perceived in a raag bilawal is not the way they're perceived in Mozart. They're not even perceived in a C major scale which stops on F in the same way that they're perceived in one which stops on G, or continues to A, B or C.


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## millionrainbows

Woodduck said:


> If we play just the first half of a C major scale, ascending from C and stopping on F, we have the feeling of establishing the key of F. I understand that the source of that perception is the fact that C is an overtone of F, making F the stronger tone, the fundamental - in musical terms, the keynote or tonic. However, that feeling of moving to the key of F depends on our stopping on F. If we continue up the scale and stop on G, the feeling that F is a keynote doesn't arise: we've established the tonality of C firmly by ending on its fifth, and the F simply settles into place as part of the major scale and causes no disturbance or distraction.
> 
> The difference in feeling we get from the F in these two procedures is a difference in _musical context._ This shows that the C major scale is not inherently "unstable" and doesn't "tend," by itself, to modulate to the key of F. We merely use its elements to modulate to F when we arrange them in certain ways.


That doesn't disprove anything I've said. All you've done is listed a possible exception, which is unrelated.



> How are they to be taken? Figuratively? Metaphorically? Poetically? Advisedly?


Not literally. You're trying to use terminology to invalidate the ideas.



> Well, that's a Brobdingnagian "if"! _If_ we discard those things, there's nothing left of your claim that major scales are unstable and tend to modulate. The simple fact is that in non-Western music there is no suggestion of movement to another key - and I contend that even in Western music, tendencies to modulate depend on musical context. A major scale by itself, played from C to shining C, doesn't suggest that any modulation is immanent or necessary.


A scale has harmonic implications, though. Same net result in Indian music and its scales.



> Well, here's a lovely raag bilawal ("bilawal" indicates the use of the major scale) in which we can hear the use and effect of all the scale tones.
> 
> 
> 
> 
> 
> 
> I hear no "weakening" of the tonality, no suggestion, at any point, that the fourth scale degree could be, or become, a keynote.


Of course not, since Indian music doesn't modulate. It's all based on harmonic tension against the drone. Your use of Indian music is ridiculous as an argumentative tool.



> My "tack" acknowledges harmonic principles. But it doesn't overlook the way those principles are perceived to different effect in different artistic contexts.


Neither does mine; but right now, in this thread, I'm looking at some underlying harmonic principles of the C major scale, not Indian raga.



> The way they're perceived in a raag bilawal is not the way they're perceived in Mozart. They're not even perceived in a C major scale which stops on F in the same way that they're perceived in one which stops on G, or continues to A, B or C.


Of course they aren't. All you're doing is spouting more 'horizontal' exceptions.

Harmonic "color" and qualities of harmonic tension apply to _any_ music.


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## isorhythm

Woodduck said:


> _But this depends on contextual factors, including our perception that we are actually in that mode._


Yes, I made a bad/sloppy post, it doesn't really work.

I think I have to give up on this thread, which has not shown any tendency to resolve.


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## millionrainbows

isorhythm said:


> I think I have to give up on this thread, which has not shown any tendency to resolve.


I think you're right; Woodduck is on another one of his "search and destroy" missions. :lol:


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## isorhythm

OK I've already lost my resolve and am going to try one more thing. If you're right, million, shouldn't the most common modulation from the tonic in classical music be to the subdominant? But in fact it's not - it's to the dominant.

"Liked" for the Iggy Pop song.


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## millionrainbows

isorhythm said:


> OK I've already lost my resolve and am going to try one more thing. If you're right, million, shouldn't the most common modulation from the tonic in classical music be to the subdominant? But in fact it's not - it's to the dominant.
> 
> "Liked" for the Iggy Pop song.


Yes, in the key of C, G (the dominant V) _is _the most closely related key harmonically. The fact that the C major scale instead suggests F is evidence that the major scale is "unstable", harmonically speaking. For Western music, which modulates, this is very useful. Developed CP Western music is not "droney," and does not want to be "stable" and confined to one key; it wants to modulate.

You can see from this that I'm not "putting down" the major scale; in fact, it's a perfect vehicle for the restless modulations of Western tonality.


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## isorhythm

It's true that western classical music uses major scales, and also modulates a lot. I'll leave it at those points of agreement.


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## Woodduck

millionrainbows said:


> That doesn't disprove anything I've said. All you've done is listed a possible exception, which is unrelated.


Exceptions test the value of theories, and have a way of discrediting them.



> You're trying to use terminology to invalidate the ideas.


I'm questioning _your_ terminology. There are no good arguments without proper terminology.



> A scale has harmonic implications, though. Same net result in Indian music and its scales.


Harmonic "implications" vary depending on how the scales are used.



> Of course not, since Indian music doesn't modulate. It's all based on harmonic tension against the drone.


I wouldn't say that Indian music is "based on" that.



> Your use of Indian music is ridiculous as an argumentative tool.


No it isn't. It suggests very strongly that the "implications" you read into the major scale are not present apart from musical considerations that suggest or require them. It's an example of a centuries-old musical tradition which exhibits extraordinary sensitivity to pitch and melody, yet seems not to have perceived the third tone of the major scale as a "leading tone."

This thread is filled with clear observations, cogent arguments and perceptive questions with which you've been unable or unwilling to engage. A couple of examples:

In post #79 Isorhythm asked: _"Sincere question: how do you account for the fact that different musical traditions treat melody and harmony so differently, if they're supposed to be governed by universal laws?"_ Your answer was: "I'm not a rigid thinker, so I can't answer that."

In post #117, mikeh375 says:_ "Functionally, the note f is under the influence of the tonic of C in normal CP practice until the notes and or harmony around it suggest otherwise in say a modulation. It is more likely subservient to the mediant and dominant ( especially melodically, but harmonically too). The mediant itself surely has no obligation to become a leading note, unless as before, the surrounding environment compels it to act as such. It's all about the context and in a CP context, I can't agree with you on this." _ To this you made no reply at all.

Mike here supports my own objection to your claims that the C major scale has an inherent tendency to modulate to F and that the E is a "leading tone." He sees that such sensations and functions are dependent on how the components of the scale are used in a musical context. He doesn't need to cite examples of music from outside of Western common practice to make his point, but it's perfectly reasonable to do that, as I've done in citing the music of India. That music makes in an obvious way the points that the major scale in and of itself does not feel "unstable" or "ambiguous," that playing it generates no urge or need to modulate, and that E is not inherently a "leading tone." Indian music can demonstrate all this in an effective way because there is no harmonic system which might set up expectations of modulation. But, really, no demonstration is needed beyond the simple act of playing the scale: C-D-E-F-G-A-B-C...

It's true, and reasonable to point out, that the lower tetrachord of the C major scale is intervalically identical to the upper tetrachord of the F major scale, and that this provides a handy pivot for moving from C major to F major. If we do that, the E does indeed become the leading tone in the new key. But merely as a component of the scale, absent a reason for modulating, the E does not "lead" to F, there is no "urge" to travel from C to F, and no "instability"or "ambiguity" in the C scale that makes us uncomfortable and in need of finding a new tonal center. What we have is an _opportunity_ for modulation, not a need, urge, or incentive.


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## Guest

I've enjoyed the debating!! Food for thought.


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## millionrainbows

Woodduck said:


> Mike here supports my own objection to your claims that the C major scale has an inherent tendency to modulate to F and that the E is a "leading tone." He sees that such sensations and functions are dependent on how the components of the scale are used in a musical context.


So you're both "horizontal" thinkers who refuse to engage with vertical speculation. What else is new?



> (Indian) music makes in an obvious way the points that the major scale in and of itself does not feel "unstable" or "ambiguous," that playing it generates no urge or need to modulate, and that E is not inherently a "leading tone." Indian music can demonstrate all this in an effective way because there is no harmonic system which might set up expectations of modulation.


I disagree. There is harmonic tension created by the raga's scale against the "drone" underneath. I've already given two examples of harmonic proof that the C major scale has internal tensions:

1) The tendency to hear C-F as "root" on top, and "F" as the note which is in basic contention with C; and

2) the stacking of fifths to create the scale, C-G-D-A-E-B-F, which is spoiled by the tritone B-F on top. Go to any keyboard and try it.



> It's true, and reasonable to point out, that the lower tetrachord of the C major scale is intervalically identical to the upper tetrachord of the F major scale, and that this provides a handy pivot for moving from C major to F major. If we do that, the E does indeed become the leading tone in the new key.
> 
> But merely as a component of the scale, absent a reason for modulating, the E does not "lead" to F, there is no "urge" to travel from C to F, and no "instability"or "ambiguity" in the C scale that makes us uncomfortable and in need of finding a new tonal center. What we have is an _opportunity_ for modulation, not a need, urge, or incentive.


As I just replied, there is harmonic evidence as well, which does not rely on "leading tone" tendencies, but is simply the note-content and placement of those tones heard harmonically.

You're repeating yourself over & over.


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## millionrainbows

I'd like to take this opportunity to urge all musical thinkers: don't be afraid to speculate! Don't become entrenched in academia! Explore all possibilities, and keep an open mind! 

There are different ways to approach music, and the contrast of vertical/horizontal thinking demonstrated here is evidence of those possibilities.


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## mikeh375

millionrainbows said:


> *So you're both "horizontal" thinkers who refuse to engage with vertical speculation.* What else is new?


Jeez MR, why not read my post 117....keep up for chrissakes, it'll do you a favour.


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## millionrainbows

mikeh375 said:


> Jeez MR, why not read my post 117....keep up for chrissakes, it'll do you a favour.


Why don't you back off, mike375. Frankly, this discussion has become very tedious, and I've got better things to do. If you are a vertical thinker, then be pro-active and stop blaming me for reacting to Woodduck's implication that you are. Remember?



Woodduck said:


> Mike here supports my own objection to your claims that the C major scale has an inherent tendency to modulate to F and that the E is a "leading tone." He sees that such sensations and functions are dependent on how the components of the scale are used in a musical context. He doesn't need to cite examples of music from outside of Western common practice to make his point, but it's perfectly reasonable to do that, as I've done in citing the music of India.


The culprit here is Woodduck, for representing YOUR views, as you say, incorrectly.

As far as you being in agreement with me as a vertical thinker, you said this way back in post #117:



mikeh375 said:


> ...whilst it's not difficult to imagine what you say has some theoretical credence MR, especially if one looks at the symmetry in the tetrachords, in reality, *there is no parity between f and c as tonics within the one scale in CP. Functionally, the note f is under the influence of the tonic of C in normal CP practice until the notes and or harmony around it suggest otherwise in say a modulation. *It is more likely subservient to the mediant and dominant ( especially melodically, but harmonically too). The mediant itself surely has no obligation to become a leading note, unless as before, the surrounding environment compels it to act as such. It's all about the context and in a CP context, I can't agree with you on this.


You have misunderstood my basic assertion.I never said that C and F were "tonics within the one scale in CP" simultaneously, but assert a "tendency" which weakens the efficacy of C major as a "reinforcing" scale of the key of C major.


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## mikeh375

So read the post...and then see how stupid your assumption is - you even _liked_ the post. Wooduck implies no such thing and his post accurately reflects my views on your assertion. This does not mean I only think horizontally, no composer does that. I've also studied the Hanson and often involute chordal shapes as part of my vertical thinking. 
Telling me to back off isn't going to work when you have assumed and posted something about me that has been clearly and proactively stated (actually by me) to be other than what you have concluded.


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## millionrainbows

mikeh375 said:


> So read the post...*and then see how stupid your assumption is *- you even _liked_ the post. Wooduck implies no such thing and his post accurately reflects my views on your assertion. This does not mean I only think horizontally, no composer does that. I've also studied the Hanson and often involute chordal shapes as part of my vertical thinking.
> Telling me to back off isn't going to work when you have assumed and posted something about me that has been clearly and proactively stated (actually by me) to be other than what you have concluded.


Now you are slipping into ad-hominem territory.

If "Wooduck implies no such thing and his post accurately reflects my views on your assertion," then you should have waited for my complete edited post instead of "jumping the gun." Here it is:

"You have misunderstood my basic assertion.I never said that C and F were "tonics within the one scale in CP" simultaneously, but assert a "tendency" which weakens the efficacy of C major as a "reinforcing" scale of the key of C major."

So if Woodduck's post "accurately reflects your views," it is a mistake, because y_ou have misunderstood my basic assertion_.

I never said that C and F were "tonics within the one scale in CP" simultaneously, but assert a "tendency" which weakens the efficacy of C major as a "reinforcing" scale of the key of C major.


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## mikeh375

Oh I see we've now read post 117 eh....so do you still like it, or is there a tendency for you to not like it now? I fully understand your assertion, it's not that hard to grasp (and I do have 8 letters after my name), I just don't agree with it and that MR, is from a horizontal _and_ vertical thinker.


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## mikeh375

millionrainbows said:


> Now you are slipping into ad-hominem territory.


Ad hominem? Oh grow a pair please and apologise for your incorrect assumption. That will do no end of good rather than trying to divert attention by feigning insult.


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## millionrainbows

mikeh375 said:


> Oh I see we've now read post 117 eh....so do you still like it, or is there a tendency for you to not like it now? I fully understand your assertion, it's not that hard to grasp (and I do have 8 letters after my name), I just don't agree with it and that MR, is from a horizontal _and_ vertical thinker.


To tell you the truth, the reason I "liked" your post was because you said you were a guitarist, and were forthcoming in a friendly way. Certainly not for the way you're acting now.

A click for "like" never means that anyone totally agrees with every assertion in a post. You're being rigid in your thinking.


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## mikeh375

"rigid in my thinking"...ad hominem...ad hominem...ad nauseum. 
Still not big enough to apologise...ah well. Whatever dude as the young folk seem to say.

I've never been an enemy to alternative views MR, at least you should have picked up on that.


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## Bwv 1080

LCC was the first cohesive chord-scale theory in Jazz that opened the door for modal jazz and post-bop. In jazz not that many people take the mystic primacy of Lydian seriously as Jazz players tend to be practical musicians - if LCC has some useful ideas then they will use them. Later Jazz theorists incorporated the Russell’s chord-scale ideas but largely abandoned the idea of the primacy of the Lydian mode (which of course makes little sense for music whose basic tonality is built off ii-V7-I, not II7 -Vmaj7 -I.

It’s true that Lydian is brighter or ‘more major’ than Ionian , just as Phyrigian is darker or more ‘minor’ and the #11 is played in jazz over major chords and the natural 11 is rare. But that is as far as it goes. LCC has no historical precedent in classical music and it is useless in describing common practice tonality. The 4-3 tonal resolution is stronger than as #4-5, which is why dominant 7th and vii0 chords are so effective.


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## Woodduck

millionrainbows said:


> You're repeating yourself over & over.


This is not a pot calling a kettle black. It's an entire coal mine.


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## millionrainbows

Woodduck said:


> This is not a pot calling a kettle black. It's an entire coal mine.


Be sure to include those big round white eyeballs.


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## isorhythm

Bwv 1080 said:


> Later Jazz theorists incorporated the Russell's chord-scale ideas but largely abandoned the idea of the primacy of the Lydian mode


Yes this is another thing that's struck me - it seems like Russell's belief about the Lydian mode is actually not very important to his theory, almost a side show actually, despite the fact that he put it in the title of his book.


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## BabyGiraffe

Actually, if we take all permutations of major and minor chords over one root we can get C and F major OR minor chords (there is also one A minor chord and one Ab major chord there), but this is improper melodically scale and doesn't quite work harmonically with the rest of normal Western music theory (and has nothing to do with Lydian jazz modal pseudo-theory). That's actually Partch's 5-limit tonality diamond - he uses another method for generating it, not from chords, but the result is the same. Over any frequency (chromatic pitch from any equal/unequal temperament that support 5-limit mapping) we can build a chord from this subset of infinite 5-limit just intonation pitch lattice.

0: 1/1 0.000000 unison, perfect prime
1: 6/5 315.641287 minor third
2: 5/4 386.313714 major third
3: 4/3 498.044999 perfect fourth
4: 3/2 701.955001 perfect fifth
5: 8/5 813.686286 minor sixth
6: 5/3 884.358713 major sixth, BP sixth
7: 2/1 1200.000000 octave

This can be extended to 13 notes for septimal tetrads with Partch's theory (15 notes is actually the lattice with all possible permutations of tetrads, but two of the ratios are complex, so they are left out.)

The best ideal compositional space for triads is 7 equal (including all topological deformations of it like diatonic-7 in 12 equal or any other meantone, schismic or diaschismic system etc), but what is the best for tetrads? - basic combinatorics or geometry gives 13 equal - the problem is that the "Neo-riemannian tetrad" there is not a major or minor chord with added third on top, but closer to half-diminished chord (I guess Wagner had a good intuition.) 12 equal can be though as 13 equal with the two "tritones" glued together, so it somehow supports this type of writing even if septimal ratios are way off.
(Pentads is 21 equal, hexads - 31 equal - this one is very close to whole tone scale; anyway, I doubt anyone would bother with 21 or 31 tone scales, but 13 pitches is manageable extension of standard chromatic harmony).


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## millionrainbows

Bwv 1080 said:


> LCC was the first cohesive chord-scale theory in Jazz that opened the door for modal jazz and post-bop. In jazz not that many people take the mystic primacy of Lydian seriously as Jazz players tend to be practical musicians - if LCC has some useful ideas then they will use them. Later Jazz theorists incorporated the Russell's chord-scale ideas but largely abandoned the idea of the primacy of the Lydian mode (which of course makes little sense for music whose basic tonality is built off ii-V7-I(maj7), not II7 -Vmaj7 -I(maj7).


I'll see your V7, and raise you a I maj7.

George Russell's Lydian Chromatic Concept uses the chord-scale system. It does not posit a single scale for a ii-V7-I progression.

For a ii-V7-Imaj7 progression, the C major scale is no better than the Lydian simply because it has the b7 of G domonant;it still has the "clam" of F in the I major seventh chord.

The F#-G of lydian works better for a Imaj7 chord.

You need to consider the lydian in terms of harmonic consonance, C-G-D-A-E-B-F#, which is superior to a major scale C-G-D-A-E-B-F, with its ugly tritone on top.

Just because the F of a major scale can be the b7 of a V chord does not mean that the Lydian scale is less tonally congruent, or is less suitable for a ii-V7-I progression in jazz (which was derived from major scale harmony anyway, via tin-pan alley standards). "F" still clashes with the I maj7.

What could be more primal than maximum harmonic consonance over a chord, and the ability to move away from that consonance in increments, to whatever degree the player desires?



> It's true that Lydian is brighter or 'more major' than Ionian , just as Phyrigian is darker or more 'minor' and the #11 is played in jazz over major chords and the natural 11 is rare. But that is as far as it goes.


In jazz, that's a far as you need to go, since the thinking is based on harmonic considerations, i.e., how it sounds.



> LCC has no historical precedent in classical music and it is useless in describing common practice tonality.


That's irrelevant, since the thinking in classical music is based on procedures and mechanisms which were devised by horizontal thinkers. This tendency to avoid "pure harmonic" thinking in favor of "devised" and "invented" procedures which can only take place in a horizontal, narrative (literate) landscape seems to be the way Western music "developed" away from "primitive" and "folk" thinking, which is based on sound, not *ideas* about sound.

Oh, yes, and I almost forgot: there is no "I major seventh chord" in CP classical music.



> The 4-3 tonal resolution is stronger than as #4-5, which is why dominant 7th and vii0 chords are so effective.


Says who? "Strength" and "effectiveness" are in the eyes of the beholder. A 4-3 tonal resolution favors an "inferior" tone, the major third. The #4-5 favors the 5th, a stronger tone, as well as inferring (via a new 4th) that "(G) 5th is now root" and "ascends" in strength.

In Western music, dominant chords want to resolve, but we are in Equal Temperament (or close to it).

In African musics, the flat-seven is harmonic, much flatter, and has less tendency to "want" to resolve. The residual effect of this "legacy" of harmonic sevenths is still present in blues and jazz, where the I, IV, and V are all flat sevens.

See https://en.wikipedia.org/wiki/Harmonic_seventh

In short, Western tonality is much more "contrived" than ethnic, "primitive," folk, popular, tin-pan-alley, or blues/jazz music. In this sense, it's rather mannered, archaic and historically dated. It must be learned, not absorbed.


----------



## millionrainbows

BabyGiraffe said:


> Actually, if we take all permutations of major and minor chords over one root we can get C and F major OR minor chords (there is also one A minor chord and one Ab major chord there), but this is improper melodically scale and doesn't quite work harmonically with the rest of normal Western music theory (and has nothing to do with Lydian jazz modal pseudo-theory). That's actually Partch's 5-limit tonality diamond - he uses another method for generating it, not from chords, but the result is the same. Over any frequency (chromatic pitch from any equal/unequal temperament that support 5-limit mapping) we can build a chord from this subset of infinite 5-limit just intonation pitch lattice.
> 
> 0: 1/1 0.000000 unison, perfect prime
> 1: 6/5 315.641287 minor third
> 2: 5/4 386.313714 major third
> 3: 4/3 498.044999 perfect fourth
> 4: 3/2 701.955001 perfect fifth
> 5: 8/5 813.686286 minor sixth
> 6: 5/3 884.358713 major sixth, BP sixth
> 7: 2/1 1200.000000 octave
> 
> This can be extended to 13 notes for septimal tetrads with Partch's theory (15 notes is actually the lattice with all possible permutations of tetrads, but two of the ratios are complex, so they are left out.)
> 
> The best ideal compositional space for triads is 7 equal (including all topological deformations of it like diatonic-7 in 12 equal or any other meantone, schismic or diaschismic system etc), but what is the best for tetrads? - basic combinatorics or geometry gives 13 equal - the problem is that the "Neo-riemannian tetrad" there is not a major or minor chord with added third on top, but closer to half-diminished chord (I guess Wagner had a good intuition.) 12 equal can be though as 13 equal with the two "tritones" glued together, so it somehow supports this type of writing even if septimal ratios are way off.
> (Pentads is 21 equal, hexads - 31 equal - this one is very close to whole tone scale; anyway, I doubt anyone would bother with 21 or 31 tone scales, but 13 pitches is manageable extension of standard chromatic harmony).


I made a set of wind chimes tuned to equal-7, and it begins to sound like a major scale, because it has 7 notes. You can pick out familiar tunes and identify them easily, even though it's 7-ET. This is melodically, not harmonically or hearing tuning.


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## BabyGiraffe

millionrainbows said:


> I made a set of wind chimes tuned to equal-7, and it begins to sound like a major scale, because it has 7 notes. You can pick out familiar tunes and identify them easily, even though it's 7-ET. This is melodically, not harmonically or hearing tuning.


7 equal is the proto-anything related to heptatonic scale, it is a rank-1 temperament. The theory of maximal eveness structures is one of the few researches related to music that has any usage outside of music.

In other words" 7 equal <-> any other 7 note scale via topological (free style continuous pitch scales) or discrete (JI) transformations.

If we use a distortion of any of the 7 edo steps as a generator (and octave) we get families of rank-2 temperaments in bigger systems than 7 equal. All these have a mode that is very close to Dorian (which is closest to 7 equal).

Using two pitches is a 2-dimensional system - that's why Riemann's functional theory is superior to the linear pythagorean generation of rank-2 temperament - the basic unit is a major or minor triad - that's a 2d system - and is closer to actual musical practice that is based on triadic chords, not on modal melodies.

Meantone-12 is not a triadic system. After 7 notes it degenerates to lower rank temperament.

"For instance, a harpsichord tuner it might think of quarter-comma meantone tuning as having three generators-the octave, the just major third (5:4) and the quarter-comma tempered fifth-but because four consecutive tempered fifths produces a just major third, the major third is redundant, reducing it to a rank-two temperament. "

https://en.wikipedia.org/wiki/Regular_temperament


----------



## millionrainbows

Bwv 1080 said:


> Later Jazz theorists incorporated the Russell's chord-scale ideas but largely abandoned the idea of the primacy of the Lydian mode (which of course makes little sense for music whose basic tonality is built off ii-V7-*I*, not II7 -Vmaj7 -*I*.


You mean ii-V7-I maj7?

It's sort of a gaffe for Bwv 1080 to try to "test" and apply the LCC to Classical music. While it's true that ii-V7-I progressions are common to jazz, this came from the use of tin-pan alley popular songs, like Gershwin's "I Got Rhythm" and "Georgia Brown," not classical music.

Additionally, there are no "major 7th" chords in classical which function as I.

What is "primacy" supposed to mean on a practical level? The Lydian scale is more "harmonically primal" than the major scale in terms of reinforcing the key note of the scale.


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## BabyGiraffe

Someone on reddit ran a computer search for heptatonic scales, sharing the most harmonics:

Complexity:

0.6679 1 9/8	5/4	11/8	3/2	27/16	15/8 
0.6704 1	16/15	6/5	4/3	3/2	8/5	9/5 
0.6705 1	9/8	5/4	21/16	3/2	27/16	15/8 
0.6732 1	9/8	5/4	4/3	3/2	5/3	15/8 
0.6732 1	9/8	5/4	4/3	3/2	27/16	15/8 
0.6743 1	11/10	6/5	7/5	3/2	8/5	9/5 
0.6744 1	9/8	5/4	11/8	3/2	27/16	7/4 
0.6756 1	10/9	7/6	4/3	3/2	5/3	7/4 
0.6756 1	16/15	6/5	7/5	3/2	8/5	9/5 
0.6769 1	9/8	5/4	21/16	3/2	27/16	7/4 
0.6785 1	10/9	7/6	4/3	3/2	5/3	11/6 
0.6794 1	9/8	7/6	4/3	3/2	5/3	7/4 

First one is between Natural major (Ionian) and Lydian. It's called "Maqam 'Ajam Murassah".
Second one is modern Phrygian mode, Greek Dorian (medieval scholars messed up the names).
Thrid one is Major/Ionian with syntonic and septimal commas difference in two ratios, compared to just version of Intense diatonic.
Fourth - Ptolemy's just major scale aka modern NATURAL MAJOR in just tuning with syntonic commas.
5th - same thing - A is a syntonic comma higher
6th - Ukranian Dorian/Minor Gypsy variant/ whatever it is called in oriental maqam theory?
7th - Just lydian dominant/Bartok/Overtone scale - big differences between it and 12 equal version, of course
8th - Some kind of Afro/Septimal "dorian" scale
9th - Some kind of Indian looking scale.
10th - Mixolydian with septimal seventh
11th - "Melodic minor" in some kind of Afro/Oriental tuning?
12th - Septimal "Dorian".

No Lydian anywhere except first one that is NOT the real lydian or pure major scale. ( Maybe Russel was thinking about such scale - it can be thought as a variant of diatonic in any tuning with intervals close to 1/4 tones.)

And here is the pentatonic version:

0.7000	1	7/6	4/3	3/2	5/3 
0.7049	1	6/5	7/5	8/5	9/5 
0.7083	1	10/9	4/3	3/2	5/3 
0.7090	1	7/6	4/3	3/2	7/4 
0.7098	1	9/8	5/4	3/2	7/4 
0.7120	1	7/6	5/4	3/2	7/4 
0.7135	1	6/5	7/5	3/2	9/5 
0.7165	1	9/8	5/4	3/2	27/16	
0.7219	1	6/5	4/3	3/2	9/5 
0.7234	1	7/6	4/3	3/2	11/6 
0.7240	1	9/8	4/3	3/2	5/3	
0.7240	1	9/8	4/3	3/2	27/16	
0.7249	1	6/5	5/4	3/2	9/5	
0.7263	1	9/8	45/32	3/2


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## Guest

millionrainbows said:


> I'd like to take this opportunity to urge all musical thinkers: don't be afraid to speculate! Don't become entrenched in academia! Explore all possibilities, and keep an open mind!
> 
> There are different ways to approach music, and the contrast of vertical/horizontal thinking demonstrated here is evidence of those possibilities.


Agree. The trouble is that some people are Junkyard Dogs and being vicious comes naturally, no matter what the topic. Barking, snapping and threatening replace discussion and respect.

Thanks for the interesting discussion points from those who have thought it all through.


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## millionrainbows

Actually, the real problem here is that I come from a jazz background, and I'm more likely to see harmonic/vertical aspects of music, and am not as much a believer in "context" and horizontal classical procedures as others here.

That being said, Schoenberg thought outside the box, and modern musical thinkers in general are more receptive to vertical/harmonic thinking.

One "big gaffe" here was Bwv 1080's trying to compare George Russell's Lydian Chromatic Concept to classical music. Regardless, my assertions here, using the lydian scale as comparison, are based on harmonic considerations not strictly tied to George Russell's ideas, and are applicable to any music as 'basic truths.'


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## isorhythm

Deleted, misread a post.

Though while I'm at it...not sure I buy that jazz is more concerned with the vertical aspects of music and classical with the horizontal, as a general rule.


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## millionrainbows

isorhythm said:


> Deleted, misread a post.
> 
> Though while I'm at it...not sure I buy that jazz is more concerned with the vertical aspects of music and classical with the horizontal, as a general rule.


Oh, I thought that was why Woodduck was making all the fuss. Perhaps you're right, and he's making a big to-do out of nothing.


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## Woodduck

millionrainbows said:


> Oh, I thought that was why Woodduck was making all the fuss. Perhaps you're right, and he's making a big to-do out of nothing.


The "fuss" isn't exclusive to me. Unless you have a Trumpean propensity to overestimate your "crowd size," you should note that your notions of "two tonics" and the "instability" of scales haven't won you many followers.

A scale is not a "vertical" phenomenon, and neither is the very idea of "instability." Now if we want to stack the notes of scales up into chords, then we might talk about which scales sound most "stable." Interestingly, if you play together in a "vertical" cluster all the notes of the major scale, and compare the sound of that with the Lydian played the same way, it's the Lydian that sounds more unstable - in need of resolution - with the tritone between the first and fourth degrees a howling dissonance more tonally disruptive than the corresponding steps in the major scale, where the dissonant fourth degree is under the control of the third, to which it would typically resolve.

With the scales thus played "vertically" (as chords), the fourth degree of the Lydian seems to refer to a different tonal center in conflict with that of the scale, while the fourth degree of the Major scale is pulled into the scale's tonality and largely absorbed, with no need to become a tonal center itself.

As for "leading tones," when the scales are played "horizontally" (the notes in sequence), the fourth degree of the Lydian - F# in a C scale - sounds more like a leading tone to G than the E of the Major scale sounds like a leading tone to F; the F# wants to resolve to G (G being the tonal center most closely related to C), whereas in C major the E is stable and doesn't need to resolve (which a "leading" tone should by definition). It's the F that wants to resolve, and into the established tonality. Hence I hear a greater instability - tendency to modulate - in a Lydian than in a Major tonality.


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## EdwardBast

Woodduck said:


> Hence I hear a greater instability - tendency to modulate - in a Lydian than in a Major tonality.


So, seemingly, has virtually everyone else who has ever composed music in the Western art music and folk music traditions. Were the Lydian mode an unmatched paragon of stability, people would have been using it. In fact, even music avowedly in the Lydian mode, especially plainchant, tends to liberally alter the 4th degree.


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## Woodduck

EdwardBast said:


> Were the Lydian mode an unmatched paragon of stability, people would have been using it. In fact, even music avowedly in the Lydian mode, especially plainchant, tends to liberally alter the 4th degree.


My aural memory tells me that in plainchant the fourth degree is more likely to be "Lydianized" (raised) when ascending, while descending it's apt to be "Ionianized" (lowered). Am I correct? Was a descending Lydian scale felt to be somewhat awkward, less smooth and natural? This brings to mind the ascending and descending forms of the melodic minor scale.


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## EdwardBast

Woodduck said:


> My aural memory tells me that in plainchant the fourth degree is more likely to be "Lydianized" (raised) when ascending, while descending it's apt to be "Ionianized" (lowered). Am I correct? Was a descending Lydian scale felt to be somewhat awkward, less smooth and natural? This brings to mind the ascending and descending forms of the melodic minor scale.


Sounds like a reasonable hypothesis. I'd have to get out the old Liber Usualis and do a statistical analysis to know for sure.


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## Woodduck

Searching for some examples of music using mixed Major and Lydian scales, I just tripped over this article which sets forth exactly the same arguments as millionrainbows does:

https://www.musical-u.com/learn/the-lydian-scale-part-2-lydian-meets-major/

The author tells us: 1. "each interval has it's own tonic, it's own tonal gravity field"; and 2. "within the major scale, the fourth degree exerts a strong gravitational pull-so strong, that the major scale has earned the moniker diatonic scale. The scale with two tonics!" Obviously the "two tonics" misconception has caught on in some quarters.

Discussing the difference between Major and Lydian scales, the author offers sound samples to demonstrate the influence of the supposed tonal gravity field upon each scale step in both Major and Lydian scales. He purports to demonstrate that the fourth degree of the Major scale is not within the tonal gravity field of the keynote but rather reverses the attraction by asserting its own field of gravitation. He then claims to show that the raised fourth degree of the Lydian scale affirms the tonal gravity field of the keynote, and he assumes that when we hear his demonstration we'll agree with this. Well, I don't agree!

One member of a tritone might well function within the "tonal gravity field" of the other, but a musical context is needed to give it such a function. In a bare Lydian scale it's absurd to use the interval of the tritone to prove that "each interval has its own tonic," and fanciful to imagine that the tonic to which that note refers is the keynote of the scale. Indeed, if we insist on looking for a tonal center to which the dissonant, raised fourth degree could relate (and I don't insist, but merely suggest!), it would be the semitone above it, the fifth scale degree; the emergence of the "dominant" key as the principal subordinate tonal center in Western music suggests that this is exactly what people intuited. As for the Major scale, we easily relate the fourth degree to the keynote, for two reasons: because it's a simple inversion of a perfect fifth and thus not as "alien" as the raised Lydian fourth, and because its closeness to the third of the scale creates a downward pull, back into the major tonality of the scale. The raised fourth degree of the Lydian scale, by contrast, can't be related to the keynote at all; if it refers to anything, it points to a tonic as yet unheard, the tonic which will become the "dominant" key in common practice tonality.

I would dispute the notion that "each interval has its own tonic." Some intervals are more suggestive of a tonality than others, and the tritone needs a context to bestow tonal significance on it. But if a naked tritone implies a tonal center at all, that center is not one of the notes that constitute it.


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## EdwardBast

Woodduck said:


> Searching for some examples of music using mixed Major and Lydian scales, I just tripped over this article which sets forth exactly the same arguments as millionrainbows does:
> 
> https://www.musical-u.com/learn/the-lydian-scale-part-2-lydian-meets-major/
> 
> The author tells us: 1. "each interval has it's own tonic, it's own tonal gravity field"; and 2. "within the major scale, the fourth degree exerts a strong gravitational pull-so strong, that the major scale has earned the moniker diatonic scale. The scale with two tonics!" Obviously the "two tonics" misconception has caught on in some quarters.
> 
> Discussing the difference between Major and Lydian scales, the author offers sound samples to demonstrate the influence of the supposed tonal gravity field upon each scale step in both Major and Lydian scales. He purports to demonstrate that the fourth degree of the Major scale is not within the tonal gravity field of the keynote but rather reverses the attraction by asserting its own field of gravitation. He then claims to show that the raised fourth degree of the Lydian scale affirms the tonal gravity field of the keynote, and he assumes that when we hear his demonstration we'll agree with this. Well, I don't agree!
> 
> One member of a tritone might well function within the "tonal gravity field" of another, but a musical context is needed to give it such a function. In a bare Lydian scale it's absurd to use the interval of the tritone to prove that "each interval has its own tonic" and that the tonic to which that note refers is the keynote of the scale. Indeed, if we insist on looking for a tonal center to which the dissonant, raised fourth degree could relate, it would be the semitone above it - the fifth scale degree - and the emergence of the concept of the "dominant" key in Western music suggests that this is exactly what people intuited. I think that when we hear a Major scale we easily relate the fourth degree to the keynote because it's a simple inversion of the perfect fifth. But the raised fourth degree of the Lydian can't be related to the keynote at all, and points to a tonic as yet unheard, the tonic which will become the "dominant" key in common practice tonality.
> 
> I would dispute the notion that "each interval has its own tonic." Some intervals are more suggestive of a tonality than others, and the tritone needs a context to bestow tonal significance on it. But if a naked tritone implies a tonal center at all, that center is not one of the notes that constitute it.


Ha! Maybe MR is one of the author's aliases?

I feel no need to get into extra leading tones and gravity fields given the looming absence of the (freaking) subdominant in the Lydian mode. That hole alone sinks the hapless theory.


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## BabyGiraffe

We can check the interval pattern of any mode and be sure that Locrian and Lydian are the most useless. 
The most melodically interesting are Mixolydian and Aeolian. 
Ionian and Phrygian are inversionally related - the first one is good for ascending motion, the second - for descending.
Dorian can go up or down and is the best for symmetrical motives.


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## jegreenwood

Woodduck said:


> Searching for some examples of music using mixed Major and Lydian scales, I just tripped over this article which sets forth exactly the same arguments as millionrainbows does:
> 
> https://www.musical-u.com/learn/the-lydian-scale-part-2-lydian-meets-major/
> 
> The author tells us: 1. "each interval has it's own tonic, it's own tonal gravity field"; and 2. "within the major scale, the fourth degree exerts a strong gravitational pull-so strong, that the major scale has earned the moniker diatonic scale. The scale with two tonics!" Obviously the "two tonics" misconception has caught on in some quarters.
> 
> Discussing the difference between Major and Lydian scales, the author offers sound samples to demonstrate the influence of the supposed tonal gravity field upon each scale step in both Major and Lydian scales. He purports to demonstrate that the fourth degree of the Major scale is not within the tonal gravity field of the keynote but rather reverses the attraction by asserting its own field of gravitation. *He then claims to show that the raised fourth degree of the Lydian scale affirms the tonal gravity field of the keynote, and he assumes that when we hear his demonstration we'll agree with this. Well, I don't agree! *
> 
> One member of a tritone might well function within the "tonal gravity field" of the other, but a musical context is needed to give it such a function. In a bare Lydian scale it's absurd to use the interval of the tritone to prove that "each interval has its own tonic," and fanciful to imagine that the tonic to which that note refers is the keynote of the scale. Indeed, if we insist on looking for a tonal center to which the dissonant, raised fourth degree could relate (and I don't insist, but merely suggest!), it would be the semitone above it, the fifth scale degree; the emergence of the "dominant" key as the principal subordinate tonal center in Western music suggests that this is exactly what people intuited. As for the Major scale, we easily relate the fourth degree to the keynote, for two reasons: because it's a simple inversion of a perfect fifth and thus not as "alien" as the raised Lydian fourth, and because its closeness to the third of the scale creates a downward pull, back into the major tonality of the scale. The raised fourth degree of the Lydian scale, by contrast, can't be related to the keynote at all; if it refers to anything, it points to a tonic as yet unheard, the tonic which will become the "dominant" key in common practice tonality.
> 
> I would dispute the notion that "each interval has its own tonic." Some intervals are more suggestive of a tonality than others, and the tritone needs a context to bestow tonal significance on it. But if a naked tritone implies a tonal center at all, that center is not one of the notes that constitute it.


In a podcast from the same website (starting at about 12:30), the author of the article describes the tritone as not really wanting to resolve anywhere, although he then claims it is more of a downward resolution. I don't hear that.


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## millionrainbows

Woodduck said:


> The "fuss" isn't exclusive to me. Unless you have a Trumpean propensity to overestimate your "crowd size," you should note that your notions of "two tonics" and the "instability" of scales haven't won you many followers.


Irrelevant.



> A scale is not a "vertical" phenomenon...


A scale is an index of notes. It is presented as a series of ascending notes merely as a convention. Since it is an unordered set of notes, it has inter-relations of a harmonic (vertical) nature, and these are primary. When these interval relations are spread-out over time, they become melodic (horizontal). So, in this sense of a 'static index' of notes, a scale is firstly vertical, not horizontal.



> it's the Lydian that sounds more unstable - in need of resolution - with the tritone between the first and fourth degrees....in the major scale....the dissonant fourth degree is under the control of the third, to which it would typically resolve.


Conversely, the tritone F-B in lydian is under control of the fifth (G), so it resolves _up_ to G as a leading tone. With Lydian, the F#-G is not heard as a suspension, but as a leading tone to G.



> With the scales thus played "vertically" (as chords), the fourth degree of the Lydian seems to refer to a different tonal center in conflict with that of the scale...


Yes, I've always said that F# in a C Lydian scale is a leading tone to G, the next most closely-related key to C.



> ...The fourth degree of the Major scale is pulled into the scale's tonality and largely absorbed, with no need to become a tonal center itself.


Only if you resolve it down. If you see it as a leading tone, it goes up to F, a less related key. The movement "up" to F is further emphasized by the interval C-F, which we hear as "root" on top (F).



> As for "leading tones," when the scales are played "horizontally" (the notes in sequence), the fourth degree of the Lydian - F# in a C scale - sounds more like a leading tone to G than the E of the Major scale sounds like a leading tone to F...


I've no quibble with F# sounding like a leading tone to G, in a C Lydian scale.

As far as E-F in a Major scale _not_ sounding like a leading tone to F, that's not true: the movement "up" to F is further emphasized harmonically by the interval C-F, which we hear as "root" on top (F). Your "suspension/resolution" of F down to E is an arbitrary counterpoint device, which fights against the C-F we hear. The suspension is the tension of C-F, which wants to be heard as F. Your Western solution, using a suspension, is totally contrived.



> ...the F# wants to resolve to G (G being the tonal center most closely related to C), whereas in C major the E is stable and doesn't need to resolve (which a "leading" tone should by definition).


The problem is not E, but F. There is no corresponding perfect fourth in lydian; therefore, it must resolve up, F#-G, as a leading tone.
With the perfect fourth C-F present in C major, the conflict is between the perfect fifth C-G and its inverse, C-F. Both are strong intervals (3:4 and 4:5), and both produce strong harmonic gravity: the fifth is heard as "root on bottom" (C-G), and the fourth is heard as "root on top" (C-F).

We must now question the Western CP notion of the perfect fourth as a "dissonance," which I say is not. When "C-D-E-F" is stated, it does not need to resolve; it has achieved C-F, a new consonance. The "resolution" down to E is a contrived afterthought which fights against the harmonic reality of C-F.



> It's the F that wants to resolve, and into the established tonality. Hence I hear a greater instability - tendency to modulate - in a Lydian than in a Major tonality.


No, the F does not need to resolve. It is now a fourth, and has achieved independence as a perfect fourth. Western tonality devised the "suspension" as a way to cover the inherent ambiguity of the major scale with its "F" glitch note.


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## isorhythm

Woodduck said:


> My aural memory tells me that in plainchant the fourth degree is more likely to be "Lydianized" (raised) when ascending, while descending it's apt to be "Ionianized" (lowered). Am I correct? Was a descending Lydian scale felt to be somewhat awkward, less smooth and natural? This brings to mind the ascending and descending forms of the melodic minor scale.


I thought this was actually a more or less hard-and-fast rule, though maybe I'm wrong. Same with the sixth in the Dorian.


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## millionrainbows

EdwardBast said:


> Were the Lydian mode an unmatched paragon of stability, people would have been using it.


Western music does not seek "unmatched paragons of harmonic stability" like Indian raga, folk, and "primitive" tone-centric modal music. it is intended to modulate; thus, the ambiguous C major scale, with its harmonic instability, is good for this. Now you can have "suspension/resolutions" to play with.


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## millionrainbows

Woodduck said:


> My aural memory tells me that in plainchant the fourth degree is more likely to be "Lydianized" (raised) when ascending, while descending it's apt to be "Ionianized" (lowered). Am I correct? *Was a descending Lydian scale felt to be somewhat awkward, less smooth and natural?* This brings to mind the ascending and descending forms of the melodic minor scale.





isorhythm said:


> I thought this was actually a more or less hard-and-fast rule, though maybe I'm wrong. Same with the sixth in the Dorian.


Don't forget where you are in the scale, gentlemen. *The Ionian scale has a perfect fourth above its key note; the Lydian does not.*


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## millionrainbows

Woodduck said:


> Searching for some examples of music using mixed Major and Lydian scales, I just tripped over this article which sets forth exactly the same arguments as millionrainbows does:
> 
> https://www.musical-u.com/learn/the-lydian-scale-part-2-lydian-meets-major/
> 
> The author tells us: 1. "each interval has it's own tonic, it's own tonal gravity field"; and 2. "within the major scale, the fourth degree exerts a strong gravitational pull-so strong, that the major scale has earned the moniker diatonic scale. The scale with two tonics!" Obviously the "two tonics" misconception has caught on in some quarters.


I won't argue with that.



> Discussing the difference between Major and Lydian scales, the author offers sound samples to demonstrate the influence of the supposed tonal gravity field upon each scale step in both Major and Lydian scales. He purports to demonstrate that the fourth degree of the Major scale is not within the tonal gravity field of the keynote but rather reverses the attraction by asserting its own field of gravitation.


He is obviously referring to C-F, which creates the perfect fourth gravitation of F: "root" on top.



> He then claims to show that the raised fourth degree of the Lydian scale affirms the tonal gravity field of the keynote, and he assumes that when we hear his demonstration we'll agree with this. Well, I don't agree!


Maybe he is referring to G as the fifth of the keynote C.



> One member of a tritone might well function within the "tonal gravity field" of the other, but a musical context is needed to give it such a function.


The tritone's position _within the scale_ is what gives it potential function, no context needed.



> In a bare Lydian scale it's absurd to use the interval of the tritone to prove that "each interval has its own tonic," and fanciful to imagine that the tonic to which that note refers is the keynote of the scale. Indeed, if we insist on looking for a tonal center to which the dissonant, raised fourth degree could relate (and I don't insist, but merely suggest!), it would be the semitone above it, the fifth scale degree; the emergence of the "dominant" key as the principal subordinate tonal center in Western music suggests that this is exactly what people intuited.


Leading tones do this, not the tritone.



> As for the Major scale, we easily relate the fourth degree to the keynote, for two reasons: because it's a simple inversion of a perfect fifth and thus not as "alien" as the raised Lydian fourth, and because its closeness to the third of the scale creates a downward pull, back into the major tonality of the scale.


With the perfect fourth C-F present in C major, the conflict is between the perfect fifth C-G and its inverse, C-F. Both are strong intervals (3:4 and 4:5), and both produce strong harmonic gravity: the fifth is heard as "root on bottom" (C-G), and the fourth is heard as "root on top" (C-F).

We must now question the Western CP notion of the perfect fourth as a "dissonance," which I say is not.



> The raised fourth degree of the Lydian scale, by contrast, can't be related to the keynote at all; if it refers to anything, it points to a tonic as yet unheard, the tonic which will become the "dominant" key in common practice tonality.


As I've always said.


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## millionrainbows

From WIK:

George Russell, in his 1953 Lydian Chromatic Concept of Tonal Organization, presents a slightly different view from classical practice, one widely taken up in Jazz. He regards the tritone over the tonic as a rather consonant interval due to its derivation from the Lydian dominant thirteenth chord (Russell 2008, p. 1).

In effect, he returns to a Medieval consideration of "harmonic consonance": that intervals when not subject to octave equivalence (at least not by contraction) and correctly reproducing the mathematical ratios of the harmonic series are truly non-dissonant.

Thus the harmonic minor seventh, natural major ninth, half-sharp eleventh note (untempered tritone), half-flat thirteenth note, and half-flat fifteenth note must necessarily be consonant. Octave equivalence (minor ninth in some sense equivalent to minor second, etc.) is no longer unquestioned.
Note that most of these pitches exist only in a universe of microtones smaller than a halfstep; notice also that we already freely take the flat (minor) seventh note for the just seventh of the harmonic series in chords. Russell extends by approximation the virtual merits of harmonic consonance to the 12TET tuning system of Jazz and the 12-note octave of the piano, granting consonance to the sharp eleventh note (approximating the harmonic eleventh), that accidental being the sole pitch difference between the Major scale and the Lydian mode.
(In another sense, that Lydian scale representing the provenance of the tonic chord (with major seventh and sharp fourth) replaces or supplements the Mixolydian scale of the dominant chord (with minor seventh and natural fourth) as the source from which to derive extended tertian harmony.)

Dan Haerle, in his 1980 The Jazz Language (Studio 224 1980, p. 4), extends the same idea of harmonic consonance and intact octave displacement to alter Paul Hindemith's Series 2 gradation table from The Craft of Musical Composition (Hindemith & 1937-70, 1:[page needed]). In contradistinction to Hindemith, whose scale of consonance and dissonance is currently the de facto standard, Haerle places the minor ninth as the most dissonant interval of all, more dissonant than the minor second to which it was once considered by all as octave-equivalent. He also promotes the tritone from most-dissonant position to one just a little less consonant than the perfect fourth and perfect fifth.

For context: unstated in these theories is that musicians of the Romantic Era had effectively promoted the major ninth and minor seventh to a legitimacy of harmonic consonance as well, in their fabrics of 4-note chords (Tymoczko 2011, p. 106).


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## Bwv 1080

Took Dan Haerle’s Jazz theory class in the mid 90s, what an awesome guy. Where I first heard of the LCC


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## isorhythm

You might try playing around with this on a piano/keyboard. Play your 13th chord on C with an F sharp, then see if it really does reinforce a tonic of C.

If you play that chord and then just play the note C, how does it sound to you? If you play your 13th chord, then G, then C, how does that sound? Does the G sound like a dominant, or like a tonic? Does the final C chord sound like a tonic, or like a subdominant?

I realize playing three chords isn't enough to establish any tonal center firmly, but I still think this is instructive.

As some other people have said...I think the "Lydian" fourth just sounds better because it avoids the tritone and minor ninth you get with the natural fourth.


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