# Tonality Never Really Existed



## millionrainbows (Jun 23, 2012)

The whole tone scale is an 6-tone based on the projection of the major second. The scale's interval content is M2s, M3s, and tritones. It repeats symmetrically; no matter which note you begin on, the resulting intervals are the same. It divides evenly at the tritone.

Tonality uses the 7-note diatonic scale, and its "dividing point" is the fifth.

That's because the 12-note chromatic scale was derived from the projection of the fifth; thus the circle of fifths. This is an acoustically-based method.

But actually, the 12-note scale is an anomaly, an approximation, based on the attempt to close the octave after 12 cycles of 3:2 fifths.

Thus, "12" is the resulting mathematical result of this error or approximation; there is no acoustic ("tonal") reason for its existence, other than that it approximates fifths. In ET, all these fifths are 2 cents flat, to compensate for this error, and to close the octave, which would otherwise spiral onward into irrational values. No "non-1 ratio," such as the 3:2 fifth, can be divided into "1" (the octave) evenly.

The fifth (3:2), and octave (2:1) come out relatively unscathed in this 12-cycling scheme; what really suffers is the major third, a full 14 cents sharp in ET. All the variants of "mean tone" tuning were attempts to preserve a purer major third. None of the other acoustically pure intervals fare much better; not the minor third, nor the flat seventh.

Thus, all the resulting symmetries created by "12" are mathematical in nature, and thus have a way of degrading tonality's supposed "acoustic" nature of ratios, and turning music into a mathematically/geometrically based system. 

Thus, the "undoing" of tonality was always inherent in the "12" based scale of Pythagoras. And, I might add, the inevitability of serialism or structural/mathematical based systems always existed.


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## Andreas (Apr 27, 2012)

millionrainbows said:


> Thus, the "undoing" of tonality was always inherent in the "12" based scale of Pythagoras. And, I might add, the inevitability of serialism or structural/mathematical based systems always existed.


So would it be even possibly to play 12-tone music correctly with regular instruments that are equal-tempered or otherwise made to fit the diatonic scale?


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## amfortas (Jun 15, 2011)

millionrainbows said:


> Thus, the "undoing" of tonality was always inherent in the "12" based scale of Pythagoras. And, I might add, the inevitability of serialism or structural/mathematical based systems always existed.


Wouldn't you expect this undoing of tonality to also undo the twelve-note system supporting it? Yet for some reason Western atonal music has largely stayed with what must seem an increasingly arbitrary scale.


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## millionrainbows (Jun 23, 2012)

Andreas said:


> So would it be even possibly to play 12-tone music correctly with regular instruments that are equal-tempered or otherwise made to fit the diatonic scale?


It's possible to play in one key, and be truly "in tune," as is the intent of the tonal system, as long as you don't change key. Might I suggest some North Indian raga, perhaps Ravi Shankar, or maybe Terry Riley?

All else is "close enough for rock and roll."


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## millionrainbows (Jun 23, 2012)

amfortas said:


> Wouldn't you expect this undoing of tonality to also undo the twelve-note system supporting it? Yet for some reason Western atonal music has largely stayed with what must seem an increasingly arbitrary scale.


It's possible to divide the octave in other ways. The Thai scale is a 7-note ET, divided evenly.

Pythagoras' scale had uniquely-sized intervals.

It's funny that the pentatonic scale is the "complement" of the diatonic 7-note scale; both add up to 12.

The Chinese seemed to have stopped at 5 notes (5 stacked fifths);

The Arabs kept the fifths cycle going, not stopping until 17 notes in the octave. They did this to get certain microtonal nuances, though; all 17 notes were not used at once, but served as an "index" to work out scales derived from it.

I'll go into further detail about the Chinese method of deriving the scale, later.


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## Andreas (Apr 27, 2012)

millionrainbows said:


> Tonality uses the 7-note diatonic scale, and its "dividing point" is the fifth.
> 
> That's because the 12-note chromatic scale was derived from the projection of the fifth; thus the circle of fifths. This is an acoustically-based method.
> 
> But actually, the 12-note scale is an anomaly, an approximation, based on the attempt to close the octave after 12 cycles of 3:2 fifths.


Nietzsche said, life without music would be an error. I'd say, if tonality is an error, we can live with that.


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## Jobis (Jun 13, 2013)

As an amateur piano player I'm quite glad we stuck with just 12 tones, the idea of playing 17 or 19 TET music gives me the horrors!


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## Piwikiwi (Apr 1, 2011)

The asymmetry of the major/minor scales are actually the things that make them interesting, the diminished(octatonic) and the whole tone scale are incredibly boring because it's all the same, there is no center and therefore they lack forward motion. 

The whole tonal system of western music is based around harmony, Indian or gamelan music don't even come close to even the simplest harmonic complexity of classical.


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## norman bates (Aug 18, 2010)

Piwikiwi said:


> The asymmetry of the major/minor scales are actually the things that make them interesting, the diminished(octatonic) and the whole tone scale are incredibly boring because it's all the same, there is no center and therefore they lack forward motion.


I guess this is a bit simplistic.


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## Piwikiwi (Apr 1, 2011)

norman bates said:


> I guess this is a bit simplistic.


No, I'm a (former) jazz musician myself and every jazz book has a warning with their entries on both of these scales that they must not be overused.


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## norman bates (Aug 18, 2010)

Piwikiwi said:


> No, I'm a (former) jazz musician myself and every jazz book has a warning with their entries on both of these scales that they must not be overused.


I think that everything should not be overused, what is important is the right context. Considering your experience with jazz, what about a standard like The peacocks? Isn't the second part of the melody based on the dimished scale? 





and still it is an absolutely gorgeous tune.


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## Piwikiwi (Apr 1, 2011)

norman bates said:


> I think that everything should not be overused, what is important is the right context. Considering your experience with jazz, what about a standard like The peacocks? Isn't the second part of the melody based on the dimished scale?
> 
> 
> 
> ...


What I mean is, you can write music based on only a major or minor scale but it is impossible to write interesting music on ONLY the diminished or whole tone scale. The fact that you say that a part of the melody is based on the whole tone scale but not the entire song.


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## Mahlerian (Nov 27, 2012)

Piwikiwi said:


> What I mean is, you can write music based on only a major or minor scale but it is impossible to write interesting music on ONLY the diminished or whole tone scale. The fact that you say that a part of the melody is based on the whole tone scale but not the entire song.


Very few things are based _entirely_ on the whole tone or octatonic scales. Except this movement:


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## millionrainbows (Jun 23, 2012)

Jobis said:


> As an amateur piano player I'm quite glad we stuck with just 12 tones, the idea of playing 17 or 19 TET music gives me the horrors!


...Or going in the other direction, staying within one key? Not a bad alternative, and good enough for Philip Glass and Terry Riley. It calms you right down.

BTW, the only reason other ET systems were devised, such as 17, 19, or 43, was to enable approximations of "just" intervals, so the "horror" you speak of would sound more consonant than our 12-tone ET, if used properly.

In addition, if these tunings ever came into use seriously, you'd probably be using the same 12-note keyboard (electric), and a computer program would be doing all the other work of alternating between notes and tunings.


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## millionrainbows (Jun 23, 2012)

Piwikiwi said:


> The asymmetry of the major/minor scales are actually the things that make them interesting, the diminished(octatonic) and the whole tone scale are incredibly boring because it's all the same, there is no center and therefore they lack forward motion.


That must mean you don't like Bartok.



Piwikiwi said:


> The whole tonal system of western music is based around harmony, Indian or gamelan music don't even come close to even the simplest harmonic complexity of classical.


Unfair comparison. That's becauseIndian and Balinese are melodic-based musics. An illogical comparison.


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## Cosmos (Jun 28, 2013)

If you said tonality is God, and now say tonality never really existed, then does this mean you're admitting to being an atheist? :lol:

Anyway, I love these theories. This is something about music makeup I never really thought of before


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## millionrainbows (Jun 23, 2012)

Piwikiwi said:


> No, I'm a (former) jazz musician myself and every jazz book has a warning with their entries on both of these scales that they must not be overused.


Too simplistic to be considered serious advice.

What about the use of diminished sonorities as extensions of V7 chords, transforming them into flat-nine dominants? That's been happening since Bach and Beethoven, and all over the place in jazz.

Why, just listen to Pat Martino solo over successive flat-nines and altered dominants:






Oh, somebody will come up with some excuse.

The point is, the minor third, and octatonic scale (diminished scale), and diminished seventh chords are all great contributors to the color of tonality, especially when used in dominant V7/9 chords.

Did you know? If you lower any tone of a diminished seventh chord, you get a dominant seventh chord. There are only 3 diminished sevenths, so that yields 3x4=all 12 dominant sevenths!


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## millionrainbows (Jun 23, 2012)

Cosmos said:


> If you said tonality is God, and now say tonality never really existed, then does this mean you're admitting to being an atheist? :lol:
> 
> Anyway, I love these theories. This is something about music makeup I never really thought of before


Thanks for the slack, Cosmos; Lord knows I need it. :lol:


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## millionrainbows (Jun 23, 2012)

Mahlerian said:


> Very few things are based _entirely_ on the whole tone or octatonic scales. Except this movement:


Listen to Beethoven's transformation of a diminished seventh into a dominant V7/9 at about 59 seconds.


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## Klavierspieler (Jul 16, 2011)

I'm still not quite sure what your point is, millionrainbows. You seem to be saying that tonality does not exist because it cannot be divided into perfectly consonant intervals, or maybe because there is simply nothing inherently tonal about our harmonic system (or something like that). I don't follow.


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## rrudolph (Sep 15, 2011)

The formation of scales and of the web of harmony is a product of artistic invention, and is in no way given by the natural structure or by the natural behaviour of our hearing, as used to be generally maintained hitherto. 
-Hermann Helmholtz, The Theory of Sound (1862)


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## BurningDesire (Jul 15, 2012)

No music ever existed. Everything is just a figment of my imagination. :3


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## Piwikiwi (Apr 1, 2011)

millionrainbows said:


> Too simplistic to be considered serious advice.
> 
> What about the use of diminished sonorities as extensions of V7 chords, transforming them into flat-nine dominants? That's been happening since Bach and Beethoven, and all over the place in jazz.
> 
> ...


I already knows all that stuff, that is jazz for dummies basically. BTW the altered scale is not diminished or whole tone, it's the 7th scale degree of a melodoc minor scale. I don't think that you ger my point though. I'm not talking about those two scales as wayd to spice up normally tonal lines, of course that works. I'm talking about using those scales as both a harmonic and melodic foundation for a piece.


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## SeptimalTritone (Jul 7, 2014)

millionrainbows said:


> The whole tone scale is an 6-tone based on the projection of the major second. The scale's interval content is M2s, M3s, and tritones. It repeats symmetrically; no matter which note you begin on, the resulting intervals are the same. It divides evenly at the tritone.
> 
> Tonality uses the 7-note diatonic scale, and its "dividing point" is the fifth.
> 
> ...


Okay so... I would be very careful because even the _diatonic_ scale has difficulties with nice just intonation. The just diatonic scale stacks the subdominant, tonic, and dominant triads up like this:

D
B
G
E
C
A
F

with all just major thirds (5/4) and minor thirds (6/5).

It turns out though that even this scale is problematic!!! If you want the Western style idea of a triad emerging from each scale tone, then this is _impossible_! You can have a just major (4-5-6) or minor (10-12-15) triad on every note except for B and D. Now, the chord on B is acceptable because it's a diminished chord, but the minor chord on D is _dissonant_ because it doesn't match with the notes F and A! This has to do with the difference between the greater whole tone (9/8) and lesser whole tone (10/9). For the G major chord, we want the D to be a _greater_ whole tone away from C, but for the D minor chord, we want the D to be a _lesser_ whole tone away from C! So we really can't even have circle of fifths progressions and diatonic functional harmony (i.e. a triad based on each scale note) with the just diatonic scale, and so some kind of temperament is _required_.

One option for the diatonic scale which extends well to chromaticism is to use quarter-comma meantone which flattens the fifth and circulates it up and down to produce the scale notes. Doing this fails to distinguish the greater whole tone and lesser whole tone, but... for functional harmony _that's exactly what we need_!

Another option is to use equal temperament which makes thirds sound somewhat noticeably out of tone but allows you to play in any chromatic key equally (unlike quarter-comma meantone where some keys are more equal than others).

Over the course of the common practice era, we gradually went from quarter-comma meantone to equal temperament as music became more and more chromatic. This makes complete sense: it would be bad for Schoenberg-style music to not treat all 12 notes the same from an intonation standpoint. But: no music can incorporate just triads on every scale note, and if in your opinion that means "tonality never existed" so be it, but to me it's a natural clever human thing to sacrifice perfect intonation for some kind of musical system.


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## ptr (Jan 22, 2013)

BurningDesire said:


> No music ever existed. Everything is just a figment of my imagination. :3


But it feels so real! Thanks for letting me be a part of Your imagination, it been a pleasure so far!

/ptr


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## millionrainbows (Jun 23, 2012)

Klavierspieler said:


> I'm still not quite sure what your point is, millionrainbows. You seem to be saying that tonality does not exist because it cannot be divided into perfectly consonant intervals...


Tonality is fashioned after a harmonic model; *one note* and its constituent harmonics, expressed as fractions or ratios in relation to that fundamental note.

Well, tonality does not "exist" as a *perfect* system, because those small-ratio consonances have been compromised. It works as a _practical _system, but *it is not ideal, or even "natural',* and uses many 'arbitrary' mathematical and numerical compromises.

The reason tonality has always been a struggle for consonance stems from the desire to *modulate* to other keys, away from "1".

*"Thou shalt have no other Gods before me."*

That means, the desire to modulate, to find _other_ "1"s, or new tonal centers, is a "polytheistic" idea. 12 keys, 12 Gods. 12 key centers. It represents the fall of Man, and his relentless desire to dominate and conquer.



Klavierspieler said:


> ...or maybe because there is simply nothing inherently tonal about our harmonic system (or something like that). I don't follow.


_To modulate is to stray from true tone-centric tonality, which is, and always has been, and forevermore shall be, "the Big Note."_

Tonality is fashioned after a harmonic model; one note and its constituent harmonics, expressed as fractions or ratios in relation to that fundamental note.


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## millionrainbows (Jun 23, 2012)

rrudolph said:


> The formation of scales and of the web of harmony is a product of artistic invention, and is in no way given by the natural structure or by the natural behaviour of our hearing, as used to be generally maintained hitherto.
> -Hermann Helmholtz, The Theory of Sound (1862)


That's true, I agree completely, and this reveals that the Western tonal system is not natural, or its "originating harmonic model" has strayed from the natural.


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## millionrainbows (Jun 23, 2012)

BurningDesire said:


> No music ever existed. Everything is just a figment of my imagination. :3


I'm sure that will come to pass.


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## millionrainbows (Jun 23, 2012)

Piwikiwi said:


> I already knows all that stuff, that is jazz for dummies basically. BTW I don't think that you ger my point though. I'm not talking about those two scales as wayd to spice up normally tonal lines, of course that works. I'm talking about using those scales as both a harmonic and melodic foundation for a piece.


Still, there is a diminished-seventh basis for all of this. To generalize octatonic diminished scales as being "boring and lacking forward direction" needs to be prefaced by the exact way you intend to use them.

Even so, I still disagree with the general put-down of octatonic scales, and my original point has been overlooked as well, so join the club of "Internet Discussions Where Nobody Listens."


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## millionrainbows (Jun 23, 2012)

SeptimalTritone said:


> ...no music can incorporate just triads on every scale note, and if in your opinion that means "tonality never existed" so be it...


It's not necessary for a triad to be on every note. That's a tonal idea.



SeptimalTritone said:


> ...but to me it's a natural clever human thing to sacrifice perfect intonation for some kind of musical system.


You mean "harmony," not system. Tonality grew out of the consequences of polyphony and its coincident sonorities.


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## SuperTonic (Jun 3, 2010)

The unspoken assumption of your argument is that tonality = just intonation, (by tonality I assume you are referring to common practice era tonality) which just doesn't make any sense to me, and it isn't supported by historical fact. CPE tonality didn't begin to develop untl western music started moving AWAY from just intonation and toward equal temperment. One of the defining aspects of CPE tonality is the ability to modulate between keys, which was highly limited by just intonation, but facilitated by equal temperment.
You can validly claim that just intonation and CPE tonality are not compatible with each other. The western tuning system had to adapt to make CPE tonality possible. However there is no logical support for the claim that tonality never existed based on those historical facts.


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## StevenOBrien (Jun 27, 2011)

Some compositions from 1555 by Nicola Vicentino using his 31-tone (as opposed to 12-tone) scale which I feel compelled to share:

http://www.mtosmt.org/issues/mto.14.20.2/wild_examples.php?id=13
http://www.mtosmt.org/issues/mto.14.20.2/wild_examples.php?id=17


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## millionrainbows (Jun 23, 2012)

SuperTonic said:


> The unspoken assumption of your argument is that tonality = just intonation...


No, that's not what I am implying. I'm pointing out that the 12-note chromatic scale was derived from the projection of the fifth (a supposed perfect 3:2); thus the circle of fifths. This is an *acoustically-based* idea.

But actually, the 12-note scale is an anomaly, an approximation, based on the attempt to close the octave after 12 cycles of 3:2 fifths.

Thus, "12" is the resulting mathematical result of this error or approximation; there is no acoustic ("tonal") reason for its existence, other than that it approximates fifths. The tonal system *wants* to be based on just fifths, but is not.



SuperTonic said:


> Common Practice Era tonality didn't begin to develop until western music started moving *AWAY from just intonation* and towards equal temperament...


Yes, away from a harmonically-based ideal towards an arbitrary mathematical system based on a 12-division of the octave.



SuperTonic said:


> You can validly claim that just intonation and CPE tonality are not compatible with each other. The western tuning system had to adapt to make CPE tonality possible.* However there is no logical support for the claim that tonality never existed based on those historical facts.*


Tonality never existed as it was intended to be; embodied by its generating ideal, which was supposedly acoustically and harmonically based.


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## millionrainbows (Jun 23, 2012)

StevenOBrien said:


> Some compositions from 1555 by Nicola Vicentino using his 31-tone (as opposed to 12-tone) scale which I feel compelled to share:
> 
> http://www.mtosmt.org/issues/mto.14.20.2/wild_examples.php?id=13
> http://www.mtosmt.org/issues/mto.14.20.2/wild_examples.php?id=17


Might I once again point out that all other equal octave divisions are used to approximate just intervals.


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## SuperTonic (Jun 3, 2010)

millionrainbows said:


> No, that's not what I am implying. I'm pointing out that the 12-note chromatic scale was derived from the projection of the fifth (a supposed perfect 3:2); thus the circle of fifths. This is an *acoustically-based* idea.
> 
> But actually, the 12-note scale is an anomaly, an approximation, based on the attempt to close the octave after 12 cycles of 3:2 fifths.
> 
> ...


Okay. So what? We took that 12 note approximation of a "perfect" intonation system (which was never mathematically possible anyway) and turned it into what is arguably the richest and most complex harmonic system known to the world. Regardless of whatever semantic game you want to play here, this tuning system has served us well over the centuries.


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## PetrB (Feb 28, 2012)

_____________________From_

*Tonality Is God*: Started by millionrainbows, Jul-20-2014

____________We Come -- Full-Circle -- To_

*Tonality Never Really Existed*: Started by millionrainbows, Aug-11-2014

____________Does this mean God never existed?_


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## xpangaeax (Oct 1, 2013)

Excellent topic. It's really great to go back and consider how all of the things that we take as fact are human constructs. Take time, for example. It's a system so imperfect that we have to compensate for it with "leap years." To bring it to music, we go by beats per minute for our tempi - but again a minute is only 1/60th of 1/24th of what *sort of* constitutes a full revolution of the Earth on its axis. I don't think the OP is trying to tell us that the basis for all of our Western music is false and not to be enjoyed because it's based on a false system. More like food for thought, really.

Anxiously awaiting the promised post on the Chinese system.


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## millionrainbows (Jun 23, 2012)

SuperTonic said:


> Okay. So what? We took that 12 note approximation of a "perfect" intonation system (which was never mathematically possible anyway) and turned it into what is arguably the richest and most complex harmonic system known to the world. Regardless of whatever semantic game you want to play here, this tuning system has served us well over the centuries.


Over the centuries? What tuning system? Do you mean equal temperament? That was slowly developed, and not achieved until 1917. For proof, refer to this book:

  


Historically, there has always been a struggle to achieve smooth sonorities, and all the mean-tone tunings were an attempt to recover the sonorous major third, which in ET is a full 14 cents sharp.

Remember, "12" is totally arbitrary; it is the result of stacking (projecting) 3:2 fifths, and that's where "12" came from. All Pythagoras accomplished was an approximation of the fifth, and the preservation of the octave.

What if Pythagoras had sought to preserve, instead of the fifth, say, the major third? It would have gone like this: see next post.


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## millionrainbows (Jun 23, 2012)

So, the "12 cycle" we take for granted is itself imperfect, the stacked circle of 3/2 fifths not really perfectly "reconnecting" with itself after 12 notes have been generated. Thus, Pythagorus coined the term "close enough for rock & roll."

What if we did the same thing with the major third, and used a stack of 'just' major thirds (5/4) to generate our cycle? Where will it stop, this Pythagoran Wheel of Fortune?

I decided to do it with cents. We know that an octave is 1200 cents, and that a 'just' major third is 14 cents flat of our equal-tempered third (400 cents), making the 'just' M3rd about 386 cents (386.3 is closer).

So, how many times do we have to "stack" this 5/4 major third spiral before it (apparently) comes back to its starting point, thus preserving our octave?? We're shooting for some multiple of 1200 cents, since that's the octave.

These are the octave multiples. We can "close" our projected spiral of major thirds somewhere in one of these octaves:

Okay, 1200 + 1200 is 2400, + 1200 is 3600, 4800, 6000, 7200, 9600, 10,800, 12,000, 13,200, 14,400, 15600, 16,800, 18,000, 19,200, 20,400, 21,600, 22,800, 24,000, 25200, 26400, 27,600, 28,800, 30,000, 31,200, 32,400, 33,600, 34,800, 36000,

Now, we start adding up the stacked (projected) 5/4s, or 386.3s:

That gives us 386.3, 772.6, 1158.9, 1545.2, 1931.5, 2317.8, 2704.1, 3090.4, 3476.7, 3863.0, 4249.3, 4635.6, 5021.9, 5408.2, 5794.5, 6180.8, 6567.1, 6953.4, 7339.7, 7726.0, 8112.3, 8498.6, 8884.9, 9271.2, 9657.5, 10043.8, 10430.1, 10816.4, 11202.7, 11589.0, 11975.3, 12361.6, 12747.9, 13134.2, 13520.5, 13906.8, 14293.1, 14679.4, 15065.7, 15452.0, 15838.3, 16224.6, 16610.9, 16997.2, 17383.5, 17769.98, 18156.1, 18542.4, 18928.7, 19315.0, 19701.3, 20087.6, 20473.9, 20860.2, 21246.5, 21632.8, 22019.1, 22405.4, 22791.7, 23178.0, 23564.3, 23950.6, 24336.9, 24723.2, 25109.5, 25495.8, 25882.1, 26268.4, 26654.7, 27041.0, 27427.3, 27813.6, 28199.9, 28586.2, 28972.5, 29358.8, 29745.1, 30131.4, 30517.7, 30904.0, 31290.3, 31676.6, 32062.9, 32449.2, 32835.5, 33221.8, 33608.1, *Wait! Bingo! 33,608.1 is almost equal to 33, 660: only 8.1 cents off!* I say, let's go for it, before our calculators run out of battery power.
So how many cycles of 5/4s is that? Let's see...33,608.1 divided by 386.3 is 87!

So our Pythagoran "major third" scale is 87 notes per octave!


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## millionrainbows (Jun 23, 2012)

PetrB said:


> _____________________From_
> 
> *Tonality Is God*: Started by millionrainbows, Jul-20-2014
> 
> ...


Blame it on science, The Enlightenment, mathematics, Newton, Einstein, pedophile priests, Galileo, Keppler, the liberal Democrats...but not me. Sorry, I can't take on the guilt of the world.


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## PetrB (Feb 28, 2012)

Klavierspieler said:


> I'm still not quite sure what your point is, millionrainbows. You seem to be saying that tonality does not exist because it cannot be divided into perfectly consonant intervals, or maybe because there is simply nothing inherently tonal about our harmonic system (or something like that). I don't follow.


_The deity = symmetry_... or some such. That's a very limited view, imho, and not near enough to satisfactorily arrive at that equation, but then again I'm no polymath cosmologist / philosopher / theologist / music theoritician / mathematician ;-)


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## millionrainbows (Jun 23, 2012)

xpangaeax said:


> Excellent topic. It's really great to go back and consider how all of the things that we take as fact are human constructs. Take time, for example. It's a system so imperfect that we have to compensate for it with "leap years." To bring it to music, we go by beats per minute for our tempi - but again a minute is only 1/60th of 1/24th of what *sort of* constitutes a full revolution of the Earth on its axis. I don't think the OP is trying to tell us that the basis for all of our Western music is false and not to be enjoyed because it's based on a false system. More like food for thought, really.
> 
> Anxiously awaiting the promised post on the Chinese system.


Oh, good, xpangaex! Are you Chinese? If so, groovy! Yes, I'm not advocating a totally "just" music system, because I like the change of key as much as anyone. However, with computers (see Wendy Carlos' Beauty In The Beast for examples) this is becoming a reality.

Okay, since you asked, I'll dig out the CD that has the info on the Chinese division of the octave.

Also, interestingly, there is another way to "divide" the octave, unlike Pythagoras' division of the string, and this is based on projecting larger divisions; used, I think, in constructing wind instruments. I will look up that info as well.

I'm so glad that everyone is open to discussion on this.


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## millionrainbows (Jun 23, 2012)

PetrB said:


> _The deity = symmetry_... or some such. that's a very limited view, imho, and not near enough to satisfactorily arrive at that equation, but then again I'm no polymath cosmologist / philosopher / theologist / musician / mathematician ;-)


But you've got ears, don't you?

The truth of the "drone" is self-evident...The Beatles discovered this, India has always known it, bluesmen do it, most folk music exemplifies it, and, I think, every musician with a good ear knows that you derived everything from the drone, or "1", or The Big Note (Zappa), or God...


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## millionrainbows (Jun 23, 2012)

.......ooooooooooommmmmmm.....


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## xpangaeax (Oct 1, 2013)

Not Chinese, but I am definitely interested. I do have an interest in Chinese history / art / music, and speak Mandarin so, it's totally relevant to my interests. Always trying to expand upon my musical knowledge too!


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## SeptimalTritone (Jul 7, 2014)

millionrainbows said:


> Blame it on science, The Enlightenment, mathematics, Newton, Einstein, pedophile priests, Galileo, Keppler, the liberal Democrats...but not me. Sorry, I can't take on the guilt of the world.


Did you just lump together _pedophile priests_ with some of the greatest physicists of old... and my favorite Korean member of this forum?!?

Joking aside, I think the Buddhists would consider God to be in more than just a single tone, or a pure just 4-5-6 triad. Indeed, God is in everything, from Palestrina to Mozart to Schoenberg to Messiaen, and any artwork that brings a heightened conscious alertness within the listener takes him or her closer to God. It does not have to be a single OM, and although a single OM is perhaps most effective at bringing stillness to the mind, one cannot dismiss more complex and dissonant sequences of notes as representing less than the "purity" of God.


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## millionrainbows (Jun 23, 2012)

SeptimalTritone said:


> Did you just lump together _pedophile priests_ with some of the greatest physicists of old... and my favorite Korean member of this forum?!?
> 
> Joking aside, I think the Buddhists would consider God to be in more than just a single tone, or a pure just 4-5-6 triad. Indeed, God is in everything, from Palestrina to Mozart to Schoenberg to Messiaen, and any artwork that brings a heightened conscious alertness within the listener takes him or her closer to God. It does not have to be a single OM, and although a single OM is perhaps most effective at bringing stillness to the mind, one cannot dismiss more complex and dissonant sequences of notes as representing less than the "purity" of God.


The short answer is "1". If you conceive "God", then for me that implies that God is the ultimate reference, to which all things are related. Sooner or later, you will deal with "1" or the cosmic singularity.

Thus, all just intervals, and all dissonances, expressed as ratios, are all related to "1" for their identity. 4534/7856 is a fraction, just like 3/2 is...only it's much more complicated and dissonant. The beauty of simple intervals is their...simplicity; and don't forget that this has a human dimension: our ears vibrate with waves, so these ratios are more than just numerical models or correllaries: they actually exist on our eardrums and in the air as physical vibrations.


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## millionrainbows (Jun 23, 2012)

This particular Chinese 5-tone division of the octave has other implications, just as Indian raga scales do: The five elements: wood, fire, earth, metal, and water; the five organs, liver, heart, spleen, lungs, and kidneys; these five organs are linked with the five viscera: gall bladder, small intestine, stomach, large intestine, and bladder; the five orifices: eyes, tongue, mouth, nose, and ears; the five emotions: anger, gaiety, uneasiness, melancholy, and fear; and so on.

I see it on the reverse of this album cover depicted as a circle:










Mine is volume 5, so I can't show it here. It's self-evident, though, and I extrapolated the notes (in cents) by studying the circle and its divisions.

The circle is divided firstly into 4 parts, by simply drawing 2 perpendicular (90) diameter lines. That's easy enough. Then, by drawing two lines across the circle, from two of the adjacent points of the 4 points, across, to one of the 4 large circle segments we initially derived, the quadrant is divided evenly, thus giving us another point, and 5 tones.

In cents, the first intervals, which divide the circle into fourths, would be, starting arbitrarily at the 12 o'clock point, zero, 300 cents, 600 cents, 900 cents, and back to "zero" at 1200 cents (an octave is 1200 cents).

The other fifth note, which we got by halving one of the 300-cent segments, would be, starting at zero, 150 cents.

This five note scale can be used "modally," starting on any note, and supposedly produces different healing effects, depending on the mode.

Here is the breakdown of the scale, in cents. All notes except one correspond exactly to ET notes, since this is basically a five-tone ET scale.

Zero............Let's call it "C"
150 cents....between a C# and D
300 cents....E flat, which is just like ours
600 cents....F sharp...ditto
900 cents....A...ditto

So, the scale is C-C#/D cusp-Eb-F#(Gb)-A.


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## science (Oct 14, 2010)

SeptimalTritone said:


> my favorite Korean member of this forum


I suspect that's me, and I'm flattered! But I'm as American as apple pie, and white as Yellowstone in the middle of winter. I only live and work in Seoul... my heart and home will always be where the Rockies meet the Great Plains (like this).


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## SeptimalTritone (Jul 7, 2014)

millionrainbows said:


> Here is the breakdown of the scale, in cents. All notes except one correspond exactly to ET notes, since this is basically a five-tone ET scale.
> 
> Zero............Let's call it "C"
> 150 cents....between a C# and D
> ...


Now that's interesting: it's pentatonic but not in the way we normally think of the pentatonic scale because it's totally equal tempered. I will have to check this out! Thanks.


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## Guest (Aug 15, 2014)

Try as I might, I'm really failing to muster up any semblance of interest in this thread.


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## KenOC (Mar 7, 2011)

arcaneholocaust said:


> Try as I might, I'm really failing to muster up any semblance of interest in this thread.


I think we need a separate "tonality" forum, just for these threads. Gotta think ahead! After all, there are infinite thread possibilities, as is becoming apparent...


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## Itullian (Aug 27, 2011)

arcaneholocaust said:


> Try as I might, I'm really failing to muster up any semblance of interest in this thread.


So don't post in it then.


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## Guest (Aug 15, 2014)

KenOC said:


> I think we need a separate "tonality" forum, just for these threads. Gotta think ahead! After all, there are infinite thread possibilities, as is becoming apparent...


With a subforum about fruitless philosophy with no relevance to a listening experience?


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## Guest (Aug 15, 2014)

Itullian said:


> So don't post in it then.


Oh if only we could post solely about things we like. Needless to say, I'm the least of your problems in that regard


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