# The Major Second Is Not Dissonant



## millionrainbows

C-D for example.

Haven't you ever heard this as a harmonic when a note is filtered on a synth? C-G-C-G-C-*D*-E-G-Bb-C. I can't believe anyone would question this. 
Also, any electric guitarist can coax this overtone series from any open string: C-G-C-G-C-*D*-E-G-Bb-C.
No difference tone, no amplification, I hear C-D as non-dissonant.

In chords, it is commonly used in pop songs as a second, right next to the triadic third, distinguished from a ninth. It's used to create a very smooth, rich, harmonic sound. 

If anyone insists that C-D or any major second is a dissonance, then they are more academic than I realized, and I am very disappointed. I suggest that they avoid 'diaphonic' music, like the Bulgarian Women's Choir.

With the advent of perfect equal temperament, Debussy obviously heard this as well; the modern piano tuned in ET creates a very consonant, colorful "sheen" of sound when major seconds are stacked, which Debussy obviously exploited in his use of whole-tone scales. It's very pleasing to the ear, and creates a dreamy sheet of sound. How could this interval, even when multiplied and stacked on itself, ever be called "dissonant?"

Also, more proof: C-D suggests a stack of perfect fifths, as in C-G-D.

As well, the M2 is in flatted seventh chords, next to the root, as in D7, where C is the flat seven. Mixolydian scales and seventh chords have always sounded more consonant than the major scale, with its ugly B-C and E-F. That's why untrained blues players, and trained jazz players favor seventh chords for blues progressions.

The M2 may be _called_ 'dissonant' in academic CP theory, but in reality, as a sound, it is _consonant._


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## Kjetil Heggelund

...but sometimes it really wants to go down to the tonic or up to the 3rd


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## millionrainbows

Kjetil Heggelund said:


> ...but sometimes it really wants to go down to the tonic or up to the 3rd


This proves nothing, harmonically. It's just a CP rule.

C-D doesn't have to "resolve" up or down, except by academic CP rules. It's perfectly acceptable _to the ear _as a ninth chord (C-E-G-Bb-D), or as a "major 2" chord (C-D-E-G-C).


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## Bwv 1080

millionrainbows said:


> or as a "major 2" chord (C-D-E-G-C).


the mu chord!
.........


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## Woodduck

Given your fondness for calling people who disagree with you "academics," I'll adopt a similar practice and suggest that the idea of this thread is a specimen of rationalization, for which the term "academic" might not be inappropriate, in the sense that it relies on some system of concepts rather than simple sensory experience.

From a non-"academic," purely sensory standpoint, we would say that a major second is _relatively _consonant or dissonant depending on what we're comparing it with. It's obviously less dissonant than a minor second, but it's also obviously more dissonant than a minor third. Dissonance, like other sensations - pain, pleasure, softness, hardness, smoothness, roughness, hot, cold - is relative. There are degrees of it. This is something we notice quite early in life, long before we're able to attend an "academy."

Consulting the harmonic series as evidence, as you like to do, we don't hear a major second as an overtone. D is the 9th member of the series over a fundamental C, is quite remote from C, and is generally not even audible (on my piano I hear nothing above the 7th partial, Bb, no matter how hard I strike the C in the bass). But even if we could hear it, we would not be hearing a major second. Play an actual major second - the D above the fundamental - and the complex, clashing overtones which would assail our ears would make the relative dissonance of the interval unmistakably clear.

It's actually amusing that after making the absolute statement that a major second is not dissonant, you begin citing musical contexts in which it's considered pleasant. Musical contexts? Pleasure? What are we talking about now? Do I misremember, or did you not recently denounce me as an "academic" in some earlier discussion for pointing out that the perception of dissonance is context-dependent? Yes, a major second can sound pleasant in certain musical contexts. So can any other interval. Pleasure is beside the point.


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## Johann Sebastian Bach

i suggest millionrainbows and Woodduck get a room together and try to procreate a real musician.

This argument is vacuous and perfectly placed for the polemicist and her/his prey.

Get in a choir and sing Gesualdo. You'll then learn music from the inside and know that this interval (and any interval) can be consonant or dissonant.

Context is everything (and I mean the context of real music, not the fakery you seem to deal in).


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## Woodduck

Johann Sebastian Bach said:


> *i suggest millionrainbows and Woodduck get a room together and try to procreate a real musician.*
> 
> This argument is vacuous and perfectly placed for the polemicist and her/his prey.
> 
> Get in a choir and sing Gesualdo. You'll then learn music from the inside and know that this interval (and any interval) can be consonant or dissonant.
> 
> *Context is everything* (and I mean the context of real music, not the fakery you seem to deal in).


Since you agree with me ("the perception of dissonance is context-dependent" - post 5, paragraph 4), why would you condemn me to a room with millionrainbows? What did I ever do to you?


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## Bwv 1080

All-interval 12 note chords are not necessarily dissonant in certain contexts


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## Woodduck

Bwv 1080 said:


> All-interval 12 note chords are not necessarily dissonant in certain contexts


One could produce such a chord by dropping a piano out a window. How dissonant it seems might depend on where you're standing on the sidewalk.


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## mikeh375

Timbre also has a bearing on how an interval is perceived. Two oboes at forte or more playing a maj2nd can be harsh depending on the surrounding music and register - in fact similar timbres (and especially strident ones) often increase the perception of dissonance. Tempering dissonance to taste and/or effect with instrumental colour is a skill hard won in orchestration.
To my ears, the maj2nd is not dissonant at all, but one has to acknowledge as Wooduck has said, that context matters greatly because that is where it is encountered.

Speaking of encounters, I'm no peeping Tom, but what room and where? I'll supply the popcorn...


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## millionrainbows

Major seconds are associated with small-number intervals. From WIK:
Major seconds can occur in at least two different frequency ratios:9:8 (about 203.9 cents) and 10:9 (about 182.4 cents). As you can see, the 9/8 interval is almost the same size as an equal tempered second (200 cents). It's only off by 3.9 cents. This is very close!

By contrast, our ET major third is 400 cents, and a "real" major third, in just intonation, corresponds to a pitch ratio of 5:4 or 386.31 cents; this 400 cent "third" is 13.69 cents _wider _than the 5:4 ratio! Ugly, ugly!

Also, note that there are TWO harmonics associated with the major second:


Origin of large and small seconds and thirds in harmonic series.

Clearly, the fifth and second are the preferred intervals in equal temperament; the major third (considered a "consonance" in CP theory) is NOT.


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## millionrainbows

Woodduck said:


> One could produce such a chord by dropping a piano out a window. How dissonant it seems might depend on where you're standing on the sidewalk.


I see The Who have been up to their old tricks...


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## millionrainbows

Johann Sebastian Bach said:


> i suggest millionrainbows and Woodduck get a room together and try to procreate a real musician.
> 
> This argument is vacuous and perfectly placed for the polemicist and her/his prey.
> 
> Get in a choir and sing Gesualdo. You'll then learn music from the inside and know that this interval (and any interval) can be consonant or dissonant.
> 
> Context is everything (and I mean the context of real music, not the fakery you seem to deal in).


I think you got it wrong as well; Woodduck seems to be in agreement with you concerning context.

I think the "context" argument is weak, especially since C-D, a major second, is a relatively close interval, and can be used in a stepwise melodic context. As such, the "resolution" or "tension" has more to do with the movement of voices, rather than harmonic tension.

As a harmonic entity, there is no question in my mind that it is consonant. This was proved in spades to me after hearing The Bulgarian Women's Choir.











__________________________

Also, listen to Billy Gibbon's use of the major second in his solo from _Sharp Dressed Man_ (at 1:54); we hear the _splendor and magnificence_ of the major second through a Marshall speaker cabinet:











Clearly, Gibbons is using the major second (b7-root) as a _harmonic _entity, not as a "melodic" procedure.


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## mikeh375

The context argument is not weak imv when you factor in timbre, dynamics and orchestration. In fact it is a deciding factor in the perception. I'm with you in that it's not a dissonance to modern ears, but context really does matter.


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## millionrainbows

mikeh375 said:


> The context argument is not weak imv when you factor in timbre, dynamics and orchestration. In fact it is a deciding factor in the perception. I'm with you in that it's not a dissonance to modern ears, but context really does matter.


You seem to be conflating the "voice/counterpoint" argument with the "harmonic" argument when you say "In fact it is a deciding factor in the perception."

Counterpoint resolution and tension of a major second in a melodic line is not so much based on _harmonic_ perception of the major second as it is a desire to reach a _goal of resolution,_ which is a consonant chord.

The major second is therefore seen as a linear "aberration" of a consonant chord, not as a harmonic entity unto itself. In this context, it remains a _linear_ excursion in the _melodic_ realm.

You even acknowledge this when you say "I'm with you in that it's not a dissonance to modern ears, but _context_ really does matter."

"Context" is not perceptual, it's cerebral; as result of counterpoint rules and considerations, not harmonic perception. This conclusion is bolstered by the existence of threads such as "*How can I make sense of all of these arbitrary voice-leading rules?", *where the "listening intuition/perception" is confounded by "rules" which seem to have no connection to the perception of the music. 
To CP academics, it's all brain, no ear.


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## mikeh375

I'm not conflating anything at all, methinks you are not seeing the wood for the trees because of your particular stance regarding CP and wanting to combat it. I offer you real world stuff for some balance.
Actually timbre impacts decisively on dissonance and can soften or exaggerate it. The timbral context is also a vehicle for perception, a visceral, physical one too, not cerebral and in this regard the colouring in of our dissonance has a decisive impact on its efficacy either way. Imagine c+d played on 2 muted trumpets at ff and then the same notes on 2 flutes at p. The difference is clear, the dissonance is less abrasive on the flutes. To complicate it further, 2 _different_ timbres can soften dissonance too in the right context because dissonance is sometimes harsher with similar timbres, but this aint Orchestration 101.

No I'm not thinking about CP at all, but you seem to be, even if only to denigrate it....how disappointing,...


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## millionrainbows

mikeh375 said:


> I'm not conflating anything at all, methinks you are not seeing the wood for the trees because of your particular stance regarding CP and wanting to combat it. I offer you real world stuff for a balance.
> Actually timbre impacts decisively on dissonance and can soften or exaggerate it. The timbral context is also a vehicle for perception, a visceral one too, not cerebral and in this regard and the colouring in of our dissonance has a decisive impact on its efficacy either way.
> No I'm not thinking about CP at all, but you seem to be, even if only to denigrate it....how disappointing,...


I've backed-up my assertions to a much greater degree than you have.
As far as opposition to CP practice, It's not that I am opposed to it simply because it is CP, but to the fact that CP is to a large extent arbitrary, and not based on visceral factors, but cerebral ones.

When you say "timbre impacts decisively on dissonance and can soften or exaggerate it," this is a matter of degree, and demonstrates that you do not see harmonic considerations as _separate_ from contrapuntal considerations.

The true nature of a major second cannot be "cajoled" towards dissonance or consonance by marginal, inessential factors such a timbre. It exists as a ratio, and as part of the harmonic series. Apparently you are not able to "abstract out" the essence of this interval. Your argument is too vague for me.


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## mikeh375

oh c'mon MR. Do you really think I "do not see harmonic considerations as separate from contrapuntal considerations'? Really? I've been doing music very well professionally for 30 odd years, I'm no fool and I'm most likely more qualified, able and experienced than you in every aspect of music making. I can assure you I can abstract out of the harmonic series a maj2nds essence, what you can't seem to do is live in the real world of music making and have a pleasant tone in your posts, instead posting damming assumptions that goad. And so yet again we are at loggerheads.

My posts about timbre don't chime with your agenda, I get that, but take it from a professional, timbral context matters for the composer and the end user when it comes to degrees of dissonance/consonance and their perception.


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## millionrainbows

mikeh375 said:


> ...what you can't seem to do is live in the real world of music making.


I think the ZZ Top/Billy Gibbons example is a very good indicator that I am, indeed, living in the "real world" of music, and that when I listen, no matter the source, I am listening intelligently.



> My posts about timbre don't chime with your agenda, I get that...


Okay.



> ...but take it from a professional, timbral context matters for the composer and the end user when it comes to degrees of dissonance/consonance and their perception.


You haven't specified anything in particular. All my examples bolster my argument, that a major second is harmonically consonant.

Anyway, _I thought all this was cleared up in an earlier thread,_ in which "consonance/dissonance" has two definitions, one for actual harmonic perception, and another for CP/academic/linear thinkers who see tension/resolution as defined by CP practice as being central.

I still think you are conflating these two opposing views.

If there's anything you should know about me, it's that I am a vertical/harmonic thinker, and I have posted several blogs about my views on this.

I think harmonic considerations ALWAYS take precedence over linear/time line considerations, because I see the former as primal and timeless, and the latter as based on time-based notions which are _based on_ and _derived_ from vertical factors, but which pan-out to be more cerebral, especially when filtered through the glass of CP tonality.


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## mikeh375

millionrainbows said:


> *I still think you are conflating these two opposing views*.


What, even though I've told you I'm not? Honestly? Think what you want, even the horses mouth isn't good enough for you apparently. Re read post 16 for a simple real world example, you might have missed it as it was an edit. If you had studied orchestration to a high level, you would I'm sure appreciate my valid slant on your OP.

Yes the interval is consonant to my ears too and all I need is my ears to affirm that. Enough said as I'm writing music at present...with I might add, some added dissonance in the harmony that although much more complicated than a maj2nd, (although that is included too), also sounds consonant to me...and no, CP is not in evidence anywhere apart from the common musical sense aspect.

I know about your vertical thinking, we've already done this, do keep up. I too am a vertical thinker which stems from my jazz guitar days (remember) with chord construction. My own harmonic theory was influenced by Hanson's involution theories and I regularly use synthetic scales which I like to think I've made up, but probably haven't. These combined with a strong background in CP harmony and counterpoint give me all I need to write freely. Please remember as it's boring typing out the same things again.


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## Woodduck

Arguments that certain sounds "ARE" consonant or dissonant in some Platonic essence are fundamentally absurd and vacuous. Are we talking about music at all on this forum? MUSIC IS AS MUSIC SOUNDS. A major second can sound consonant or dissonant, to varying degrees, in different syntactic contexts, played by different instruments and in different registers.

If we're not actually discussing music, but want to define consonance and dissonance in abstract physical terms, we have to draw a definitional line in order to say that a given interval is absolutely consonant or dissonant. If such a line is drawn, conversation can proceed rationally. Otherwise it's all just a pseudo-debate between Catholics and Protestants.

So which is it? Are we talking music or physics, and what is the operative - _operative,_ not sole - definition of consonance/dissonance?


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## Guest

Woodduck said:


> ...
> 
> So which is it? Are we talking music or physics, and what is the operative - _operative,_ not sole - definition of consonance/dissonance?


I don't see any conflict between a music and physics definition of consonance/dissonance. Intervals are consonant to the extent that their overtone series align, due to the way our ears work. The unison is maximally consonant, the octave, fifth, forth, major third, minor third, major second, etc, are progressively more dissonant. A dissonance can be more or less noticeable depending on the context. A dissonance can give character to an otherwise consonant harmony, or can add frisson when it resolves to something more consonant. Just as pure alcohol taste like poison, but adds just the right taste to a fine wine, beer or cocktail.

Weird that we are still talking about this.


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## Bwv 1080

Right so the M2 is a ‘dissonance’ because it is a tighter ratio than 6 of the 11 intervals (3,4,5,7,8,9). Its a spectrum and the M2 is on the dissonant half


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## Woodduck

Baron Scarpia said:


> I don't see any conflict between a music and physics definition of consonance/dissonance. Intervals are consonant to the extent that their overtone series align, due to the way our ears work.


That's only one way of defining dissonance.


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## millionrainbows

Bwv 1080 said:


> Right so the M2 is a 'dissonance' because it is a tighter ratio than 6 of the 11 intervals (3,4,5,7,8,9). Its a spectrum and the M2 is on the dissonant half


That may be true in just intonation, using ratios, but not so in ET. The ET major third (386.31 cents) is off 13.69 cents; more than the major second, at 203.9 cents (9:8).

Eleven intervals? 3 is eliminated as explained above, and 4 or 5 are eliminated (take your pick). The fourth is an inversion of the fifth, so that doesn't count as two intervals; there are only six: m2, M2, m3, M3, P4 and tritone.

I'm not sure what you mean by 7, 8, and 9.

Clearly, the fifth (fourth) and second are preferred intervals in equal temperament; the major third (considered a "consonance" in CP theory) is NOT.


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## millionrainbows

Woodduck said:


> That's only one way of defining dissonance.


You can't define a comparative term except as a ratio; dissonance and consonance are ratios, not quantities.

1/2 can mean half of anything: half of a million dollars or half of a dime. 
_
Ratios, and consonance/dissonance, are not quantities; they are relationships.
_
Therefore, consonance/dissonance cannot be "defined" or identified *as such* unless we use ratios. The smaller and simpler the ratio, the more consonant it is.

The subjective "context" argument is vague and un-Platonic.


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## millionrainbows

Woodduck said:


> Arguments that certain sounds "ARE" consonant or dissonant in some Platonic essence are fundamentally absurd and vacuous.


Yes, that is correct. They must be compared. You can't define an interval as "consonant" or "dissonant" unless you compare it to other intervals; dissonance and consonance are ratios, not quantities.

1/2 can mean half of anything: half of a million dollars or half of a dime. 
Therefore, an interval such as the major second cannot be "defined" or identified in terms of consonance/dissonance unless we use ratios. The smaller and simpler the ratio, the more consonant it is.

The major second (ideally a 9:8) is one of the more consonant of all the intervals, at 203.9 cents, only 3.9 sharp of the ET M2 of 200 cents.

That's already better than the major third, which is 4:5 (386.31 cents), off by 13.69 cents from the ET M3 of 400 cents.



> Are we talking about music at all on this forum? MUSIC IS AS MUSIC SOUNDS. A major second can sound consonant or dissonant, to varying degrees, in different syntactic contexts, played by different instruments and in different registers.


I disagree; intervals must be compared to each other. If the relative consonance of a M2 is "overcome" or "superseded" by a M3 in an ET composition, this cannot be based on actual "consonance/dissonance" as a ratio comparison; it is coming from some other quarter. If this is "keynote" comparison of tonality (D in relation to _the idea of C as a keynote, not an actual sound), _then you should be prepared to admit that this is also a "Platonic" idea. (No pun intended with the use of "Pla-*tonic*.")



> If we're not actually discussing music, but want to define consonance and dissonance in abstract physical terms, we have to draw a definitional line in order to say that a given interval is absolutely consonant or dissonant.


That's not possible, since consonance and dissonance are comparative terms; they do not denote one thing, but a relationship of degree.



> If such a line is drawn, conversation can proceed rationally. Otherwise it's all just a pseudo-debate between Catholics and Protestants. So which is it? Are we talking music or physics, and what is the operative - _operative,_ not sole - definition of consonance/dissonance?


Quadrivium: music is both physics and art.


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## millionrainbows

Woodduck said:


> It's actually amusing that after making the absolute statement that a major second is not dissonant, you begin citing musical contexts in which it's considered pleasant.


I did not make an "absolute" statement by saying that a M2 is not a dissonance, as CP theory considers it. I understand that consonance/dissonance are comparative terms, not absolutes.



> Musical contexts? Pleasure? What are we talking about now? Do I misremember, or did you not recently denounce me as an "academic" in some earlier discussion for pointing out that the perception of dissonance is context-dependent? Yes, a major second can sound pleasant in certain musical contexts. So can any other interval. Pleasure is beside the point.


The perception of dissonance is not dependent on any context which "considers" it as such, for systemic reasons such as CP tonality procedural practices.

I'm only interested in sounds as sounds, as harmonic entities, not as abstract components of a system.


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## Woodduck

Your "scientific" standard of acoustic consonance and dissonance is not a necessary standard, but merely the one you prefer. Using a different, obvious, and common standard, we find that the M3 not only occurs lower, and thus more audibly, in the overtone series than does the M2, but it predictably creates less beating (is "cleaner") when sounded, especially noticeable when the intervals are played in the lower register of the piano. Obviously the tuning system used will affect somewhat the sound of these intervals when played, but this doesn't change the relative consonance or dissonance of the pure intervals, which equal temperament approaches closely enough. We hear the M3 as a clear, natural, consonant component of a tone because we can often literally hear it when a tone is sounded, which is why it became a basic component of common practice tonality. We don't normally hear the M2 in the overtone series, unless the fundamental tone is deep and strong.

I'm not questioning that the M2 can have a pleasant sound (more or less, depending on other factors already mentioned).


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## Bwv 1080

millionrainbows said:


> That may be true in just intonation, using ratios, but not so in ET. The ET major third (386.31 cents) is off 13.69 cents; more than the major second, at 203.9 cents (9:8).
> 
> Eleven intervals? 3 is eliminated as explained above, and 4 or 5 are eliminated (take your pick). The fourth is an inversion of the fifth, so that doesn't count as two intervals; there are only six: m2, M2, m3, M3, P4 and tritone.
> 
> I'm not sure what you mean by 7, 8, and 9.
> 
> Clearly, the fifth (fourth) and second are preferred intervals in equal temperament; the major third (considered a "consonance" in CP theory) is NOT.


11 intervals excluding octave/unison and >octave

7 is P5th, 8 is minor 6th etc


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## millionrainbows

Bwv 1080 said:


> 11 intervals excluding octave/unison and >octave
> 
> 7 is P5th, 8 is minor 6th etc


Okay, you're going by semitones. Still, there are only 6 intervals if you exclude inversions: m2, M2, m3. M3, P4 and tritone. _The inversion of the tritone, which remains the same, is obvious proof of the redundancy of inversion in a tonal system._

Those translate to semitones as 1, 2, 3, 4, 5, and 6.

In tonality, each note is an interval in relation to the key note (C), and this can be reached from the "bottom" as in C-D, C-E, C-F, etc., or to the "top" C, as in G-C, A-C, or B-C.


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## millionrainbows

Woodduck said:


> Your "scientific" standard of acoustic consonance and dissonance is not a necessary standard, but merely the one you prefer.


My "scientific" method corresponds _exactly_ to what I hear. I'm only interested in intervals as they sound.




> Using a different, obvious, and common standard, we find that the M3 not only occurs lower, and thus more audibly, in the overtone series than does the M2, but it predictably creates less beating (is "cleaner") when sounded, especially noticeable when the intervals are played in the lower register of the piano. Obviously the tuning system used will affect somewhat the sound of these intervals when played, but *this doesn't change the relative consonance or dissonance of the pure intervals, *which equal temperament approaches closely enough.



I disagree; the ET major third, which is ideally 4:5 (386.31 cents), is off by 13.69 cents from the ET M3 of 400 cents. _My view is reinforced because all the mean-tone tuning schemes throughout history were attempts to correct this discrepancy.
_
Your justification using pure ratio comparisons is ironically a "platonic" attempt, something you criticized me for earlier.

The real "problem" is the Pythagorean method of dividing the octave into 12 notes by "stacking" fifths, which is the favored interval in this 12-division.


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## millionrainbows

I'm like Debussy in this regard.


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## Woodduck

millionrainbows said:


> My "scientific" method corresponds _exactly_ to what I hear. I'm only interested in intervals as they sound.


You say you hear a major 2nd as more consonant than a major 3rd. I hear the opposite. You think you're justifying your judgment by talking about "cents." I think I'm justifying my judgment by talking about the greater audibility of the major third in the overtones of a sounded pitch, and about the less audible beating, the greater clarity of the sound, when the intervals are sounded.

Obviously, my sole interest here is in "intervals as they sound." If this is also your perspective (which I doubt), you have no monopoly on it.



> the ET major third, which is ideally 4:5 (386.31 cents), is off by 13.69 cents from the ET M3 of 400 cents. My view is reinforced because all the mean-tone tuning schemes throughout history were attempts to correct this discrepancy.


The impurity of the ET major 3rd is slight enough that the sense of the interval as relatively consonant is not undermined. I think it's safe to assume that most people will hear it as corresponding to the interval clearly audible in the overtone series. Strike a bass C on the piano, listen to the Overtone E, then strike the E. The discrepancy will not be heard by most people.



> Your justification using pure ratio comparisons is ironically a "platonic" attempt, something you criticized me for earlier.


There's nothing "platonic" about it. You're the one talking about "ideal" or "perfect" quantities that most listeners' ears either can't hear or are indifferent to. Most listeners' ears easily identify the equal temperament major third as the satisfying consonance audible in the harmonic series. Would people prefer the pure third if they heard it? Not unlikely, but in practice it generally doesn't matter. I found your characterization of the ET M3 as "ugly, ugly" simply ridiculous. The sound of an organ or an orchestra playing a major triad in equal temperament - let's take the final B major chord of _Tristan und Isolde,_ which Richard Strauss found particularly beautiful - is satisfying and moving in itself, and not merely because it constitutes a resolution of foregoing harmonies. It's as if the whole harmonic series, an audible cosmos of sound generated by the root B, is resonating in our bodies. The effect of a similar chord using the second rather than the third above the root would not be the same, although it might afford its own sort of pleasure.



> The real "problem" is the Pythagorean method of dividing the octave into 12 notes by "stacking" fifths, which is the favored interval in this 12-division.


Talk about "platonic" - or "academic"! I think it's safe to say that no one listening to music experiences that "real problem."


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## Johann Sebastian Bach

OK millionrainbows and Woodduck - I may have been a bit harsh putting the two of you in a room together.

Forgive the tangent, but I don't visit TC very often, partly because I'm a working musician and partly because I can't stand the posturing of some of the posts on here. There's a subset of people who know very little about music but enjoy pretending that they're smart and, perhaps unkindly, I assumed you belonged to this set of polemicists. 

I was fortunate that my conducting professor when I was at music college introduced me to Gesualdo. Through him, I learnt that even the context of dissonance has little meaning. In order to come to this realisation, you need to get in a choir and SING his music. Only then do you really understand (this is partly because pitches shift with his harmony - i.e. a Bb in one chord may be sung sharper than a Bb in the next chord). Fortunately, the human voice isn't tied to keys, valves or frets.


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## Woodduck

Johann Sebastian Bach said:


> OK millionrainbows and Woodduck - I may have been a bit harsh putting the two of you in a room together.


In a way, we're ALL in a room together. Oh, that it should come to this! What WAS it all for?


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## millionrainbows

What WAS it all for?
It was for that major second that Billy Gibbons played in his solo on "Sharp Dressed Man."
That is a magical sound, especially through a Marshall 4x12 cabinet, which is known to produce "undertones" or difference tones, due to its resonant characteristics. Now,_ there's_ a context I can heartily endorse.


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## Bwv 1080

millionrainbows said:


> That is a magical sound, especially through a Marshall 4x12 cabinet, which is known to produce "undertones" or difference tones, due to its resonant characteristics. Now,_ there's_ a context I can heartily endorse.




yes, magical because its dissonant, would be boring if it wasnt


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## millionrainbows

Bwv 1080 said:


> yes, magical because its dissonant, would be boring if it wasnt


It's dissonant? Compared to what? Not a minor second.

Yes, it's dissonant compared to a unison. Unless the unison is more than 6 cents off....but a major second has much more leeway than a unison. It can be a 9:8 (203.9 cents) or a 10:9 (182.4 cents).
The major second was historically considered one of the most dissonant intervals of the diatonic scale, although much 20th-century music saw it reimagined as a consonance.

Phhhtt!


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## Woodduck

millionrainbows said:


> Yes, it's dissonant compared to a unison. Unless the unison is more than 6 cents off....but a major second has much more leeway than a unison. It can be a 9:8 (203.9 cents) or a 10:9 (182.4 cents).
> The major second was historically considered one of the most dissonant intervals of the diatonic scale, although much 20th-century music saw it reimagined as a consonance.


Back in post #32 you made a point of saying that "the ET major third, which is ideally 4:5 (386.31 cents), is off by 13.69 cents from the ET M3 of 400 cents." Here you say that a major second can vary by as much as 21.5 cents. I don't know what any of this is intended to prove, though it might suggest that the second has a greater chance of sounding dissonant than the third. It seems to me that approaching the question of consonance and dissonance through the vagaries of tuning systems is basically unhelpful. And now, when you add to the above that the major second is dissonant relative to something else, and that it was considered one of the most dissonant intervals until it was "reimagined", aren't you undercutting any argument for the interval as being definitely consonant, and aren't you supporting the views advanced by others that its consonance or dissonance are contextual? Given all these variables, what sense is left in the proposition, "the major second is not dissonant"? Is it consonant only because you've "reimagined" it that way?


----------



## millionrainbows

Woodduck said:


> Back in post #32 you made a point of saying that "the ET major third, which is ideally 4:5 (386.31 cents), is off by 13.69 cents from the ET M3 of 400 cents." Here you say that a major second can vary by as much as 21.5 cents. I don't know what any of this is intended to prove, though it might suggest that the second has a greater chance of sounding dissonant than the third. It seems to me that approaching the question of consonance and dissonance through the vagaries of tuning systems is basically unhelpful. And now, when you add to the above that the major second is dissonant relative to something else, and that it was considered one of the most dissonant intervals until it was "reimagined", aren't you undercutting any argument for the interval as being definitely consonant, and aren't you supporting the views advanced by others that its consonance or dissonance are contextual? Given all these variables, what sense is left in the proposition, "the major second is not dissonant"? Is it consonant only because you've "reimagined" it that way?


I'm interested in intervals as _harmonic entities,_ which does not have to "tie" them to being consonant or dissonant.

It might be helpful to refer to the flatted seventh, or minor seventh (C-Bb), the inversion of the major second, which can also appear as a major second (Bb-C) using the upper C. It's used ubiquitously in dominant seventh chords. In Western CP music, the seventh is tension-producing, and this tension needs resolution.

However, there is also a septimal (7:4) "harmonic seventh" which is flatter (969 cents) than the ET minor seventh (1000 cents) by a good 30 cents, which is quite noticeable.

*Our ET seventh is derived from the "just" minor seventh (9:5 or 1018 cents).*

From WIK, we read:

The harmonic seventh arises from the harmonic series as the interval between the fourth harmonic (second octave of the fundamental) and the seventh harmonic; in that octave, harmonics 4, 5, 6, and 7 constitute a purely consonant major chord with added seventh (root position)...

The harmonic seventh is also expected from barbershop quartet singers when they tune dominant seventh chords (harmonic seventh chord), and is considered an essential aspect of the barbershop style.

It was used in organs as well:

In ¼ comma meantone tuning, standard in the Baroque and earlier, the augmented sixth is 965.78 cents - only 3 cents below 7:4, well within normal tuning error and vibrato. Pipe organs were the last fixed-tuning instrument to adopt equal temperament. With the transition of organ tuning from meantone to equal-temperament in the late 19th and early 20th centuries the formerly harmonic Gmaj7♭ and B♭maj7♭ became "lost chords" (among other chords).
The harmonic seventh differs from the Pythagorean augmented sixth by 225/224 (7.71 cents), or about ⅓ comma. The harmonic seventh note is about ⅓ semitone (≈ 31 cents) flatter than an equal-tempered minor seventh. *When this flatter seventh is used, the dominant seventh chord's "need to resolve" down a fifth is weak or non-existent. This chord is often used on the tonic (written as I7) and functions as a "fully resolved" final chord.

*So this flatter seventh, which is used in barbershop quartet harmony, has no need to "resolve" and renders the dominant seventh chord's "need to resolve" down a fifth to become _weak or non-existent. That's because it is heard as a consonance.

_This is where the *I7*-IV7-V7 of blues music came from; Africans originally used instruments tuned this way. Thus, the WIK reference to a I chord makes obvious sense: *This chord is often used on the tonic (written as I7) and functions as a "fully resolved" final chord.
**
*The minor seventh, appearing as its inversion, a major second, is indeed a consonance, especially when it is functioning as a flatted seventh against an upper root. This is not context; this is the harmonic truth of intervals.

This also considerably weakens the "context" argument that a major second, as a C-D in the lower range (not as a flatted seventh) is a "dissonance" in any harmonic sense, if in this context the D is not a chord tone. It can only be considered as "needing to resolve" for contrapuntal reasons, as a stepwise melodic movement, not harmonic in nature.

This "need to resolve" is based on movement of a line _as a logical expectation of melodic movement in time;_ NOT as an instantaneous "harmonic" phenomenon.

This "need to resolve" is thus based on expectation (through time) of the _expected or predicted movement_ of a melody line. That's because we are designed to predict the movement of prey.

If in C-D the chord is a D minor seventh (ii 7), then the harmonic factor kicks in, and the C-D is no longer dissonant.

Of course, we need to remember that a major second or its inversion, the minor seventh, is used in ET Western music _based on a "just" seventh._  A "just" minor seventh, has an intonation ratio of 9:5 (about 1018 cents).

That large, sharp seventh needs resolving, down, towards harmonic truth, towards the harmonic stability of the harmonic seventh.

Is my idea flawed? No; _the system is flawed._

Thus, we see in our 12-division Pythagorean system_ the fifth_ as the favored interval, with thirds and sevenths both suffering, forcing us to simply ignore the major third, and to conflate the harmonic seventh with a sharp, ugly "just" seventh derived from Pythagorean procedures.


----------



## Bwv 1080

Is this 'spicy'?


----------



## BabyGiraffe

16/9 - Pythagorean minor seventh
9/5 - just minor seventh 
and 7/4 - octave reduced seventh harmonic 
are clearly distinct ratios - meantone temperament maps together in different equal temperaments that support meantone pythagorean and just minor version. Fifths in meantone are flatter than just - 12 equal is actually the sharpest meantone tuning of all of them.
In non-meantone systems we can find mapping of 16/9 and 7/4 together, this is a septimal pythagorean tuning - 22 and 27 equal are decent for it - we get sharper than just intonation perfect fifths. (One strangeness of any pythagorean tuning - close to just intonation major thirds are actually diminished fourths, wow. The difference between JI major third and pythagorean diminished fourth is called schisma - it's a comma that even 53 equal - the most accurate small 5 and 3 limit system - gets rid of and closes the circle of 53 fifths. The next more accurate fifth comes after we go into equal temperaments where schisma becomes a step, that's too accurate to be even theoretically useful.)

12 equal's version is closest to 16/9, which is a characteristic dissonance used in dominant seventh chords even when playing in just intonation.

Here are all octave ratios that are more consonant than 9/8, if we are concerned about beating.

3/2 perfect fifth
4/3 perfect fourth
5/3 major sixth, BP sixth
5/4 major third
6/5 minor third
7/4 harmonic seventh
7/5 septimal tritone
7/6 septimal minor third
8/5 minor sixth
8/7 septimal whole tone
9/5 just minor seventh
9/7 septimal major third (this one sounds to me like a dissonance, honestly)
9/8 major whole tone !!!

9/4, 9/2 and 9/1 will blend way better in a harmonic texture than transposed in octave versions of 8/7 or 10/9 - the other choices that million offers for major second.

All this is facts from basic acoustics.
Being exposed to these and culturally accepting their sound is another fact.


----------



## millionrainbows

Is this dissonant?


----------



## BabyGiraffe

Here is one great "jazzy" chord that doesn't sound dissonant- 4:5:7:9 = 1-5/4-7/4-9/4 - C-E-Bb*- D(octave higher)


----------



## millionrainbows

BabyGiraffe said:


> Fifths in meantone are flatter than just - *12 equal is actually the sharpest meantone tuning* of all of them.


Fifths are 2 cents *flat* in ET; ET is not "meantone;" what are you trying to say?



> Here are all octave ratios that are more consonant than 9/8, if we are concerned about beating.
> 
> 3/2 perfect fifth
> 4/3 perfect fourth
> 5/3 major sixth, BP sixth
> 5/4 major third
> 6/5 minor third
> 7/4 harmonic seventh
> 7/5 septimal tritone
> 7/6 septimal minor third
> 8/5 minor sixth
> 8/7 septimal whole tone
> 9/5 just minor seventh
> 9/7 septimal major third (this one sounds to me like a dissonance, honestly)
> 9/8 major whole tone !!!
> 
> 9/4, 9/2 and 9/1 will blend way better in a harmonic texture than transposed in octave versions of 8/7 or 10/9 - the other choices that million offers for major second.


I didn't "offer" any particular M2. What are you trying to say I'm saying, or do I not know? :lol:


----------



## Bwv 1080

BabyGiraffe said:


> Here is one great "jazzy" chord that doesn't sound dissonant- 4:5:7:9 = 1-5/4-7/4-9/4 - C-E-Bb*- D(octave higher)


ok dom 9th chords aren't dissonant?


----------



## Larkenfield

millionrainbows said:


> This proves nothing, harmonically. It's just a CP rule.
> 
> C-D doesn't have to "resolve" up or down, except by academic CP rules. It's perfectly acceptable _to the ear _as a ninth chord (C-E-G-Bb-D), or as a "major 2" chord (C-D-E-G-C).


Look. I believe you just don't like the thought of rules, period, because you may not understand the principles behind them, perhaps because you've never taken them seriously to begin with and would rather fly by the seat of your pants. Rules or principles of composition seem academic, inhibiting or restrictive to rebel against even though composers such as Haydn, Mozart, and Beethoven used them-and that's why most theory teachers teach what they used as a starting point and mental discipline in understanding harmony and voice leading... I don't admire that rebellious outlook until there's some genuine understanding of some of the basic principles, including the ability to use them creatively, because I see too much wishful thinking about some of the fundamentals of music. So the subject becomes a mess... I believe it's truly necessary to define what era of music you're talking about because if one is going to talk rules or principles that were followed at the time-what was consider good harmony and voice leading changed from one era to another. In the classical era, the D would not be left hanging or unresolved and under most (all) circumstances would resolve to the tonic, the major or minor third, or the 5th ( C, E or Eb, or G). In the classical era, a work would not be expected to end on a 7th or 9th chord, would it? The example D is not necessary a dissonance but was generally considered to be unstable and in need of being resolved to a consonant tone. But the rules or principles change and evolved when the Romantic and Modern eras came in and there were different thoughts on what the stable and unstable tones were that needed resolution... In modern classical or jazz harmony, all kinds of altered chords are permissible because the ears were ready for a change. Unlike the classical era, one could end a composition on a Major 7th chord with or without a 9th. Modern ears have adjusted and the Major 7th is no longer shocking and didn't need to be resolved to the C, and the D could be used without it being resolved because it added fullness and richness to the chord... But you have to be clear about what era of music you're talking about and that's usually left out and leads to a confusing mess regarding music theory... There's also a difference between a dissonance, sharply clashing tones (such as a minor second C to C# or Db interval) and a major second interval (C-D) where there's a _tension_ that may be considered unstable and simply seeks to be resolved. But it truly depends upon the era one is referring to and I believe that learning some of the fundamental principles that might have been used by Bach, Mozart and Beethoven should, under most normal circumstances,be encouraged because it can sharpen and discipline the lazy mind which thinks that one can essentially rely solely upon his ears rather than learning something that might actually be useful regarding the basic understanding of harmony and voice leading. Not everyone has the ears that Debussy had and can break the rules and have the music work. Yet the understanding of the principles (or rules) is too often dismissed without even knowing the knowledge or talent level of the student who might be struggling or rebelling against them. The learning of such principles might be the best thing in the world for them at this point in their studies and give them something to rebel against knowingly or consciously later. Just because Debussy broke the conventional rules at the time doesn't mean that he didn't know them. It's known that he studied harmony with César Franck though he usually rebelled against those teachings. But then, Debussy was a genius and heard music in his head that didn't match Franck's teachings and so he eventually went his own way.


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## millionrainbows

Larkenfield said:


> Look. I believe you just don't like the thought of rules, period, because you may not understand the principles behind them, perhaps because you've...etc.


Is there any "issue" or idea about music, or an opinion that you have about some aspect of _music_ that compels you to discuss it passionately? You need to focus on that, not me.


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## BabyGiraffe

millionrainbows said:


> Fifths are 2 cents *flat* in ET; ET is not "meantone;" what are you trying to say?


12 ET is 1/11 meantone. 
Meantone means that 81/80 is tempered. So 12 equal is meantone. 
So, the mapping is something like 7 equal, 12 equal, 19 equal, 26, 31, 43 and many others. Out of these 7 and 26 are very distorted compared to just intonation.
In non-meantone D 10/9 and D 9/8 are separate pitches.

Here is 41 equal:
steps: pitch
33: 965.854 cents 
34: 995.122 cents 
35: 1024.390 cents

Here is 46 equal:

37: 965.217 cents 
38: 991.304 cents 
39: 1017.391 cents

here is 53 equal:

43: 973.585 cents 
44: 996.226 cents 
45: 1018.868 cents

These 3 are non-meantone, but also non-septimal pythagorean (where 16/9 and 7/4 would be mapped to one step), so in practice we have a choice of 3 slightly different "dominant" chords.

Bwv 1080

"ok dom 9th chords aren't dissonant? "

They shouldn't be in close to just (septimal) tuning, but in this case there is no fifth. There is noticeable difference in texture - it is way less tense.


----------



## millionrainbows

BabyGiraffe said:


> 12 ET is 1/11 meantone.
> Meantone means that 81/80 is tempered. So 12 equal is meantone.
> So, the mapping is something like 7 equal, 12 equal, 19 equal, 26, 31, 43 and many others. Out of these 7 and 26 are very distorted compared to just intonation.
> In non-meantone D 10/9 and D 9/8 are separate pitches.
> 
> Here is 41 equal:
> steps: pitch
> 33: 965.854 cents
> 34: 995.122 cents
> 35: 1024.390 cents
> 
> Here is 46 equal:
> 
> 37: 965.217 cents
> 38: 991.304 cents
> 39: 1017.391 cents
> 
> here is 53 equal:
> 
> 43: 973.585 cents
> 44: 996.226 cents
> 45: 1018.868 cents
> 
> These 3 are non-meantone, but also non-septimal pythagorean (where 16/9 and 7/4 would be mapped to one step), so in practice we have a choice of 3 slightly different "dominant" chords.
> 
> Bwv 1080
> 
> "ok dom 9th chords aren't dissonant? "
> 
> They shouldn't be in close to just (septimal) tuning, but in this case there is no fifth. There is noticeable difference in texture - it is way less tense.


I see what you're trying to say, but it's not accurate. According to WIK:

Meantone temperaments are constructed the same way as Pythagorean tuning, as a stack of equal fifths, but in meantone each fifth is narrow compared to the perfect fifth of ratio 3:2.

Also,

Equal temperament, obtained by making all semitones the same size, each equal to one-twelfth of an octave (with ratio the 12th root of 2 to one (12√2:1), narrows the fifths by about 2 cents or 1/12 of a Pythagorean comma, and produces thirds that are only slightly better than in Pythagorean tuning. *Equal temperament is roughly the same as 1/11 comma meantone tuning*.

So roughly, you are kind of right...sorta.


----------



## BabyGiraffe

millionrainbows said:


> I see what you're trying to say, but it's not accurate. According to WIK:
> 
> Meantone temperaments are constructed the same way as Pythagorean tuning, as a stack of equal fifths, but in meantone each fifth is narrow compared to the perfect fifth of ratio 3:2.
> 
> Also,
> 
> Equal temperament, obtained by making all semitones the same size, each equal to one-twelfth of an octave (with ratio the 12th root of 2 to one (12√2:1), narrows the fifths by about 2 cents or 1/12 of a Pythagorean comma, and produces thirds that are only slightly better than in Pythagorean tuning. *Equal temperament is roughly the same as 1/11 comma meantone tuning*.
> 
> So roughly, you are kind of right...sorta.


Man, _*mean*_tone means (forgive me this pun, wow) that instead of the two types of simple "D" that exist in 5-limit just intonation we use their average.
None of equal temperaments is exactly x/y comma meantone/pythagorean/diaschismic/septimal or whatever, because these also have infinite pitches, but in practice they are, because the difference is super small.
Noone cares if you use 699.(and something) for 1/11 meantone or 697.(and something) for 1/4 meantone, because in practice these two sound and give respectively 12 and 31 equal and the small difference is a fraction of the cent. Noone cares about irrational numbers that give infinite pitch gamuts, because if we wanted infinite number of pitches, we would have been sticking to just intonationl!!!


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## BabyGiraffe

31 equal (aka 1/4 comma meantone) is maybe important, because the geometric mean of 5/4 (major third) is for all practical purposes the "D" note in 31.
Here is the approximation of it:
" 31: 5 5 21 N M DE S SD: 0.5055 c. M:-0.7831 c. 
56: 9 9 38 N M DE S SD: 0.3869 c. M: 0.5994 c. 
87: 14 14 59 N M DE S SD: 0.0690 c. M: 0.1068 c. 
205: 33 33 139 N M DE S SD: 0.0179 c. M:-0.0277 c. 
292: 47 47 198 N M DE S SD: 0.0080 c. M: 0.0123 c. 
497: 80 80 337 N M DE S SD: 0.0027 c. M:-0.0042 c. 
789: 127 127 535 N M DE S SD: 0.0012 c. M: 0.0019 c. 
1286: 207 207 872 N M DE S SD: 0.0003 c. M:-0.0004 c. 
"


----------



## millionrainbows

BabyGiraffe said:


> Man, _*mean*_tone means (forgive me this pun, wow) that instead of the two types of simple "D" that exist in 5-limit just intonation we use their average.
> None of equal temperaments is exactly x/y comma meantone/pythagorean/diaschismic/septimal or whatever, because these also have infinite pitches, but in practice they are, because the difference is super small.


Then I think it is misleading to say that our 12-note ET is a "meantone" temperament; it is an "equal" temperament, especially now that we have frequency meters which can ensure that our ET is spot-on accurate.



> *No one cares *if you use 699.(and something) for 1/11 meantone or 697.(and something) for 1/4 meantone, because in practice these two sound and give respectively 12 and 31 equal and the small difference is a fraction of the cent. No one cares about irrational numbers that give infinite pitch gamuts, because if we wanted infinite number of pitches, we would have been sticking to just intonation.


In practical terms, probably not; but let's get our terms correct, at least.

I'm just saying that you are using this inexactitude for your own license in calling our 12-note ET a "meantone" temperament. This is inaccurate, and misleading.


----------



## millionrainbows

BabyGiraffe said:


> 31 equal (aka 1/4 comma meantone) is maybe important, because the geometric mean of 5/4 (major third) is for all practical purposes the "D" note in 31.
> Here is the approximation of it:
> " 31: 5 5 21 N M DE S SD: 0.5055 c. M:-0.7831 c.
> 56: 9 9 38 N M DE S SD: 0.3869 c. M: 0.5994 c.
> 87: 14 14 59 N M DE S SD: 0.0690 c. M: 0.1068 c.
> 205: 33 33 139 N M DE S SD: 0.0179 c. M:-0.0277 c.
> 292: 47 47 198 N M DE S SD: 0.0080 c. M: 0.0123 c.
> 497: 80 80 337 N M DE S SD: 0.0027 c. M:-0.0042 c.
> 789: 127 127 535 N M DE S SD: 0.0012 c. M: 0.0019 c.
> 1286: 207 207 872 N M DE S SD: 0.0003 c. M:-0.0004 c.
> "


If you want anyone to really get what you are trying to say, you need to take more time with your posts and identify some of these numbers. Are the numbers on the far left equal octave divisions?


----------



## BabyGiraffe

" I'm just saying that you are using this inexactitude for your own license in calling our 12-note ET a "meantone" temperament. This is inaccurate, and misleading. "

If it follow meantone mapping, IT IS MEANTONE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

You obviously have a problem with accepting that 12 edo is meantone - if it wasn't, standard chord progressions wouldn't work at all, requiring enharmonic modulation aside from the few basic chord chord changes in the 5-limit tonality diamond (like most neo-riemannian chord changes which work only because of tempered commas, of course, in other equal temperaments we have other neo-riemannian progressions)... 
Idk, man, I wrote a long post, explaining plenty of stuff but the damn forum/server crashed and all is lost now. I can recommend you Barbour/xenharmonic wikipedia/tonalsoft encylopedia/even reading more carefully standard wikipedia or taking private lessons by someone versed in tuning theory. I have no energy anymore for forums.
Farewell.


----------



## millionrainbows

BabyGiraffe said:


> " I'm just saying that you are using this inexactitude for your own license in calling our 12-note ET a "meantone" temperament. This is inaccurate, and misleading. "
> 
> If it follow meantone mapping, IT IS MEANTONE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!


It doesn't follow meantone mapping exactly, so don't place ET, an "equal temperament," in the "meantone" category.



> You obviously have a problem with accepting that 12 edo is meantone - if it wasn't, standard chord progressions wouldn't work at all, requiring enharmonic modulation aside from the few basic chord chord changes in the 5-limit tonality diamond (like most neo-riemannian chord changes which work only because of tempered commas, of course, in other equal temperaments we have other neo-riemannian progressions)...
> Idk, man, I wrote a long post, explaining plenty of stuff but the damn forum/server crashed and all is lost now. I can recommend you Barbour/xenharmonic wikipedia/tonalsoft encylopedia/even reading more carefully standard wikipedia or taking private lessons by someone versed in tuning theory. I have no energy anymore for forums.
> Farewell.


You should get with a really good editor, and write a book.


----------



## millionrainbows

BabyGiraffe said:


> Idk, man, I wrote a long post, explaining plenty of stuff but the damn forum/server crashed and all is lost now.


Some advice: always copy your writing before you post it. As long as you're at it, paste it into your e-mail and save it as a draft.

Sometimes a post will take a long time to write, and the server will "time out," making it necessary to re-log-in.

Also, it may be possible that a lengthy post might raise some sort of a red flag to the mods, who may try to make it impossible to post. Just make sure you copy all your work, or it may vanish.


----------



## hammeredklavier

The drama in this thread is actually funny :lol:



millionrainbows said:


> then they are more academic than I realized, and I am very disappointed.





Woodduck said:


> why would you condemn me to a room with millionrainbows?


The choice of words in the context is funny :lol: 
not just "put", but "condemn".



Woodduck said:


> What did I ever do to you?


_"What did I ever do to you??? Why would you *condemn* me to such misery???"_



mikeh375 said:


> oh c'mon MR.


I mistakenly read it at first as "oh come on, MISTER." :lol:



mikeh375 said:


> what you can't seem to do is live in the real world of music making and have a pleasant tone in your posts, instead posting damming assumptions that goad.


MR sure is skillful in frustrating people with constant unpleasant dissonances in his posts :lol:


----------



## EdwardBast

hammeredklavier said:


> MR sure is skillful in frustrating people with constant unpleasant dissonances in his posts :lol:


Talk about the rabbit yelling big-ears!


----------



## millionrainbows

hammeredklavier said:


> The drama in this thread is actually funny :lol:The choice of words in the context is funny :lol:
> not just "put", but "condemn"._"What did I ever do to you??? Why would you *condemn* me to such misery???"_I mistakenly read it at first as "oh come on, MISTER." :lol:MR sure is skillful in frustrating people with constant unpleasant dissonances in his posts :lol:


Forsooth! Methinks the clavier is hammered again!


----------



## MAXSWAGGER

The context determines the sound.


----------



## millionrainbows

MAXSWAGGER said:


> The context determines the sound.


Contexts are ideas, cerebral. Sound is sound. I'm sure John Cage would be offended by this.

Most dissonant intervals to most consonant intervals, within one octave:
1. minor seventh (C-Bb) 9:16
2. major seventh (C-B) 8:15
3. major second (C-D) 8:9
4. minor sixth (C-Ab) 5:8
5. minor third (C-Eb) 5:6
6. major third (C-E) 4:5
7. major sixth (C-A) 3:5
8. perfect fourth (C-F) 3:4
9. perfect fifth (C-G) 2:3
10. octave (C-C') 1:2
11. unison (C-C) 1:1

The steps of our tonal scales, and the "functions" of the chords built thereon, are the direct result of interval ratios, all in relation to a "keynote" or unity of 1; the intervals not only have a dissonant/consonant quality determined by their ratio, but also are given a specific scale degree (function) and place in relation to "1" or the Tonic. This is where all "linear function" originated, and is still manifest as ratios (intervals), which are at the same time, physical harmonic phenomena.


----------



## robin4

millionrainbows said:


> Contexts are ideas, cerebral. Sound is sound. I'm sure John Cage would be offended by this.
> 
> Most dissonant intervals to most consonant intervals, within one octave:
> 
> 1. minor seventh (C-Bb) 9:16
> 2. major seventh (C-B) 8:15
> 3. major second (C-D) 8:9
> 4. minor sixth (C-Ab) 5:8
> 5. minor third (C-Eb) 5:6
> 6. major third (C-E) 4:5
> 7. major sixth (C-A) 3:5
> 8. perfect fourth (C-F) 3:4
> 9. perfect fifth (C-G) 2:3
> 10. octave (C-C') 1:2
> 11. unison (C-C) 1:1
> 
> The steps of our tonal scales, and the "functions" of the chords built thereon, are the direct result of interval ratios, all in relation to a "keynote" or unity of 1; the intervals not only have a dissonant/consonant quality determined by their ratio, but also are given a specific scale degree (function) and place in relation to "1" or the Tonic. This is where all "linear function" originated, and is still manifest as ratios (intervals), which are at the same time, physical harmonic phenomena.




Tom Sutcliff has an honours degree in Physics from Manchester University and a Masters degree in Music Theory and Analysis from Goldsmiths College (London University).

He now lives in London, England and has spent most of his career as a computer manager.

He has been interested in and researched musical theory for many years. He studied flute privately and has performed with several semi-professional orchestras in the London area.

https://www.harmony.org.uk/book/voice_leading/consonance_and_dissonance.htm


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## millionrainbows

My chart showed diatonic (white-note) intervals, so for completeness, I will include the minor second and tritone.

Most dissonant intervals to most consonant intervals, within one octave:

1. Tritone (augmented fourth) (C-F#) 45:32
2. Tritone (diminished fifth) (C-Gb) 25:18
3. minor second (C-Db) 16:15
4. minor seventh (C-Bb) 9:16
5. major seventh (C-B) 8:15
6. major second (C-D) 8:9
7. minor sixth (C-Ab) 5:8
8. minor third (C-Eb) 5:6
9. major third (C-E) 4:5
10. major sixth (C-A) 3:5
11. perfect fourth (C-F) 3:4
12. perfect fifth (C-G) 2:3
13. octave (C-C') 1:2
14. unison (C-C) 1:1


_"The steps of our tonal scales, and the "functions" of the chords built thereon, are the direct result of interval ratios, all in relation to a "keynote" or unity of 1; the intervals not only have a dissonant/consonant quality determined by their ratio, but also are given a specific scale degree (function) and place in relation to "1" or the Tonic. This is where all "linear function" originated, and is still manifest as ratios (intervals), which are at the same time, physical harmonic phenomena."_
-Harry Partch, from _Genesis of a New Music
_
Credentials: https://en.wikipedia.org/wiki/Harry_Partch


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## millionrainbows

In standard practice, the intervals are in this order:

unison (C-C) 1:1
octave (C-C') 1:2
perfect fifth (C-G) 2:3
major third (C-E) 4:5
minor third (C-Eb) 5:6
major sixth (C-A) 3:5
minor sixth (C-Ab) 5:8
major second (C-D) 8:9
minor seventh (C-Bb) 9:16
*perfect fourth (C-F) 3:4*
augmented fourth (C-F#) 45:32
diminished fifth (C-Gb) 25:18
minor second (C-Db) 16:15
major seventh (C-B) 8:15

There are no problems between the "reality vs. theory" of interval ratios until we reach *the perfect fourth,* which I have always maintained has no place in a C major scale, which, like all scales, should _ostensibly_ reinforce its harmonic key center (the starting note of the C major scale, C).

This "perfect fourth" as "mildly dissonant" differs from its true harmonic identity and sound; this classification is an artificial compromise based on cerebral procedures and rules, designed to prevent "F" from becoming a new key center. "F" is thus seen as a "suspension" of the C major triad, overriding its natural tendency to become a new key center, via E-F, with E as leading tone.

In my world, dissonance/consonance are comparative terms (not absolute or arbitrary values), based on _the real world_ _of physics, waves, and beating membranes of eardrums.

_I.e.,_ sound,_ not theory.


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## millionrainbows

Woodduck said:


> Given your fondness for calling people who disagree with you "academics," I'll adopt a similar practice and suggest that the idea of this thread is a specimen of rationalization, for which the term "academic" might not be inappropriate, in the sense that it relies on some system of concepts rather than simple sensory experience.
> 
> From a non-"academic," purely sensory standpoint, we would say that a major second is _relatively _consonant or dissonant depending on what we're comparing it with. It's obviously less dissonant than a minor second, but it's also obviously more dissonant than a minor third. Dissonance, like other sensations - pain, pleasure, softness, hardness, smoothness, roughness, hot, cold - is relative. There are degrees of it. This is something we notice quite early in life, long before we're able to attend an "academy."
> 
> Consulting the harmonic series as evidence, as you like to do, we don't hear a major second as an overtone. D is the 9th member of the series over a fundamental C, is quite remote from C, and is generally not even audible (on my piano I hear nothing above the 7th partial, Bb, no matter how hard I strike the C in the bass). But even if we could hear it, we would not be hearing a major second. Play an actual major second - the D above the fundamental - and the complex, clashing overtones which would assail our ears would make the relative dissonance of the interval unmistakably clear.
> 
> It's actually amusing that after making the absolute statement that a major second is not dissonant, you begin citing musical contexts in which it's considered pleasant. Musical contexts? Pleasure? What are we talking about now? Do I misremember, or did you not recently denounce me as an "academic" in some earlier discussion for pointing out that the perception of dissonance is context-dependent? Yes, a major second can sound pleasant in certain musical contexts. So can any other interval. Pleasure is beside the point.


"A major second is not dissonant" is just a benign way of saying "don't be scared off by it" and don't think it always has to resolve, as suggested in post #2.

If you are thinking modally and harmonically, such as in C Ionian, it's perfectly acceptable to have a chord such as C-D-E-G. It sounds fine to the ear.
This is contrary to CP theory, in which it would have to resolve melodically.



> From a non-"academic," purely sensory standpoint, we would say that a major second is _relatively _consonant or dissonant depending on what we're comparing it with.


Yes, I agree, dissonance is always a relative term; that's right. I was comparing CP with modern modal harmonic thinking, in which the M2 _is_ considered dissonant. Sorry if that confused you.



> Consulting the harmonic series as evidence, as you like to do, we don't hear a major second as an overtone. D is the 9th member of the series over a fundamental C, is quite remote from C, and is generally not even audible (on my piano I hear nothing above the 7th partial, Bb, no matter how hard I strike the C in the bass). But even if we could hear it, we would not be hearing a major second. Play an actual major second - the D above the fundamental - and the complex, clashing overtones which would assail our ears would make the relative dissonance of the interval unmistakably clear.


That may be true, but it doesn't apply to my thread idea.



> It's actually amusing that after making the absolute statement that a major second is not dissonant, you begin citing musical contexts in which it's considered pleasant. Musical contexts? Pleasure? What are we talking about now? Do I misremember, or did you not recently denounce me as an "academic" in some earlier discussion for pointing out that the perception of dissonance is context-dependent? Yes, a major second can sound pleasant in certain musical contexts. So can any other interval. Pleasure is beside the point.


I'm not making an absolute statement; that's just a provocative thread title. As I said, _"A major second is not dissonant"_ is just a benign way of saying "don't be scared off by it" and don't think it always has to resolve, as suggested in post #2.

If you are thinking modally and harmonically, such as in C Ionian, it's perfectly acceptable to have a chord such as C-D-E-G. It sounds fine to the ear.
This is contrary to CP theory, in which it would have to resolve melodically.

By your reply, you are acting as if the post idea is wrong, but I don't think you're making any effort to acknowledge _what I think you know I am saying, _which is not an "absolute" statement at all; merely an observation of a "different thought-style" (harmonic/modal) which goes against the grain of academic CP 'counterpoint' thinking.

BTW, look at how easy I've made it for you to reply, by including your post in its entirety, and _then _fragmenting it into the smaller quotes to which I wish to reply. I'd appreciate if you could do the same for me in the future.


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## Woodduck

millionrainbows said:


> "A major second is not dissonant" is just a benign way of saying "don't be scared off by it" and don't think it always has to resolve, as suggested in post #2.
> 
> If you are thinking modally and harmonically, such as in C Ionian, it's perfectly acceptable to have a chord such as C-D-E-G. It sounds fine to the ear.
> This is contrary to CP theory, in which it would have to resolve melodically.
> 
> Yes, I agree, dissonance is always a relative term; that's right. I was comparing CP with modern modal harmonic thinking, in whicg the M2 _is_ considered dissonant. Sorry if that confused you.
> 
> That may be true, but it doesn't apply to my thread idea.
> 
> I'm not making an absolute statement; that's just a provocative thread title. As I said, _"A major second is not dissonant"_ is just a benign way of saying "don't be scared off by it" and don't think it always has to resolve, as suggested in post #2.
> 
> If you are thinking modally and harmonically, such as in C Ionian, it's perfectly acceptable to have a chord such as C-D-E-G. It sounds fine to the ear.
> This is contrary to CP theory, in which it would have to resolve melodically.
> 
> By your reply, you are acting as if the post idea is wrong, but I don't think you're making any effort to acknowledge _what I think you know I am saying, _which is not an "absolute" statement at all; merely an observation of a "different thought-style" (harmonic/modal) which goes against the grain of academic CP 'counterpoint' thinking.
> 
> BTW, look at how easy I've made it for you to reply, by including your post in its entirety, instead of fragmenting it into little quotes. I'd appreciate if you could do the same for me in the future.


Here's your post in its entirety, as requested. And now _I_ will request that you not dig up lengthy posts from months ago as if the discussion were still ongoing or as if anyone is going to want to go back and figure out what the hell it's all about.

This is probably just another episode in your campaign of "poking the bear," responding to my posts wherever you find them in order to "get one over."


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## millionrainbows

Woodduck said:


> Arguments that certain sounds "ARE" consonant or dissonant in some Platonic essence are fundamentally absurd and vacuous. Are we talking about music at all on this forum? MUSIC IS AS MUSIC SOUNDS. A major second can sound consonant or dissonant, to varying degrees, in different syntactic contexts, played by different instruments and in different registers.
> 
> If we're not actually discussing music, but want to define consonance and dissonance in abstract physical terms, we have to draw a definitional line in order to say that a given interval is absolutely consonant or dissonant. If such a line is drawn, conversation can proceed rationally. Otherwise it's all just a pseudo-debate between Catholics and Protestants.
> 
> So which is it? Are we talking music or physics, and what is the operative - _operative,_ not sole - definition of consonance/dissonance?


I didn't make an absolute statement, that was just a thread title designed to draw academic thinkers into the thread. I'm just comparing sound with the CP system of "dissonance." Music theory teachers out there should always make this distinction clear. The way CP is taught, these *teachers *are the "absolute" thinkers.



> If we're not actually discussing music, but want to define consonance and dissonance in abstract physical terms, we have to draw a definitional line in order to say that a given interval is absolutely consonant or dissonant. If such a line is drawn, conversation can proceed rationally.


I agree that it's a relative term, but you are still pretending to misconstrue the thread idea, which should be even more obvious from the succeeding exchanges.



> Otherwise it's all just a pseudo-debate between Catholics and Protestants.


 ...or between academic CP thinking, modal thinking, and downright mean-spirited thinking.


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## millionrainbows

Baron Scarpia said:


> I don't see any conflict between a music and physics definition of consonance/dissonance. Intervals are consonant to the extent that their overtone series align, due to the way our ears work. The unison is maximally consonant, the octave, fifth, forth, major third, minor third, major second, etc, are progressively more dissonant. A dissonance can be more or less noticeable depending on the context. A dissonance can give character to an otherwise consonant harmony, or can add frisson when it resolves to something more consonant. Just as pure alcohol taste like poison, but adds just the right taste to a fine wine, beer or cocktail.
> 
> Weird that we are still talking about this.


Yes, I agree, it's weird. I think you are correct, and on the right track: if you consider consonance and dissonance in terms of ratios, then, yes, intervals get more dissonant as they relate to "1" (the tonic keynote). Simple.


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## millionrainbows

Larkenfield said:


> Look. I believe you just don't like the thought of rules, period, because you may not understand the principles behind them, perhaps because you've never taken them seriously to begin with and would rather fly by the seat of your pants. Rules or principles of composition seem academic, inhibiting or restrictive to rebel against even though composers such as Haydn, Mozart, and Beethoven used them-and that's why most theory teachers teach what they used as a starting point and mental discipline in understanding harmony and voice leading...


The academic thinkers, and Music pedagogues I have encountered, in life and on this forum, act as if CP music is the only music. This is a big mistake. Students are surrounded by modal music, like Star Wars, all the time. If they want to stay relevant, they need to upgrade.



> I don't admire that rebellious outlook until there's some genuine understanding of some of the basic principles, including the ability to use them creatively, because I see too much wishful thinking about some of the fundamentals of music. So the subject becomes a mess... I believe it's truly necessary to define what era of music you're talking about because if one is going to talk rules or principles that were followed at the time-what was consider good harmony and voice leading changed from one era to another. In the classical era, the D would not be left hanging or unresolved and under most (all) circumstances would resolve to the tonic, the major or minor third, or the 5th ( C, E or Eb, or G). In the classical era, a work would not be expected to end on a 7th or 9th chord, would it? The example D is not necessary a dissonance but was generally considered to be unstable and in need of being resolved to a consonant tone. But the rules or principles change and evolved when the Romantic and Modern eras came in and there were different thoughts on what the stable and unstable tones were that needed resolution... In modern classical or jazz harmony, all kinds of altered chords are permissible because the ears were ready for a change. Unlike the classical era, one could end a composition on a Major 7th chord with or without a 9th. Modern ears have adjusted and the Major 7th is no longer shocking and didn't need to be resolved to the C, and the D could be used without it being resolved because it added fullness and richness to the chord...


Your reply above assumes that the CP era and its system are 'fundamental' and axiomatic, and that any deviation from this is "breaking the rules." I think this is a horrible way to teach music. Your hindsight on this is 20/20. This thread idea is benign; it was attacked by what I see as bad intentions more than my unclear way of presenting anything. Besides, I _hear_ things! I have a good ear. By your standards, this is a curse, not a blessing.



> But you have to be clear about what era of music you're talking about and that's usually left out and leads to a confusing mess regarding music theory... There's also a difference between a dissonance, sharply clashing tones (such as a minor second C to C# or Db interval) and a major second interval (C-D) where there's a _tension_ that may be considered unstable and simply seeks to be resolved. But it truly depends upon the era one is referring to and I believe that learning some of the fundamental principles that might have been used by Bach, Mozart and Beethoven should, under most normal circumstances,be encouraged because it can sharpen and discipline the lazy mind which thinks that one can essentially rely solely upon his ears rather than learning something that might actually be useful regarding the basic understanding of harmony and voice leading. Not everyone has the ears that Debussy had and can break the rules and have the music work. Yet the understanding of the principles (or rules) is too often dismissed without even knowing the knowledge or talent level of the student who might be struggling or rebelling against them. The learning of such principles might be the best thing in the world for them at this point in their studies and give them something to rebel against knowingly or consciously later. Just because Debussy broke the conventional rules at the time doesn't mean that he didn't know them. It's known that he studied harmony with César Franck though he usually rebelled against those teachings. But then, Debussy was a genius and heard music in his head that didn't match Franck's teachings and so he eventually went his own way.


Well, thank God there are jazz programs in colleges now. Your post above assumes that music is CP and that "rules are broken" by hearing things based on direct experience. In this regard, I would have had an easier time with academics if I'd had a tin ear!


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## millionrainbows

Woodduck said:


> Here's your post in its entirety, as requested. And now _I_ will request that you not dig up lengthy posts from months ago as if the discussion were still ongoing or as if anyone is going to want to go back and figure out what the hell it's all about.


I don't think that way; if ideas are presented, I discuss them without regard to time frames. If this irritates you, i'm sorry, that's just the way it is. And if I quote you, it's your responsibility to reply or ignore, regardless of how old the post is.



> This is probably just another episode in your campaign of "poking the bear," responding to my posts wherever you find them in order to "get one over."


No; I'm responding to your posts, and the person those posts represent. Besides, I've always heard that you should not run from a bear.


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## Woodduck

millionrainbows said:


> I don't think that way; if ideas are presented, I discuss them without regard to time frames. If this irritates you, i'm sorry, that's just the way it is. And if I quote you, it's your responsibility to reply or ignore, regardless of how old the post is.
> 
> No; I'm responding to your posts, and the person those posts represent. Besides, I've always heard that you should not run from a bear.


I would consider it atrociously bad manners to dig up a four-month-old post by someone, respond to it, and then tell them it's their "responsibility" to figure out what's going on or just ignore what I've said to them.


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## millionrainbows

Woodduck said:


> I would consider it atrociously bad manners to dig up a four-month-old post by someone, respond to it, and then tell them it's their "responsibility" to figure out what's going on or just ignore what I've said to them.


I don't think that way about it. 
I think it would be atrociously bad manners to act mean-spirited, and pretend you don't know what the other person is conveying, on a constant daily basis. This kind of "real time pursuit" is worse than going back.


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## Woodduck

Whatever. I would like to end this stupid conversation now. Can we do that? Just say yes or no, please, and it will be over.


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## millionrainbows

Sure, we can end our interpersonal exchange. If I have a revelation about major seconds, though, I will post.


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## Woodduck

millionrainbows said:


> Sure, we can end our interpersonal exchange. If I have a revelation about major seconds, though, I will post.


Thank you. I'll do the same.


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