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I tried to make the "best" 7-tone scale in just intonation. Specifically:

  1. The tones must be alongside the equal temperament. (7-TET here)
  2. The tones must have the least maximum harmonic distance.

This results in the following tones (based on C):

C(1/1) D(8/7) E(5/4) F(4/3) G(3/2) A♭(8/5) B♭(7/4)

According to Wikipedia, this is the Major Minor Scale. Despite that this is the approximation of 7-TET with the least maximum harmonic distance (49 from D to B♭), I've never found any music composed in this scale.

Is there any theoretical reason why Major Minor Scale is unused? (Regardless of its temperament)

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    That scale really is not very satisfyingly approximated by 7-edo. Could be interesting in 31-edo though. – leftaroundabout Oct 21 '18 at 13:32
  • I've also heard that scale called the Melodic Major scale (albeit in boring old 12-edo). – user45266 Mar 26 at 4:30
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Modern harmony revolves around tonic-dominant relationships, and part of what makes a V-I or V-i sound convincing to our ears is that the leading tone goes up a half-step to the tonic. In the common-practice era, this is why we see so many examples in minor that seem to be well described by the idea of a melodic minor scale. On the way up, we want to hear that half-step. The scale you're describing doesn't have that, because (in the key of C) it has a Bb rather than a B natural.

To ears that have gotten used to the major-minor system, I suspect that listeners would tend to hear this scale as being in F minor. The notes, F G Ab Bb C D E, are the notes of the ascending melodic minor scale. You can build chords using these scale degrees, and in fact it's fairly common to do so in jazz harmony. You get triads that are i, IV, and V7, which sound pretty familiar to most people's ears.

Of course, you could very easily set up a piece of music in which this scale would clearly be in C. You start and end the melody on C, the bass has heavy-handed emphasis on alternating between C and G, and so on. Then it would probably sound to most people like a piece of music that was in C, but with modal mixtures for effect.

Modal mixture is perfectly fine, it's used frequently, and listeners easily accept it if it's done competently. But people don't normally compose music by picking some set of 7 tones and then building everything on that as some kind of rigid structure that determines everything about the harmony and melody.

The tones must have the least maximum harmonic distance.

Could you explain what you mean by this, or point us to a source that defines this terminology? Is this something to do with psychoacoustic models of dissonance, such as tonotopic models (Kameoka and Kuriyagawa)?

  • By 'harmonic distance', I mean the product of numerator and denominator of ratio of just ratios, ignoring factors of 2. Here, D(8/7) and B♭(7/4) has ratio 49/32, resulting in harmonic distance 49. – Dannyu NDos Oct 21 '18 at 23:25
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"The tones must have the least maximum harmonic distance."

Is this a requirement that you have discovered to produce good, interesting, dramatic, beautiful etc. music? Apparently few composers agree with you!

To answer your question, there is rarely a theoretical reason why certain notes or scales SHOULD be used. (If we discount the 'composing by numbers' fad of the early 20th century anyway.) You can invent a 'theory' to justify ANY notes. Theory rather categorises and catalogues sounds and patterns that have been discovered to sound good.

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    I wish you stopped posting your standard “theory sucks” comment as an answer. Yeah, this is a valid position, a valid opinion, but it's not helpful for questions about well-confined theoretical models, and it disregards the fact that the music lots of people prefer does stick for much of the time to rules that can be explained very well with simple mathematical ratios. Whereas that “‘composing by numbers’ fad” illustrates pretty well that rules which are made up for no good physical reasons work rather less well, going by popularity of the thus composed music. – leftaroundabout Oct 21 '18 at 14:53
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    I can't help it if so many questions here are based on a false premise. They crave 'rules' but then discover that the music they prefer doesn't obey them. If the point isn't sinking in, it needs re-stating. – Laurence Payne Oct 21 '18 at 15:09
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    Or maybe it needs consideration of whether it's simply not a good point. If questions ask “why is X contradicting rule Y”, this doesn't necessarily imply that Y is worthless, but merely that X requires additionally (or instead) a different / more refined theory. It's perfectly fine if you're not interested in such refinement, but why does it bother you if other people are interested in it? – leftaroundabout Oct 21 '18 at 16:05
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    @Some_Guy but that's your interpretation of what those novices think. I see it in another way, namely they search for what the right framework is into which their ideas would fit properly. And that's the way to go IMO, not just saying “theory doesn't apply here, you're on your own”. Some theory will probably apply, if not the standard one they've already learned. – leftaroundabout Oct 21 '18 at 20:52
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    These answers almost always miss the point. This is pretty much just someone asking a question and responding with it doesn't matter. If it doesn't matter explain why it doesn't matter and in what cases it does matter. Nothing in this answer brings anyone closer to the answer asked in this question and pushes any theoretical concepts aside. – Dom Oct 22 '18 at 3:40

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