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Is there any theoretical reason for not exploring n-note scales (7<n<12) which has similar interval relationships as diatonic scales?

Context: I always feel odd when learning about non-diatonic scales, the instructor or textbooks suddenly jumps from explanations of octatonic scale to 12-note chromatic scale.

It's even more strange that octatonic scales and chromatic scales both emphasize the symmetry within them, whereas diatonic scales often emphasizes every single note in the scale has different intervals between other notes in the scale (meaning, if we're given the intervals to other 6 notes, we can uniquely determine what the note in movable-do notation is).

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    I think it's the symmetry that makes Messiaen's modes, and twelve-note scales, so attractive and useful to a composer: the absence of a tonic. Perhaps octatonic and chromatic scales do 'emphasize their symmetry': but music written with those scales doesn't. I don't understand your last paragraph. Aren't you simply saying 'diatonic scales are diatonic? – Old Brixtonian Oct 28 '20 at 5:32
  • @Aaron Sorry to have messed up the threading here. Yes you were right. – Old Brixtonian Oct 28 '20 at 5:57
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    Composers are making up sequences all the time. If I used Eb C E Ab G Bb A B for example, I guess I could re-order it and call it a scale. But although it might work well in something I'm writing, as a scale it isn't very versatile. The scales that get taught are the versatile ones: the ones that have earned their keep. – Old Brixtonian Oct 28 '20 at 6:14
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    @OldBrixtonian's comment leads me to wonder if 8-plus-pitched asymmetrical scales had little to offer composers in terms of intervallic relationships beyond those already explored within the diatonic system. Symmetrical scales required composers to come up with new ways to structure music. In fact, the only reference I could find to composing with explicitly asymmetrical scales was the work of Ezra Simms. For example, Solo in Four Movements (1987) – Aaron Oct 28 '20 at 6:28
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    @awelotta sorry I should have clarified what "similar interval relationships" mean. What I meant to say was a scale which keeps all the 7 diatonic notes and just adding one, two, three, or four notes so that Do, Re, Mi, Fa, Sol, La, Ti keep interval relationships with each other. I'm interpreting chromatic scales as diatonic scales + 5 notes and was thinking other 8 to 11-note scales as diatonic scales + 1/2/3/4 notes. – sonicom Nov 1 '20 at 5:52
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There may be no reason not to explore 8+-note asymmetrical scales: the various bebop scales are derived from diatonic scales and often contain 8 or more notes. Points of interest in these scales include the insertion of chromatic passing notes in between the familiar notes of diatonic scales such as the major scale.

Granted, bebop scales are most commonly found (or pointed out) in jazz, and it may be precisely because of their resemblance to diatonic scales that music textbooks don't tend to elaborate on them. ...Or maybe it's because music textbooks lean towards classical music (often because they end up as study material for music theory courses and exams).

  • Thank you! I wasn't aware of bebop scales and this is super helpful. I'd like to find textbooks which elaborate more on what the extra note(s) in bebop scales alter what's in diatonic scales. – sonicom Nov 1 '20 at 5:54
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    @sonicom - You may have some luck investigating the "Further reading" and "Sources" of the Wikipedia article my answer contains a link to. – Dekkadeci Nov 1 '20 at 11:08
  • I wouldn't be so sure about it. 8,9 and 10 pitches collections are ostensibly used in 20th and 21st centuries classical music (examples: Bartok, Ligeti, Lutoslawski, Penderecki, Xenakis, Ferneyhough, Adès et cetera). One can divide these collections, explore interval content or use aggregated pairs of 4 or 5-pitches chords. – Rodrigo B. Furman Nov 3 '20 at 20:43
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Music theory usually attempts to describe what has commonly been done in a particular musical practice. If you're seeing a lack of discussion of scales with more than 7 notes, it's because such scales are uncommon or perhaps have no recognised status at all in the music you're studying.

That doesn't mean you can't or shouldn't experiment with such scales yourself. But there can be only a little "theory" about them without a corresponding musical tradition that uses them.

One thing to be aware of is that there are only eleven 11-note scales, and they're all modes of each other; they're the chromatic scale with one note deleted. So this doesn't look like a very promising avenue to explore. The 10-note scales are also rather limited, although less so; they're complements of intervals (i.e. choose an interval and you get a 10-note scale that's all the other notes).

But 8- and 9-note scales may be very promising. It depends a bit on what kind of music you want to play, of course. This pdf contains many, but not all, of the possibilities (I'm the author); it's written out for guitarists but the basic information should be usable by anyone.

  • Helpful to observe that theory tends to describe what has already been done. And the comments on 10- and 11-note scales is a very good point, too. It does beg the question, though, of why 8- and 9-note scales haven't been explored more to deserve mention in theory courses (outside the octatonic "diminished" scale). My speculation - but only speculation - is that for a composer/theorist 8- and 9-note scales don't offer much that isn't already present in systems like diatonicism, chromaticism, and serialism. – Aaron Oct 29 '20 at 19:12
  • Don't two scales that are modes of each other use the exact same notes, and therefore none of the 11 possible 11-note scales are modes of each other? – Dekkadeci Oct 30 '20 at 11:17
  • @Dekkadeci Two scales that are modes of each other have the same interval structure but "starting" in different places; which notes they have depends on the "key" of the scale. E.g. C major is TTSTTTS (CDEFGABC). C Dorian is TSTTTST (CDEbFGABb). You get from TTSTTTS to TSTTTST by just moving the T at the start of the major scale to the end. If you can get from one scale to another by doing this (maybe several times), they're modes of each other. – helveticat Oct 30 '20 at 21:38
  • @Aaron That's my impression too. Big structures have always seemed less useful to me than small ones. – helveticat Oct 30 '20 at 21:39
  • @helveticat - My understanding is still that two scales that are modes of each other use the exact same notes and just start on different notes: for example, A Aeolian and D Dorian are modes of each other. offtonic.com/theory/book/7-10.html concurs with me. – Dekkadeci Oct 31 '20 at 12:51
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Check out Persichetti - 20th Century Harmony chapter 2 or other more advanced (as Tymoczko's A Geometry of Music or Kostka's Materials and Techniques of Post-Tonal Music).

There's a lot of ways to treat these big scalar materials. Usually, as it was 20th century classical music standard, you break them down into smaller sections based on equal divisions, symmetry or axis. More recently, you break into interval content and similarity. Also, with post-tonal music advancing, more and more different usage styles appeared, based on pitch class sets (a scale, in this context, is a superset, therefore it doesn't behaviour as a scale normally would in tonal contexts). Also, you can use diatonic patterns in such synthetic scales.

These books mentioned will teach you how to build and make music with any scale or pc set, giving examples and exercises in aesthetics close to where they were used. But, once learned, you're free to expand your own repertoire creating and playing with new scales or new contexts (such as pandiatonicism).

  • Also, as a way to show different examples of construction with these materials, look out to music and analyses of composers as Lutoslawski and Babbitt, and their treatment of supersets and serial rows. – Rodrigo B. Furman Nov 3 '20 at 20:47
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It's because symmetrical scales are parental forms. They have properties that non-symmetrical scales don't have .

For instance, if we look at the whole-tone scale, we can split the chromatic scale into 2 different 6 note whole-tone scales:

G A B C# D# F

C D E F# G # A#

The whole-tone scale is connected to the dominant function.

Consider: G 7 from key of C major: G is root A is 9th B is 3rd C# is #11th D# is b13th F is 7th

But look: GBD#FAC# = G9#5#11

But because the whole-tone scale is symmetrical, we have connection to 6 major keys (i.e. to the dominant function of 6 different keys)

G9#5#11 A9#5#11 B9#5#11 C#9#5#11 D#9#5#11 F9#5#11

This means that now we have a parental form with G wholetone ( 6 sep dominant functions from 6 keys).

But it does not end here.

Consider the other whole-tone scale we didn't use:

C whole-tone C D E F# G# A#

Any of the dominant chords from the first whole-tone scale can resolve to any major or minor chord built from the tones in the second whole-tone scale. That is, these chords:

G9#5#11 A9#5#11 B9#5#11 Db9#5#11 Eb9#5#11 F9#5#11

can resolve to any of these chords:

C major or C min D major or D min E major or E min F# major or F# minor G# major or G# minor A# major or A# minor

Each symmetrical scale as a parental form, in its own unique way is a larger structure then a key.

If we look at the diminished scale, say:

G HW diminished or GG# A#B C#D EF G

It contains the chords:

G7 GBDF Bb7 Bb DFG# Db7 DbFG#B E7 EG#BD

These dominants are related.

G7 is the V7 of Cmajor ( G7 to Cmajor) Db7 is tritone of G7 ( Bb7 to Cmajor) E7 is V7 of Aminor ( rel minor ) ( E7 to Aminor) Bb7 is tritone of E7 ( Bb7 to Aminor7)

This is how all 4 dominant work in C major however this works same exact way for

Key Cmajor, Key of Ebmajor, key of Gbmaj7,key of Amajor

So this symmetrical scale is parental form that connects a relationship of dominant function between these 4 keys .

All symmetrical forms have their own unique relationship.

Non symmetrical scales do not have nearly as much interesting about them .

Lastly, no matter what key your are working in (in a specific context), for example C major, you have strong beats and weak beats of the bar . Strong beats are always chord tones and weak beats are embellishments, so all 12 notes are there to be used. That is how the chromatic scale directly connects to any situation.

  • There exists a symmetric 9-tone scale. Why is this not discussed as much as the other scales? And also, the diatonic scale is not a mode of limited transposition, so why is it so discussed? – awe lotta Oct 28 '20 at 15:38
  • Good questions, a lot has to do with when you learning nusic its through a specific lens of culture and history just a tiny perspective.there some things more important than others, maddening the major key is more important then symmetrical scales .in order to utilize symmetrical scales to their fullest you have to already mastered major minor keys – MMJ2020 Oct 28 '20 at 17:37
  • The chromatic scale connects to the major scale you are in , so in any exact example you gave 12 notes that work in any context you are in . – MMJ2020 Oct 28 '20 at 17:40

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