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Permutations can be very useful for crafting varied and interesting rhythms. It is possible to explore rhythms using Pascal's triangle. Sounds and silences on two beats can be written in binary form: 00, 01, 10, 11. Although I find this insight useful in making rhythm, I don't yet know a similarly meaningful way to create harmonic progressions. How to use permutations to play progressions in the available range of scales and modes?

As this can be a very open ended question, I am looking for a starting point for exploration. How to play a triad, for example, moving through the circle of fifths? Specifically varying it in a way that is, simple, yet musical and not monotonous. Playing a major triad starting from C and transposing it in fourths on every beat is not very interesting musically. Similarly, transposing a triad in root position following a II-V-I progression is still not interesting. Chord inversions, drop-two chords and upper structures can make progressions very interesting, but I have a fragmented understanding, and I can only make fragments of harmonic progressions (I am familiar only with the first part of this book). What are simpler forms that can be extended, essentially low floor templates for making meaningful harmonic progression that can be made more complex. Perhaps using only triads, or intervals, and their inversions to play for twenty minutes while exploring progressions, patterns and making music.

Using permutations to create rhythm[^1]

[^1]: Dahlgren, M. & Elliot, F. (1963) 4-Way Coordination. Henry Adler.

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  • This seems like a very open-ended and broad question, which means it may not be suitable here. Can you please read our tour and How to Ask pages, and edit your question to be more specific.
    – Doktor Mayhem
    Nov 27, 2023 at 9:19
  • "Playing a major triad starting from C and transposing it in fourths on every beat is not very interesting musically": isn't it? Why then is the circle-of-fifths harmonic progression so common?
    – phoog
    Nov 27, 2023 at 10:18
  • After thinking about this for a few minutes, it's not open-ended, just a bit abstract. Nov 27, 2023 at 10:38
  • @phoog I would practice playing II-V-I with basic seventh chords, using the same inversion, unchanging articulation and playing one chord on each beat. This can be very boring and I wondered how to turn this practice into a meaningful and exciting exploration of harmonic patterns. How to vary the inversions, how to link transpositions, for example? Nov 27, 2023 at 14:52

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From the top of my head without actually trying this out, a theoretical abstract answer:

In rhythm, you have beat/pulse positions within a meter. In harmony, you have scale degree positions in a scale. If you can select beat positions for rhythms, do the same for pitches.

Why not make chromatic alterations to the scale. There are N positions that can be altered, pick a permutation.

To keep things anchored to the "one", put a big kick drum on beat one, and to anchor harmony, a pedal point bass on the root pitch. Unless you want to have a chord progression where the bass follows chords. And you dont't have to explicate beat one in a rhythm-for-dummies style either. :)

For constructing chords (that you don't have to explicate by playing simultaneously, you can imply them by arpeggiating or emphasizing on stronger beats in a single-voice line), in addition to using permutations of scale degree combinations, try to find all other dimensions or aspects of chords, and permute those aspects. Let's take a description of a chord

  • tertian harmony (based on stacking thirds, as opposed to fourths or fifths)
  • major scale
  • closed-voicing (as opposed to open voicing - there are many possible voicings which you could permute)
  • a seventh chord (four notes as a stack-of-thirds)
  • root on scale degree 2
  • bass on scale degree 1 (or thinking in terms of inversions, it's a third inversion)
  • the fifth of the chord is diminished (making scale degree 6 flat)

There you have a whole bunch of things about chords you can permute.

Any set of attributes you can use to describe it, you can permute. Of course, these aren't necessarily completely orthogonal, i.e. independent. If you select quartal harmony, then the rest of things may not apply. If you choose to select the bass note freely from a scale without thinking of inversions, it may change the conventional tertian-harmony interpretation of the chord's type. For example, C major with F in the bass, really nice chord but you can't get it systematically as an inversion of any stack of thirds, except as a kludge-around "Fmaj9 omit 3". Or if you choose to alter chord tones instead of scale degrees, then chords will dictate scale degree alterations. But you could choose to do it the other way around as well.

Just some abstract ideas.

___ Edit. How would you use that to create progressions?

Decide on a harmonic rhythm. Or make one as a slow rhythmic permutation. For example, one harmonic change per bar, or sometimes two per bar.

For each harmonic change, pick one or more attributes to change. Or stick to just one, for example chord root. Or chord root and inversion.

If you want to see the whole thing as one single permutation of something, consider your harmony progression as a machine with inputs and outputs. INPUT -> GENERATOR -> OUTPUT. You map all attributes and decisions the GENERATOR makes to something in INPUT, and INPUT consists of exactly X bits of data. It may be a lot of bits and permutations, but you can decide to lock most of it and permute only over a subset of input space. Just like you're already doing with rhythms - I suppose you have decided on e.g. locked bar and pulse lengths, and permute within a partial space only. So you don't have 128th note patterns of 8 bars or anything.

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  • Thank you, I will explore these ideas. I just tried to expand the blues progression E7, A7, B7, to move to different scales. Using the circle of fifths C#m seems to connect these chords, and E7 C#m7 A7 C#m7 B7 G#m7 F#7 D#m7 Db7 doesn't sound too bad. Nov 27, 2023 at 14:42

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