24, 128, approach infinity -- I know there are microtonal systems, but if you want to understand them, choose the nearest multiple-of-twelve (or really, choose whatever TET contains the closest approximations to the exact notes) TET and look where their intervals land with respect to the symmetries (factors) within that TET, and where those symmetries are broken by a note moving by a perceptual 'slide' (one note 'moves' into the other position) rather than sounding like a new distinct voice.
More like, only if you're playing Schoenberg it's about modulo 12.
Almost all sheet music that you play uses 5 or 7 unequal subdivisions of the octave, and occasionally the rest. Sure, sometimes you'll have one or two of the rest on a regular basis (blues, harmonic/melodic minor), but still most music won't use all twelve.
Isn't modulo-twelve (if we ignore microtonal) the core underlying structure, and then you pick scale (like 2 2 1 2 2 2 1) and a key as a mapping, and then use degree as an 1-based index into the scale?
I don't really know a thing about music, so I could be wrong here - but that mental model at least made some sense to me when I tried to map all the concepts I've heard about into some sort of a mental system.
24, 128, approach infinity -- I know there are microtonal systems, but if you want to understand them, choose the nearest multiple-of-twelve (or really, choose whatever TET contains the closest approximations to the exact notes) TET and look where their intervals land with respect to the symmetries (factors) within that TET, and where those symmetries are broken by a note moving by a perceptual 'slide' (one note 'moves' into the other position) rather than sounding like a new distinct voice.
More like, only if you're playing Schoenberg it's about modulo 12.
Almost all sheet music that you play uses 5 or 7 unequal subdivisions of the octave, and occasionally the rest. Sure, sometimes you'll have one or two of the rest on a regular basis (blues, harmonic/melodic minor), but still most music won't use all twelve.
Isn't modulo-twelve (if we ignore microtonal) the core underlying structure, and then you pick scale (like 2 2 1 2 2 2 1) and a key as a mapping, and then use degree as an 1-based index into the scale?
I don't really know a thing about music, so I could be wrong here - but that mental model at least made some sense to me when I tried to map all the concepts I've heard about into some sort of a mental system.
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