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# [sc-users] Re: question about scale degrees in patterns

```ddw_music wrote
>
> shiihs wrote
>> As I found out recently, to my surprise, a scale degree behaves
>> counterintuitive in patterns.
>> By adding +/- 0.1, you add/subtract a semitone.
>> What is the rationale for not making 0.5 the note that sounds exactly
>> half-way 0 and 1 (which can be different depending on the scale, octave,
>> tuning, ...)?
> Because you can't assume that 2 will always be the largest number of
> chromatic divisions between scale degrees. For instance, in C harmonic
> minor, there's Ab (degree 5 in SC) and B-natural (degree 6). What would
> 5.5 be in this case?
>
> It's really necessary to be able to distinguish between "up a chromatic
> unit" and "down a chromatic unit."

The more I think about this, the less it makes sense to me. Scale degrees in
my understanding live in a very different universe (level of abstraction)
than semitones. When working with scale degrees, to me it has no physical
meaning to "raise something a semitone". Raising a semitone is something
that makes sense only when working in a MIDI number-like chromatic space.

Scale degree, in my interpretation, says something about the index of an
element in an ordered list of notes, also known as a scale. Scales in
general needn't contain 12 divisions per octave, needn't have equal
divisions, needn't repeat at the octave (may span multiple octaves), may
consist of  different notes when rising versus when descending etc.

E.g. in a hypothetical scale consisting of only notes "c e f a b" and
repeating at the octave, c could be assigned degree 0, e : degree 1, f :
degree 2, a : degree 3 and b : degree 4). Scale degree in combination with
octave number here unambiguously identifies a note belonging to that scale.
(Octave or other period numbers only make sense for repeating scales. If you
had a collection of notes spanning multiple octaves generated from a
stochastic process, you'd have to give each note a new degree number.).

In a very strict approach, one could argue that notes like g or e-flat
cannot be assigned a degree as they do not exist in the scale "c e f a b".

In a looser interpretation, one could indirectly address such notes by
introducing fractional degrees. Fractional degree 3.5 would be halfway
between 3 and 4, so after conversion to a midi number space (at an octave of
choice) (3->a=69, 4->b=71) it could correspond to a note halfway 69 and 71,
or in other words 70=a-sharp/b-flat. In this proposal the fraction is
preserved through the mapping from scale degree space to midi number space
(mostly because I couldn't think of anything else to do with it that would
make sense).

Similarly, fractional degree 1.5 would be halfway between 1 and 2, or after
conversion to MIDI number space (1->e=64, 2->f=65), halfway e and f = 64.5
which corresponds to e quarter sharp. Fractions in scale degrees in my
interpretation therefore have no direct relation to chromatic distance.
Chromatic distances only have a meaning in a MIDI number like space.

I've converted these ideas in a (somewhat pretentiously named) TheoryQuark
https://github.com/shimpe/theoryquark.

--
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