User:VectorGraphics/Diatonic and chromatic steps

Diatonic semitones, chromatic semitones, enharmonic dieses, and subchromatic commas are four types of steps that can be found when using diatonic intervals, defined in terms of the diatonic and chromatic scales. However, there are some important considerations:

• Here, "diatonic scale" refers not explicitly to the diatonic scale but to the 7 interval classes it defines, such that a diminished third, minor third, major third, and augmented third are all in the same diatonic interval class ("third", or 2\7).
• Similarly, "chromatic scale" does not refer explicitly to the chromatic scale, but to the 12 interval classes it defines, such that a diminished fourth, a double-augmented second, and a major third are all in the same chromatic interval class (4\12). So it does not matter if m-chromatic or p-chromatic is used; both of them work the same in this context.

Here are the types of steps:

• diatonic "semitones" (alterations by 1 diatonic step and 1 chromatic step, i.e. E to F)
• chromatic "semitones" (alterations by 0 diatonic steps and 1 chromatic step, i.e. E to E#)
• enharmonic "dieses" (alterations by 1 diatonic step and 0 chromatic steps, i.e. E to Fb)
• subchromatic "commas" (alterations by 0 diatonic steps and 0 chromatic steps, i.e. E to ^E)

A more in-depth explanation follows.

WIP