Chord inversions

[henryksloan]

Executable

• Added support for inversions using slash syntax
  • C major triad / E is C major in first inversion
  • The implementation is similary error-proof to the other from_regex functions, so C/E and C major /E give the same result as the above
• Added inversion example to chord help

chord.rs

• Added inversion: u8 to Chord
• Added new constructor with_inversion, and made new construct a root-position chord by default
  • @ozankasikci correctly critiqued a similar design pattern I used for descending scales, but I think root position chords are desirable in the vast majority of cases, and that they are the "default" voicing of chords unless otherwise stated
• Modularized chord_intervals into its own function, giving the intervallic layout of a chord
• Added inversion support to from_regex
  • It checks if there is a / in the input, and if so, treats everything after the slash as a PitchClass
    • It uses PitchClass::from_regex, so it is error-safe
  • If a slash is given, followed by a valid pitch class, then:
    • The chord is first constructed in root position
    • The position of the given bass note is determined in the root position chord
    • A new chord is build with the determined inversion
  • Minimal overhead is created for invalid/root position inversions
• impl Notes for Chord generates the notes of the root position chord, rotates them based on the inversion number, and corrects the octaves such that they 1) are non-decreasing and 2) start at self.octave

test_chord.rs

• test_all_chords_in_c now generates and tests all inversions of each chord type on C
• test_inversion_octaves tests against hard-coded octave lists for every inversion of a G major ninth chord

Caveat: There is no standard (to my knowledge) for voicing inverted chords beyond the octave, i.e. placing G in G major 9 / B. For this reason (and to maximize simplicity and flexibility), my implementation enforces a non-decreasing order; G major 9 = B4 D5 F#5 A5 G6

[ozankasikci]

That's great, another very much needed feature!

I'll review this ASAP :)

[ozankasikci]

Great work.

I'd like to address an issue, although C/E is the universal notation to represent the first inversion, I think we should implement C/1 as well. That's because the former entails the user to know all the notes of the given chord while the latter is just intuitive.

Let me know what you think!

[henryksloan]

@ozankasikci Good idea, done! I had that same idea for numerical syntax, but I thought it might be a bit obscure. I added it, along with an extra example in the chords help message, so I think it's a good solution.

[ozankasikci]

Awesome, thanks! Merging :)