craigsapp
commented
4 years ago This would be useful to have in verovio, and it is not too complicated to implement. Both <note> and <keySig> need to be processed.
For transposing notes, see: http://www.ccarh.org/publications/reprints/base40 Although that article is a bit theoretical, so here is a more applied summary:
The system described in the article converts pitches into integers, then adds an integer transposition, and then converts from the resulting integer back into a diatonic pitch and chromatic alteration. It is called "base-40" since the octave interval is 40 in the system.
The Base-40 system is interval-invariant, so transposition (to any key) preserves the spelling of the notes and intervals between the notes. Base-40 will handle spellings up to double sharp/flats. If you need more, then there are higher-order bases according to this formula:
base = 7 * (2n+1) + 5Base-40 is the case where n=2, allowing up to double sharp/flats. Base-54 is the case for +/- 3 sharps/flats, and so on (which I can explain more if you want a more generalized system, since verovio allows for triple sharps/flats).
Three pieces of information can be used to construct the numbers for pitches in Base-40:
(1) A major second is the number 6 (2) A minor second is the number 5 (3) Then choose a starting number for some pitch. I assign 162 to middle C, but the paper assigns 123 to middle C. I use 162 so that dividing a pitch number by 40 will give the octave, with middle C being in the 4th octave (in other words the octave boundary is between B-double-sharp and C-double-flat).
All other intervals can be calculated from (1) and (2): a perfect fifth is equal to three major seconds and one minor second, so the interval number is:
P5 = 3 * 6 + 1 * 5 = 23.If 162 represents middle C, then the G above it is 162 + 23 = 185. To transpose from one key to another, simply add an integer to the notes to transpose them to the new key. If transposing up a Major 2nd, then add 6 to all pitches. To transpose down a minor third subtract 11, etc. The enharmonic relations will always be preserved, unless you have an overflow/underflow beyond double sharp/flats (in which case switch to a higher base).
Here are the base-40 pitch class integers:
0 = Cbb (when using 162 for middle C)
1 = Cb
2 = C
3 = C#
4 = C##
5 = unused
6 = Dbb
7 = Db
8 = D
9 = D#
10 = D##
11 = unused
12 = Ebb
13 = Eb
14 = E
15 = E#
16 = E##
17 = Fbb (note no unassigned position between diatonic notes that are a minor second apart)
18 = Fb
19 = F
20 = F#
21 = F##
22 = unused
23 = Gbb
24 = Gb
25 = G
26 = G#
27 = G##
28 = unused
29 = Abb
30 = Ab
31 = A
32 = A#
33 = A##
34 = unused
35 = Bbb
36 = Bb
37 = B
38 = B#
39 = B##The base-40 interval classes are:
0 = unison
1 = augmented unison
2 = doubly augmented unison
3 = unused
4 = diminished second
5 = minor second
6 = major second
7 = augmented second
8 = doubly augmented second
9 = unused
10 = diminished third
11 = minor third
12 = major third
13 = augmented third
14 = doubly augmented third
15 = double diminished fourth
16 = diminished fourth
17 = perfect fourth
18 = augmented fourth
19 = doubly augmented fourth
20 = unused
21 = doubly diminished fifth
22 = diminished fifth
23 = perfect fifth
24 = augmented fifth
25 = doubly augmented fifth
26 = unused
27 = diminished sixth
28 = minor sixth
29 = major sixth
30 = augmented sixth
31 = doubly augmented sixth
32 = unused
33 = diminished seventh
34 = minor seventh
35 = major seventh
36 = augmented seventh
37 = doubly augmented seventh
38 = doubly diminished octave
39 = diminished octave
40 = perfect octaveHere is an algorithm for converting from pitch names into base-40: https://github.com/craigsapp/humlib/blob/master/src/Convert-pitch.cpp#L201-L242
Here is an algorithm for converting from base-40 integers into pitch names: https://github.com/craigsapp/humlib/blob/master/src/Convert-pitch.cpp#L289-L341
earboxer
I would like to open a feature request: Music transposition with Verovio.
I think an option that allows Verovio to automatically transpose a piece up or down would be a huge improvement for this project. Currently the music file has to be manipulated to achieve this transposition. This is complicated and can not be done in an easy and fast way.
Maybe it's easier for Verovio to do this transposition when the file is loaded into memory and before the rendering process is started.