[frogs] Re: Lilypond's internal pitch representation and microtonal notation

[Carl Sorensen <c_sorensen@xxxxxxx>]

On 9/20/10 10:00 AM, "Wols Lists" <antlists@xxxxxxxxxxxxxxx> wrote:

>  On 20/09/10 14:41, Hans Aberg wrote:
>>> As a related issue, have you considered how (different kinds of)
>>> transposition would be handled in your pitch scheme?
>> 
>> 
>> This is much simpler: the linear combinations are vectors that you
>> just add. For example, if a, b, c, ... are represented by 0, M, m+M,
>> ..., and you want to transpose from b to c, just add m. A sharp is M-m
>> and a flat m-M. If you want transpose from a note x to a note y, just
>> add y - x.
> What you've missed (and I need to address) is "what is x?".
> 
> Let's say I want to transpose up three semitones. That's probably easy,
> it's a minor third, but it could be an augmented second. So, trying to
> remember the pitch class, is it (0,2,sharp) or (0,3,flat)? And, for your
> example of that, I've currently got a modified chord engraver on the
> frogs list that's added a guitar capo property. All the engraver is told
> is how many semitones to transpose, and it's got to sort out all the keys!

In reading this, I may have a suggestion for how to handle your
transposition problem with the capo.

What if instead of giving the fret number for placing the capo, you gave the
sounding key and the fretboard (capo) key.  Then you could transpose the
sounding chords by the difference in the keys, and you'd get the chord names
you want.  And you could calulate the capo fret based on the difference in
the keys as well.

The challenge we had in the past was not enough information to do the right
thing, because we were looking at just the fret count.  Then, starting from
the fret count, we tried to infer the pitch offset, but 3 semitones is
ambiguous.

Instead, if we start with the pitch offset, we can have either 2 tones minus
1 semitone or 1 tone plus 1 semitone.  Then we can convert either one into a
capo fret without any ambiguity at all.

HTH,

Carl
 


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