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Re: enharmonic problem with \transpose - should we modify it?


From: Hans Aberg
Subject: Re: enharmonic problem with \transpose - should we modify it?
Date: Fri, 17 Jun 2011 11:05:39 +0200

On 17 Jun 2011, at 07:19, Keith OHara wrote:

>> Summary: { \key c \minor  \transpose gis as { es } } produces feses in
>> output. I think it would be better if it outputted es.
> 
> I have used `\transpose gis as` to change enharmonic spellings, so probably 
> others have used it as well, so it should probably continue to function as 
> it does.
> 
> \transpose does the theoretically correct thing ...

The staff system that LilyPond uses essentially expresses the algebraic 
relations of an extended meantone system, that is, all pitches A B C D E F G 
plus those that can be derived from them by applying an arbitrary number of 
flats or sharps, no enharmonic equivalences applied.

Alternatively, these are the set of pitches p m + q M, where p, q are integers, 
and m, M formal symbols representing the minor and major seconds. One gets a 
tuning by assigning interval values to m and M, and also choosing a tuning 
frequency for one pitch.

So, to begin with, it is not possible impose enharmonic equivalences in a 
universal accepted way, because it does not work with the staff system itself. 
(Mathematically, they correspond to sections of a factor group.)

There is a musical problem: if one is not working with instruments tuned in 
E12, then the pitch will slip, with a "comma", an E31 or E53, tonestep, 
typically around 20 cents for each enharmonic equivalence introduced. Human 
performers will probably correct for that, but if not corrected, there will 
result wolf tones - the name is in fact very fitting.

So, the best way is to apply E12 equivalences in sections, like changing key 
signatures, and occasionally, if one knows that the instrument is tuned to E12.

> ...in all cases except :
> 
>> when a
>> passage like this { \key es \minor as' bes' des'' bes' ges' es' as' as' } is
>> transposed, most flat notes aren't affected (because \transpose doesn't
>> create triple flats), but some are - and intervals change, for example first
>> one changes from major second to diminished third.
>> 
> 
> because LilyPond does not have a way to display a triple flat, so a year ago
> Neil made LilyPond automatically convert triple sharp/flats to their 
> enharmonic
> equivalent so at least something would be printed.

So this is bad. It is better to make possible to print an arbitrary number of 
accidentals, so that one can see what is going on.

Hans





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