Re: turkish accidental "eksik bakiye" missing in emmentaler font

[Hans Aberg]

On 28 Nov 2013, at 03:54, Keith OHara <address@hidden> wrote:

>>>>> Philippe Ploquin <philippeploquin <at> neuf.fr> writes:
>>>>>> The accidental called "eksik bakiye" is missing in lilypond.
> 
> On Wed, 27 Nov 2013 12:08:02 -0800, Hans Aberg <address@hidden> wrote:
> 
>> In the Ph.D. thesis by Ozan Yarman, "79-tone tuning & theory for Turkish 
>> maqam music", p. 90 (PDF 106), he mentions the “eksik bakiye” or "diminished 
>> limma" of AEU. Looking a bit further in the tables, AEU apparently uses 
>> Pythagorean limit only, that is 3-limit, and not 5-limit.
>> 
>> So it should be a Pythagorean comma, it seems, though in E53 approximations, 
>> the values become the same.
>> 
> 
> I see.  This thesis has the 'eksik bakiye' altering the frequency of the 
> pitch by a fraction 3^17 / 2^27.  

Apparently, “eksik” means “diminished”, and “bakiye” means “limma”.

> That would seem to be motivated by mathematics rather than traditional 
> harmony.  

There is not much harmony, or problems with beats of simultaneous pitches, 
outside CPP music, mostly perfect fourth and fifths. So one can choose values 
quite freely.

> There is not one example in that thesis of its use in music, so it must be 
> very rare.
> 
> Since 'makam.ly' has the flat of the same size, it makes sense to have the 
> sharp just in case transpose.

There is also Ozan Yarman, “A Comparative Evaluation of Pitch Notations in 
Turkish Makam Music”, which does some comparisons.

At least the Arab tune system comes from Persian music, and the latter is 
described by Hormoz Farhat, “The Dastgah Concept in Persian music”. The 
construction goes back to 13th century Safiaddin Ormavi. 

> Also, the same glyph is used in Sabat's version of Helmholtz-Ellis notation, 
> so it seems generally useful.

Since there is so much confusion about the microtonal accidentals, I like the 
idea of using arrows for the 5-limit. In my regularE53.ly, I set it so that the 
accidentals used in Arab music agree with a Persian interpretation, which from 
a little testing seems OK also in Arab music. 

The LilyPond file for Arab music otherwise sets it to E24, but it has long been 
known that is not correct with respect to actual practise, cf. the reference to 
the 1932 Cairo Congress of Arab Music [1-2], which Bartók Béla attended.

The Persian LilyPond is set in E60 - it could now be changed to E53. But the 
Persian microtonal accidentals koron and sori are still missing in LilyPond. 
The average values that Farhat gives fits well with Pythagorean tuning where 
the sori raises two syntonic commas and koron lowers three, or the 
corresponding approximation in E53.

1. https://en.wikipedia.org/wiki/Arabic_music
2. https://en.wikipedia.org/wiki/Cairo_Congress_of_Arab_Music

3. 
https://upload.wikimedia.org/wikipedia/fa/7/7e/Koron_and_Sori_Signs_64x128.png
4. http://musescore.org/node/11423