Arabic, Turkish, Persian
Along with the Indian tradition, the music of the Middle and Near East (Arabic, Turkish, and Persian) is one of the important microtonal music traditions.
A central concept is "maqam" (pl. maqamat), which corresponds somewhat (but not exactly) to the Western "mode". An introduction to maqam theory can be found on http://www.maqamworld.com. The Arabic maqam and Turkish makam systems differ to some degree from the related Persian system of dastgah.
The use of microtones in these systems can be extremely subtle, as is demonstrated in a podcast by Arabic violin player Sami Abu Shumays: by his count, there could be 12 different notes within a half step.
Maqamat in equal temperaments
There have been various endeavors, also in recent history, to establish a common tuning standard. A few of these are described in a paper by Ozan Yarman. However, none of these have been really successful (at least not as successful as 12edo in Western music). Given the subtleties sketched in the above mentioned podcast, this task is certainly nontrivial, if not finally impossible.
Depending on the accurateness that is wanted, we can distinguish different levels.
An absolute minimal rule set a tuning system for maqams has to fulfill could be summarized as follows:
- There have to be minor and major seconds, minor and major thirds, pure fourths and the octave complements of all these. Preferably organized in a "sort-of pythagorean" structure.
- Additionally, at least one type of neutral second and neutral third is necessary.
The maqamic temperament reflects this concept in the framework of regular temperaments. Maqamic temperament can be realized in any equal temperament that supports 188.8.131.52 maqamic, including 17c (the important non-patent val for 17edo), 24edo, 31edo, and 55edo.
Systems that just fulfill level 1 are still generally considered bad compromises. An additional quite basic requirement for a more accurate maqam system is the availability of two kinds of neutral seconds, a smaller one for the Bayati tetrachord and a larger one for the Rast tetrachord. Moreover, the major second whould preferably be a "major" wholetone, while the minor second should be a "small" semitone - as a consequence, the wholetone is to be divided into a smaller semitone (limma) and a larger one (apotome). I.e. minor seconds will be available in two varieties, too.
For turkish music, Ozan Yarman also proposes 34edo, 41edo and 46edo, within limits also 29edo, as acceptable compromises. 29edo, 34edo and 41edo have the property that the larger neutral second has a character close to a minor wholetone, and, playing the Rast maqam with it, the third note is less a neutral third than a 5/4-style major third. This matches the turkish variant of Rast which indeed has such a third - the arabic variant, however, is lower. 41edo, 34edo and 29edo can thus be considered suited for turkish music but less so for arabic music.
And here we see another nemesis of the tentatives to establish a common tuning standard: there is not one middle-eastern system but many. There are, by the way, not just differences between arabic and turkish systems but also regional differences within the respective cultures...
Even 53edo and 72edo , although already containing much more pitches than many westerners can imagine, do not cover all details. For these. there are some other, still larger subdivisions that have been investigated.
A system that meets the tuning needs to a satisfactory degree is proposed in Ozan Yarman's dissertation (also summarized in the mentioned paper ): a 79-tone MOS subset of 159edo. A short description (quoting a post to the tuning list) is also here.
Unequal temperaments for maqamat
In equal temperaments, as seen above, there is always a tradeoff between the diverging requirements of high pitch accuracy and a manageable pitch count. One possible way out of this dilemma is use of unequal temperaments. These allow for playing of multiple maqamat with comparatively few notes, with, on the other hand, restrictions in the possibilities to modulate.
All these and more are available in the scala file archive.
If high pitch accuracy and possibilities to modulate are emphasized and the number of pitches matters less, we get systems as developed by Julien Jalaleddine Weiss, going beyond 100 different pitches per octave. See tuning systems for the qanun , or Stefan Pohlit's dissertation.
Arabic Maqam World (Johnny Farraj, Sami Abu Shumays et al)
The Oud (David Parfitt, discusses both Arabic and Turkish maqâm theory)
ALSIADI.com (focuses on Halabi/Aleppo traditional music; describes maq'â'm'â't in terms of 53-tone Pythagorean tuning)
Tetrachords and Makams of Turkey - another theory site
http://www.turkishmusicportal.org - listening
http://www.turkishmusic.org - listening
http://www.turkishmusic.org/index18.html - listening
http://www.oudforguitarists.com/arabic-and-persian-music-maqam-dastgah-comparison/ - comparison between arabic maqamat and persian dastgahs.
Encyclopaedia Iranica - Encyclopedia about iranian culture, including music.