Tuning systems, theoretical and performed
There is a lot of confusion as to the tuning systems of music in the makam/ maqam system. Particularly, scholars from Turkey and Egypt have developed sophisticated theories
to justify particular symmetrical tuning systems, but in reality, musicians play altogether something different.
The work of Safi al-Din (c. 1293) describes the tuning of scales based on 17 unique notes per octave. This is significant, since some fretted instruments from Turkey and Egypt,
capable of playing more than 12 notes to the octave, have frets that allow exactly 17 unique pitch classes. The baglama-saz and divan-baglama
are examples of modern instruments with this ancient tuning system in mind. Some Arab quarter-tone accordions, as well, offer 5 additional non-Western notes.
Additionally, one can define a hierarchy of important pitches based on modes (maqamat) at root position. This root position limitation restricts possible tonics to three primary:
G, A, and B "half-flat", as can be seen on the following diagram:
Now, moving to modern Turkish music, we find that with 17 notes we can represent the most common of Turkish folk and classical music modes,
though Turkish notation would describe these notes differently. Thus, the baglama-saz, the national instrument of Turkey,
is capable of playing all the common makams at root position without moving any frets.
However, one of the most common aspects to the improvisatory genre known as taksim is the use of modulation, and in particular makams modulated fromt their root position.
Thus, we find that the five non-Western notes required to represent root-position music, in transposition, form a set of somewhere between 24 and 36 unique pitch classes per octave.
Additionally, some performers and ensembles perform multiple subtle variants on one or more of the pitches: thus where I loosely mentioned two distinct notes that Western musicians may mistakenly think of as
E "half-flats," there are in fact sometimes three unique notes with this designation. Thus, where Western music has the pitches:
we would find the following potential pitches in use in standard repertoire in Turkey and Egypt:
Arab music theory versus practice
In 1931, the Cairo Congress was organized to discuss Arab music, and part of the meeting was devoted to attempting to define a universal intonation system for music of the Arab world.
Scholars, both Arab and European, as well as musicians from each country, were brought to the conference, and debated the musical characteristics of Arab music.
The main conclusion of the congress determined that Arab music could be adequately represented by a 24-note equal tempered system (all the Western notes plus the quarter tones in between).
But, at the last minute, there was discussion that two or three extra notes were needed in order to represent the most commonly played forms of several particular makams.
Thus, the official system is 24 notes equal tempered, with a defacto understanding that three extra pitches (higher versions of the E-half-flat and B-half-flat used in maqam Rast specifically,
and a lower E flat to be used in makam Nahwand) are necessary.
In practice, musicians in certain groups still play with intonations that draw more on the older style of playing;
the half flats might be a bit lower than the "technically accurate" quarter-tone for certain makams and higher for other.
Turkish music theory versus practice
In a similar move, Turkish musicologists decided that the Turkish system, which historically had not been rigorously theorized, required an equivalent system,
but without the "plus 3" assymetrical aspects of the Arab system. In the system that developed, the octave is divided into 53 equal-tempered notes to the octave
(yet through some funny math scholars deny that the intervals are indeed equal tempered and thus "out of tune" in relation to the harmonic sequence),
of which 24 are named and perhaps 36 are commonly used. The fundamental interval of Turkish music is called the koma (comma),
which is defined as being 1/9 the interval between any Western equal-tempered whole step (for example, between C and D there are 9 koma).
Though in theory this sounds great, it was not based on a rigorous measurement of intervals actually played by musicians of the time.
When one listens to Tanburi Cemil Bey or Sukru Tunar recordings, for example, so-called "1-comma flat" intervals are played consistently lower (1.5 commas or so),
while so-called "4-comma flat" intervals are played quite a bit higher (between 2 and 3 commas flat, or more close to the Arab quarter tone than to the notated pitch).
In some modes, slight intonation discrepancies are consistently used when the melody is going up, while a lower intonation is used for descending passages.
Though this can't be adequately notated with the current Turkish system, the older ways of tuning things have been passed down and by and large continue unchanged,
though some musicians today use strict 1 and 4 comma intervals rather than the in-between notes.
Thus, Arab and Turkish music are similar in that complex, mathematically-derived theories dominate published work on makam,
while musicians perform something different than the specifically notated music, or perform with an understanding that there is a system for translating the notated pitches into the actually played pitches.