I am new into turkish music (actually I am new into music theory in general). I opened this post because I wonder why just some few makams from all the possible ones are used.
I guess that the main reasons are subjective after centuries of searching for the most beautiful ones. However, without any background into music theory, I studied with my field of expertise why some makams are more popular than others. But I would appreciate any other explanation.
A Makam is a one octave scale (53 turkish commas) of 8 notes formed by combining a tetrachord and a pentachord, with a separation of 22 and 31 commas respectively. For example the tetrachord-serie Rast  is the interval [9 8 5] and the pentachord-serie Rast is the interval [9 8 5 9].
With 53 commas, there are 210 tetrachords-series than span 22 commas, and 4060 pentachords-series than span 31 commas. This translates into 11130 (210 x 53) possible tetrachords and 215180 possible pentachords (4060 x 53). However, as far as I know, not all the commas are used in the turkish music, but just some of them . This means that most of tetrachord and pentachord series cannot be transposed to all positions because some notes cannot be played. For example, with the 32 common commas, the tetrachords are reduced to 1936 and the pentachords to 21760.
The total number of makams is not the multiplication of the later numbers, because the first note of the pentachord is the last note of the tetrachord. The actual number of possible makams with the 32 commas is 762960 in 237106 makam-series, which is still a large number.
In the figure below I plot the number of transpositions for a given makam-serie. The X axis is the 210 possible tetrachord-series, the Y axis is the 4060 possible pentachord-series. The Z axis are the number of times the combination of a given tetrachord and pentachord can be transported. The red spots are Kurdi, Hicaz, Uşşâk/Husseyin, Bûselik, Çârgâh and Rast tetrachord/pentachord-series combination.
Most of the combinations (around 70%) can never be played. What I found interesting is that the basic makam-series are actually the ones that can be transposed the most, which is not surprisingly because I guess is essential when combining instruments with different tuning.
For example the Çârgâh/Çârgâh, Bûselik/Çârgâh and Kurdi/Bûselik combination can be reproduced at 15 different notes, while the Hicaz/Hicaz just at 8 notes.
In the next figure I show the total number of times a tetrachord/pentachord-series can be used. The red spots are the basic series in the same order I described above. The Kurdi, Bûselik, Çârgâh are the ones that can be reused the more, but there are other series that seem more suitable for music composition than the Usak, Rast or Hicaz. I wonder why and if there are other issues I am missing.
thanks in advance.