To Gene Ward Smith

Unfortunately for Turkish Music Theory, there is only one widely acclaimed standard which makes a mockery of the proper application of microtones in western notation. This is none other than the Arel-Ezgi system based on 24 pitches distributed unevenly in an octave (in rudimentary terms: 0. 1. 4. 5. 8. 9. commatic degrees per whole-tone). Perceive this as nothing more than a crudely detailed version of 12-tone temperaments common in the west, coupled with an apathetic disregard for ditones. Yekta was the pioneer of this standard, which he advocated fervently as a comprimise against the spread of 12-tone polyphony whose purpose was set to discard maqam music entirely during the Kemalist era.

Lately, the tendency is to punch these Arel-Ezgi pitches out of 53-EDO, and dump the rest as `unnatural sounds`. The less acknowledged theory is that of Karadeniz with 41-pitches unevenly distributed throughout the octave (similar to mine, but different in several ways). There is also a general movement encouraging the fabrication of several other theories based on any number of pitches in between. My personal opinion is that almost all these endeavours are very primitive approaches that cannot even begin to scratch the surface of what you people have been doing for the past half-century. This should not come as a surprise to you then if I tell you that the majority of Turkish theorists do not even have an inkling as to what a quarter-tone is, or what it sounds like (thanks mostly to the scholastic baubles of Yekta-Arel-Ezgi tradition).

The temperament I put forth is a combination of the 12-tone system with the microtones used in maqam music in every degree possible. I have swept the entire microtonal spectrum with the flexible symbols that allow any transposition to be made over any particular tone. A detailed version of this 41-tone system is the 51-JI Temperament that you will find on 17-18. Notice that the interval dubbed `mucenneb` is expressed with three different ratios. I suspect the flexible nature of arbitrary microtones such as this could point to hundreds more.

So if you attribute a symbol to each of these values, you will arrive at 36-tones per octave:

C +1/8 +1/4 +1/2 X
BB -1/2 -1/4 -1/8 D

If you split the half-tone into a limma and an apotome, you will arrive at a quasi-equal 41-tone octave temperament.

If you raise the flexibility of the quarter-tone region in simpler notated tonalities, you can increase the number of tones to 51-JI and further.

Please excuse any mistakes in my terminology, hope this helps.

Ozan