Safi al-Din's genera, 17-tone Pythagorean tuning and Ud fretting

Dear tuning list members, attached are SCALA scale files containing the genera (divisions of the tetrachord or pentachord) defined by Safi al-Din Urmavi in his "Risala al-Sharafiyyah", his 17-tone Pythagorean tuning, and specified ratios for fretting the Ud (Lute).

Manuel, may I request that you add these to the SCALA scale archive?

The first genus fully described is Isfahan, which gives the impression that it should be performed by playing steps 4 3 2 3, then coming to a rest, then concluding with 3 2 1 0:

Isfahan genus by Safi al-Din Urmavi
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0: 1/1 0.000 unison, perfect prime
1: 13/12 138.573 tridecimal 2/3-tone
2: 7/6 266.871 septimal minor third
3: 5/4 386.314 major third
4: 4/3 498.045 perfect fourth

An offshoot of Isfahan is Rahevi, which lacks the pure fourth above the tonic and gives the impression of Saba, except that the genus spans a 5-limit major third instead of a 7-limit one:

Rahevi genus by Safi al-Din Urmavi
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0: 1/1 0.000 unison, perfect prime
1: 13/12 138.573 tridecimal 2/3-tone
2: 7/6 266.871 septimal minor third
3: 5/4 386.314 major third

Here comes Zirefkend-i Koutchek, with apparently either the second or the third step as the alteration tone:

Zirefkend-i Koutchek genus by Safi al-Din Urmavi
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0: 1/1 0.000 unison, perfect prime
1: 10/9 182.404 minor whole tone
2: 5/4 386.314 major third
3: 9/7 435.084 septimal major third, BP third
4: 39/28 573.657
5: 3/2 701.955 perfect fifth

Related to Zirefkend-i Koutchek is Zirefkend, with the sole difference that 5/4 is omitted from the scale:

Zirefkend genus by Safi al-Din Urmavi
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0: 1/1 0.000 unison, perfect prime
1: 10/9 182.404 minor whole tone
2: 9/7 435.084 septimal major third, BP third
3: 39/28 573.657
4: 3/2 701.955 perfect fifth

Yet, It seems that Safi al-Din is persistant on calling the genre containing two 5:4 intervals as Zirefkend that he defines as Mujannab(J)+Mujannab(J)+Bakiye(B) later on in the Edvar section (65536:59049 x 2187:2048 x 256:243). In the rendition below, the span is most likely as far as 5/4 on the 3rd step in confirmation with J+J+B:

Zirefkend genus by Safi al-Din Urmavi that confirms with the 17-tone Edvar on Zirefkend
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0: 1/1 0.000 unison, perfect prime
1: 10/9 182.404 minor whole tone
2: 6/5 315.641 minor third
3: 5/4 386.314 major third
4: 9/7 435.084 septimal major third, BP third
5: 39/28 573.657
6: 3/2 701.955 perfect fifth

I enjoy to think of Buzurk as following the melody 5 4 3 2 1 2 and going to a cadence using 5 4 3 2 0:

Buzurk genus by Safi al-Din Urmavi
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0: 1/1 0.000 unison, perfect prime
1: 23/22 76.956
2: 9/8 203.910 major whole tone
3: 39/32 342.483 39th harmonic, Zalzal wosta of Ibn Sina
4: 39/28 573.657
5: 3/2 701.955 perfect fifth

Following are four unnamed genera that I identify with Nihavend, Ushshaq, Karjighar and Saba/Rast respectively:

Unnamed genus by Safi al-Din Urmavi (Nihavend-like)
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0: 1/1 0.000 unison, perfect prime
1: 16/15 111.731 minor diatonic semitone
2: 32/27 294.135 Pythagorean minor third
3: 4/3 498.045 perfect fourth
4: 18/13 563.382 tridecimal augmented fourth
5: 3/2 701.955 perfect fifth

Unnamed genus by Safi al-Din Urmavi (Ushshaq-like)
|
0: 1/1 0.000 unison, perfect prime
1: 13/12 138.573 tridecimal 2/3-tone
2: 7/6 266.871 septimal minor third
3: 4/3 498.045 perfect fourth
4: 18/13 563.382 tridecimal augmented fourth
5: 3/2 701.955 perfect fifth

Unnamed genus by Safi al-Din Urmavi (Karjighar-like)
|
0: 1/1 0.000 unison, perfect prime
1: 14/13 128.298 2/3-tone
2: 7/6 266.871 septimal minor third
3: 4/3 498.045 perfect fourth
4: 18/13 563.382 tridecimal augmented fourth
5: 3/2 701.955 perfect fifth

Unnamed genus by Safi al-Din Urmavi (Saba/Rast-like)
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0: 1/1 0.000 unison, perfect prime
1: 8/7 231.174 septimal whole tone
2: 26/21 369.747
3: 4/3 498.045 perfect fourth
4: 18/13 563.382 tridecimal augmented fourth
5: 3/2 701.955 perfect fifth

To complicate matters, you can scrutinize below the Ud ratios given by Urmavi spanning the tetrachord. Whether it is possible to execute the above-said genera over these frets is for the eye of the beholder:

Ud finger positions or frets by Safi al-Din Urmavi
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0: 1/1 0.000 unison, perfect prime
1: 256/243 90.225 limma, Pythagorean minor second
2: 18/17 98.955 Arabic lute index finger
3: 162/149 144.818 Persian neutral second
4: 54/49 168.213 Zalzal's mujannab
5: 9/8 203.910 major whole tone
6: 32/27 294.135 Pythagorean minor third
7: 81/68 302.865 Persian wosta
8: 27/22 354.547 neutral third, Zalzal wosta of al-Farabi
9: 81/64 407.820 Pythagorean major third
10: 4/3 498.045 perfect fourth

The most puzzling part comes as I provide the 17-tone Pythagorean Abjad notation that Safi Al-Din uses to elucidate the Edvar (modes spanning an octave, such as Rast, Isfahan, Zirefkend, Buzurk, etc...). Now, how can make any sense of the evident incompatibility of these three approaches?

Safiyuddin's 17-tone pythagorean scale
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0: 1/1 0.000 unison, perfect prime
1: 256/243 90.225 limma, Pythagorean minor second
2: 65536/59049 180.450 Pythagorean diminished third
3: 9/8 203.910 major whole tone
4: 32/27 294.135 Pythagorean minor third
5: 8192/6561 384.360 Pythagorean diminished fourth
6: 81/64 407.820 Pythagorean major third
7: 4/3 498.045 perfect fourth
8: 1024/729 588.270 Pythagorean diminished fifth
9: 262144/177147 678.495 Pythagorean diminished sixth
10: 3/2 701.955 perfect fifth
11: 128/81 792.180 Pythagorean minor sixth
12: 32768/19683 882.405 Pythagorean diminished seventh
13: 27/16 905.865 Pythagorean major sixth
14: 16/9 996.090 Pythagorean minor seventh
15: 4096/2187 1086.315 Pythagorean diminished octave
16: 1048576/531441 1176.540 Pythagorean diminished ninth
17: 2/1 1200.000 octave

Cordially,
Oz.