Ozan Yarman thinks he's provided a superior analysis of the 17 tone scale of Safi al-Din al-Urmawi. Yarman is hugely critical of others and hugely self aggrandizing, and often has large errors or critical omissions in his writing. I hate reading his work, but he writes about things I want to learn. Let's see what he has to say.
He's got a paper about it, "The True Tuning of Urmawi: A Katapyknotic Reinterpretation of the 17-tone Abjad System" (Yarman, Berkman, Taşdelen, 2026) and a 40 minute youtube video in Turkish. The youtube video was too slow for me, but I think I've got the gist from the paper.
Urmawi has a drawing in the Kitab al-Adwar of a lute with equally spaced frets between the nut (the lowest, unfingered string position) and the fret that gives a sound 4/3 times the open string frequency. Yarman think that this picture is more important than the text of the book, in which Urmawi describes a Pythagorean intonation for fretting. So Yarman describes a method of dividing up 4/3 into arithmetically equal pieces. Basically, we multiply 4/3 by 7/7, giving 28/21. Then our frets will have frequency ratios with the same numerator, but denominators varying between 21 and 28, i.e. [28/28, 28/27, 28/26, 28/25, 28/24, 28/23, 28/22, 28/21]. Some of these ratios reduce, giving us [1/1, 28/27, 14/13, 28/25, 7/6, 28/23, 14/11, 4/3]. Next Yarman replaces 28/25 with 9/8. He says this is for octave equivalence with other open strings? You'll have more equivalences if you turn them all into Pythagorean ratios, dude. But these two ratios only differ by 225/224, so whatever.
Here are the intervals justly associated with those frequency ratios (with 9/8 instead of 28/25):
[P1, Sbm2, ReSbAcM2, AcM2, Sbm3, DsSbd4, DeSbAc4, P4]
To get a full scale, we also need to know how the strings, all fretted with the same spacing, compare in their open string frequency ratios. Yarman says that the strings are [D2, G2. C3, F3, Bb4, Eb4]. He also places the root of his scale on C3 and describes the other strings in relation to it, with Pythagorean ratios for separation: [9/16, 3/4, 1/1, 4/3, 16/9, 64/27]. That all looks good.
If I combine every fret interval with every open string interval, and raise or lower by octaves until all the results are in the range [1/1, 2/1], then I get a huge scale. Here it is in both intervals and frequency ratios:
[P1, Sbm2, ReSbAcM2, DsSbGrd3, AcM2, DeSbm3, Sbm3, Grm3, ReSbAcM3, DsSbd4, SbGrd4, AcM3, DeSbAc4, ReSb4, SbAc4, P4, DsSbd5, SbGrd5, DeSbAc5, ReSb5, DsSbGrd6, P5, DeSbm6, Sbm6, Grm6, ReSbAcM6, DsSbGrd7, AcM6, DeSbm7, Sbm7, Grm7, DsSbd8, SbGrd8, DeSbAc8, ReSb8, P8]
[1/1, 28/27, 14/13, 224/207, 9/8, 112/99, 7/6, 32/27, 63/52, 28/23, 896/729, 81/64, 14/11, 448/351, 21/16, 4/3, 63/46, 112/81, 63/44, 56/39, 896/621, 3/2, 448/297, 14/9, 128/81, 21/13, 112/69, 27/16, 56/33, 7/4, 16/9, 42/23, 448/243, 21/11, 224/117, 2/1]
That's not the scale that Yarman shares. Instead, Yarman just ignores any frequency ratio >= 1/1 and <= 2/1. Which means that the two lowest strings, D2 and G2, and the highest string, Eb4, aren't participating in the scale at all. And now it becomes clear what Yarman meant by "octave equivalence" when he was justifying altering the third fret: the third fret of the Bb string is C4. He just wanted to go from C to C. The rest of the scale doesn't repeat. Fine.
Here's Yarman's little scale in intervals and ratios:
[P1, Sbm2, ReSbAcM2, AcM2, Sbm3, DsSbd4, DeSbAc4, P4, SbGrd5, ReSb5, P5, Sbm6, DsSbGrd7, DeSbm7, Grm7, SbGrd8, ReSb8, P8]
[1/1, 28/27, 14/13, 9/8, 7/6, 28/23, 14/11, 4/3, 112/81, 56/39, 3/2, 14/9, 112/69, 56/33, 16/9, 448/243, 224/117, 2/1]
You might wonder how this compares to the Pythagorean scale that Urwawi actually describes in this text or to 24-EDO for that matter. Let's just talk about the intervals a little first.
The scale has a Zalzalian neutral second of 14/13. I don't think you need that for any maqamat rooted on C or D or Ed, but maybe it's useful for other modes.
It has a sub-minor second instead of a minor second. A little odd, but cool.
It has a normal major second, but a sub-minor third instead of a grave minor third.
It has an unusual ratio for the neutral third of 28/23 @ 341c, but the placement isn't that odd. It also has an unusual ratio for the major third of 14/11 @ 418c, but it's only 10 cents higher than Pythagorean.
It a normal has P4 and P5, but between them we have a tritone of 56/39 at 626 cents and a half flat tritone of 112/81 at 561 cents.
We've got a sub-minor sixth instead of a grave minor sixth.
There's a neutral sixth of 112/69 @ 839c. Weird ratio, but okay.
The major sixth is a weird ratio but not that weird in its placement with 56/33 @ 916c.
The scale has a normal Pythagorean minor seventh, and then a neutral seventh of 448/243 at 1059c which is fine.
The scale's major seventh at 224/117 @ 1124c is fine. It's 15 cents sharp of Pythagorean, but maybe that gives us a stronger pull toward the octave.
It's a pretty good scale melodically. I almost hope that it's real, because I like sub-minor sounds and I've been surprised how little they show up in other middle eastern intonation analyses. While the scale is good melodically, it's obviously hot garbage harmonically.
The paper has much more content than this - it discusses modes at length, but it's not a clear presentation. I might try to decipher some other day when I'm not already angry from reading Yarman.
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