Antonije Tot is an oud player who posts on facebook about middle eastern microtonal theory. I don't think he has a website to cite.
He has lots of posts and I haven't begun to read them all, but I'll make notes here as I do.
He argues that maqam saba, which he gives as
maqam Saba: D Ed F Gb A Bb C D(b)
can be given a harmonic interpretation by likening it to the third mode of this overtonal harmonic scale:
[8, 9, 10, 11, 12, 13, 15, 16]
which he calls Harmonic Lydian. The third mode has relative frequencies of
[11/10, 12/11, 13/12, 15/13, 16/15, 9/8, 10/9]
and absolute frequencies of
[1, 11/10, 6/5, 13/10, 3/2, 8/5, 9/5, 2]
Tot claims that the first four notes of this approximate the modern Turkish intonation of the Saba tetrachord,
[D, Ed, F, Gb]
in contrast to an older intonation of the Saba tetrachord which can be written otonally as
[12, 13, 14, 15]
which has relative frequencies of
[13/12, 14/13, 15/14]
or absolutely frequencies of
[1, 13/12, 7/6, 5/4]
.
Let's write out the modern Turkish Saba and the older Saba in cents for easier comparison, because they surely don't look related when you view the just fractions:
[1, 11/10, 6/5, 13/10] : [0, 165, 316, 454]c
[1, 13/12, 7/6, 5/4] : [0, 139, 267, 386]c
Maybe I have misunderstood something.
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Tot gives just intonation for 7 tetrachord ajnas, which I appreciate. Here they are in absolute and relative frequency ratios:
Rast : [1, 9/8, 27/22, 4/3] : [9/8, 12/11, 88/81]
'Iraq : [1, 88/81, 11/9, 4/3] : [88/81, 9/8, 12/11]
Nawruz : [1, 12/11, 32/27, 4/3] : [12/11, 88/81, 9/8]
'Oushshaq : [1, 9/8, 81/64, 4/3] : [9/8, 9/8, 256/243]
Abusalik : [1, 256/243, 32/27, 4/3] : [256/243, 9/8, 9/8]
Nawa : [1, 9/8, 32/27, 4/3] : [9/8, 256/243, 9/8]
Hijazi : [1, 12/11, 81/64, 4/3] : [12/11, 297/256, 256/243]
If you make a scale by stacking two Rast ajnas, separated by a Pythagorean major second, then the 'Iraq and Nawruz are found within that scale starting on the 7th and 2nd scale degrees, respectively.
Jins 'Oushshaq is only made of Pythagorean intervals, and in particular it is the rank-2 [P1, M2, M3, P4] tetrachord. Stacking two 'Oushshaq ajnas separated by a Pythagorean major second gives you a Pythagorean major scale, among which the Abusalik and and Nawa ajnas can be found, starting on the 7th and 2nd scale degrees, respectively.
Tot doesn't relate the Hijazi tetrachord to another other ajnas in a similar way.
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In "8 Tones & 15 Tetrachords in a Perfect 4th", Antonije Tot gives frequency ratios for lots of Turkish perdes. I tried figuring out where his more unusual frequency ratios were coming from. My best guess is that he used (33/32), (19/18), (48/47) and (51/50) as super-particular commas to alter 5-limit frequency ratios. For example:
(11/9) / (33/32) = 32/27
(22/9) / (33/32) = 64/27
(44/27) / (33/32) = 128/81
(88/27) / (33/32) = 256/81
(19/10) / (19/18) = 9/5
(171/160) / (19/18) = 81/80
(57/40) / (19/18) = 27/20
(171/80) / (19/18) = 81/40
(171/60) / (19/18) = 27/10
(47/45) * (48/47) = 16/15
(47/40) * (48/47) = 6/5
(47/30) * (48/47) = 8/5
(752/405) * (48/47) = 256/135
(1504/405) * (48/47) = 512/135
(188/135) * (48/47) = 64/45
(94/45) * (48/47) = 32/15
(376/135) * (48/47) = 128/45
(51/40) / (51/50) = 5/4
(51/30) / (51/50) = 5/3
(51/20) / (51/50) = 5/2
(51/15) / (51/50) = 10/3
I want to analyze his perdes more before I talk about them, but here are the ajnas he makes with them:
1) Uşşak (D Ed F G)
2) Bûselik (D E F G)
3) Hicaz (D Ed F# G)
4) Isfahan (D Ed F F# G)
5) Rahevi (D Ed F Gd)
6) Sazkâr (D Ed Fd G)
7) Nihavend (D Eb F G)
8) Segâh (D+ Ed F G)
9) Sabâ (D Ed F Gb)
10) Old Hicaz/Irak (D Ed F+ G)
11) Nişaburek (D E F# G)
12) Sünbüle/Saba Zemzeme/old Hüzzam (D Eb F Gb)
13) Müstear (D+ Ed F# G)
14) Nişaburek alt. (D E F+ G)
15) Hard chromatic (D Eb F# G)
Antonije Tot described enharmonic functions for some of perdes. For example,
He uses one frequency ratio as both a flat minor second over D in maqam Nihavend and a semi-augmented unison over D in maqam Segâh.
He uses one frequency ratio as both a sharp major second over D in maqam Bûselik and a a semi-diminished third over D in maqam Sazkâr.
He uses one frequency ratio as both a flat diminished fourth over D in maqam Sabâ and as a neutral third over D in old maqam Hicaz.
He uses one frequency ratio forth both a sharp major third over D in maqam Hicaz and a semi-diminished fourth over D in old maqams Isfahan and Rahevi.
All of this sounds really good, right? He sounds like a guy who knows the medieval treatises and has figured some stuff out. But he's been posting stuff like this for years and a lot of it differs internally. I wish he had an up-to-date place with all of his current ideas, if not argued rejections of his old ideas.
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