Syrian Jewish Maqamat

The Syrian Jewish community uses Arabic maqamat in their liturgical music. I learned about it from Mauro Braunstein of OffTonic.com, who notates his ajnas in 53-EDO. I don't expect it to be terribly different from other sources on Arabic Maqamat, but we're going to see.

: The Syrian Jewish Ajnas

First, the ajnas. Two of Braunstein's ajnas span a neutral third at 15\53 steps.

Jins Mustaar: [10, 5]

Jins Siga: [6, 9]

Three ajnas span a Pythagorean major third at 18\53 steps:

Jins Saba: [6, 7, 5]

Jins Saba Zamzama: [4, 9, 5]

Jins Saba Busalik: [9, 4, 5]

Most of the ajnas are true tetrachords spanning a perfect fourth at 22\53:

Jins Ajam: [9, 8, 5]

Jins Bayat/Bayati: [6, 7, 9]

Jins Busalik/Nahwand: [8, 4, 10]

Jins Hijaz: [5, 12, 5]

Jins Kurd: [4, 9, 9]

Jins Nahwand: [9, 4, 9]

Jins Rast: [9, 7, 6]

Jins Awj Ara: [6, 13, 3]

And finally we have two pentachords spanning a perfect fifth of 31 steps of 53 edo:

Jins Athar Kurd: [4, 9, 13, 5]

Jins Nawa Athar: [9, 5, 12, 5]

: Comparing Syrian Jewish Ajnas With Alsiadi's Syrian Ajnas

Remember Alsiadi, the Syrian oud player who described Arabic maqamat, perhaps with a Syrian intonation, in 53-EDO? Now we have Jewish Syrian Arabic maqamat in 53-EDO. Or at least we have the ajnas. How similar do they look?

The two authors agree on jins Rast as [9, 7, 6], jins Kurd as [4, 9, 9], jins Sikah/Siga as [6, 9], jins Nahawand/Nahwand as [9, 4, 9], jins Bayati as [6, 7, 9],  And that's where the agreement ends!

Alsiadi uses both jins Nahawand and jins Busalik, but always with the same tuning, while Braunstein uses [8, 4, 10] for jins Busalik  and [9, 4, 9] for jins Nahwand.

Alsiadi's jins Ajam is a Pythagorean [9, 9, 4] while Braunstein's is [9, 8, 5].

Alsiadi gives us two version of Hijaz, [4, 14, 4] and [5, 13, 4], and neither of these matches Braunstein's [5, 12, 5].

Alsiadi gives a Musta'ar trichord of [11, 4] and a Musta'ar pentachord of [11, 4, 14, 2]. Braunstein only has a trichord, tuned to [10, 5].

Alsiadi gives jins Awj as [6, 14, 2], and Braunstein gives jins Awj Ara as [6, 13, 3].

Alsiadi has a Saba tetrachord tuned to [7, 7, 4] while Braunstein uses [6, 7, 5]. Alsiadi also gives a Saba pentachord as [6, 7, 4, 14], and doesn't have ajnas called Saba Zamzama or Saba Busalik to match Braustein.

Alsiadi gives jins Nikriz as a AcM2 plus one of his Hijaz intonations, [9, 4, 14, 4], while Braunstein uses the name jins Nawa Athar for his intonation of Hijaz on top of an AcM2, [9, 5, 12, 5].

Finally Alsiadi doesn't have jins Athar Kurd.

I get excited about differences like these between authors who write systematically and confidently and self consistently. Do these differences exist because the Syrian Jewish community plays their music a little differently than the rest of Syria? Or because everyone in the middle east plays things a little differently from their neighbor, even if they're both Muslim or both Jewish or whatever? Or because microtones are hard to hear and perform precisely and all this formalism is a little fake? I don't know! I've mostly gotten to the point where I don't believe in maqam Saba, I just believe that there are five things called Saba taught by five different people. When  you have two people differing like this with the ajnas, it isn't so bad, but, like, in Persian music there are only 12 scales and everyone is in the same country, and you might think there'd be some agreement, but the level of disagreement from one source to another is about this same level, even if you look at 14 sources.

In so much as you believe in e.g. an Arabic Hijaz or a Syrian Arabic Hijaz that isn't specific to the person teaching it, you might try to draw a triangle in 3D frequency space and place a represenative point in the middle of the intonations of Alsiadi and the intonation of Braunstein. It would be something like [4 + 2/3, 13, 4 + 1/3]\53. Isn't that nice? So Syrian.

: Just Detemperings Of Syrian Jewish Ajnas

A few of Braunstein's ajnas are obviously Pythagorean:

Jins Kurd: [4, 9, 9] ~ [256/243 * 9/8 * 9/8]

Jins Nahwand [9, 4, 9] ~ [9/8 * 256/243 * 9/8]

Jins Saba Zamzama has plausible 3-limit and 5-limit interpretations that only differ by a schisma:

Jins Saba Zamzama [4, 9, 5]

~ (256/243 * 9/8 * 2187/2048)

~ (135/128 * 9/8 * 16/15)

The 5-limit interpretations of Ajam and Hijaz look good to me:

Jins Ajam [9, 8, 5] ~ (9/8 * 10/8 * 16/15)

Jins Hijaz [5, 12, 5] ~ (16/15 * 75/64 * 16/15)

And Nawa Athar is simply Hijaz with an acute major second at the start:

Jins Nawa Athar [9, 5, 12, 5] ~ (9/8 * 16/15 * 75/64 * 16/15)

Here are three intonations for Athar Kurd:

Jins Athar Kurd [4, 9, 13, 5]

~ (256/243 * 9/8 * 32/27 * 2187/2048) # 3-limit

~ (256/243 * 9/8 * 1215/1024 * 16/15) # 5-limit

~ (21/20 * 9/8 * 25/21 * 16/15) # 7-limit

Since jins Saba Busalik also has 4\53, 9\53, 5\53, we could reuse those relative intervals from Athar Kurd. But before I did that I found these two intonations:

Jins Saba Busalik [9, 4, 5]

~ (9/8 * 135/128 * 16/15) # 5-limit

~ (9/8 * 21/20 * 15/14) # 7-limit

And they look fine, right? Everything is fine. 

For Awj Ara, the middle interval looks like a Pythagorean minor third, but the other ones could be so many things.

Jins Awj Ara [6, 13, 3]

~ (27/25 * 32/27 * 25/24) # 5-limit

~ (243/224 * 32/27 * 28/27) # 7-limit

~ (88/81 * 32/27 * 729/704) # 11-limit

~ (13/12 * 32/27 * 27/26) # 13-limit

~ (25/24 * 32/27 * 26/25) # 13-limit

In general, I find it hard to detemper neutral intervals from 53-EDO. Like four of these Zalzalian options for Rast will look familiar to you if you've read al-Farabi (and the 5-limit option is discussed in the chapter on Persian Dastgah):

Jins Rast [9, 7, 6]

~(9/8 * 208/189 * 14/13 * )

~(9/8 * 800/729 * 27/25 )

~(9/8 * 128/117 * 13/12)

~(9/8 * 12/11 * 88/81)

~(9/8 * 11/10 * 320/297)

But 53-EDO doesn't narrow down for us which one to use.

Braunstein's jins Bayat/Bayati, [6, 7, 9]\53, has the same relative intervals as Rast in a different order. I don't have a reccomendation for the intonation, but unless you know better, I reccomend being consistent and using the same relative intervals over the two tetrachords.

Braunstein calls one tetrachord "Busalik/Nahwand" with a slash like those are two different names for one thing, and they are the same in some sources, but he also has a separate jins Nahwand at [9, 4, 9]\53 with a plain Pythagorean intonation. I grant that they look similar though. I'm just going to call the non Pythagorean one Busalik from here on. I think it has a nice 7-limit interpretation:

Jins Busalik [8, 4, 10] 

~ (10/9 * 21/20 * 8/7)

Although since the middle 4-step interval didn't change from Nahwand, maybe we shouldn't change its intonation from Pythagorean. Then we might have:

~ (567/512 * 256/243 * 8/7)

~ (10/9 * 256/243 * 729/640)

Those don't look great to me. For the first and last interval, we're basically trying to generate ratios such that {(9/8) * x} and {(9/8) / x} are both low complexity, and also requiring that the interval justly associated with {x} is tuned to 1 step of 53-EDO.  I did a search and found these:

~ (39/35 * 256/243 * 945/832)

~ (891/800 * 256/243 * 25/22)

~ (243/220 * 256/243 * 55/48)

~ (143/128 * 256/243 * 162/143)

But I don't think those are an improvement over the old ones.

The first two neutral intervals of jins Saba outline a Pythagorean minor third at 13\53, so we have some familiar Zalzalian options:

Jins Saba: [6, 7, 5]

~ (27/25 * 800/729 * 2187/2048)

~ (13/12 *  128/117 * 2187/2048)

~ (88/81 * 12/11 * 2187/2048)

~ (320/297 * 11/10 * 2187/2048)

There are also two decent options with a 5-limit minor second at the end instead of the Pythagorean augmented unison:

~ (243/224 * 35/32 * 16/15)

~ (27/25 * 1125/1024 * 16/15)

You might wonder if ajnas in the Saba family should outline a diminished fourth instead of a major third, perhaps a grave diminished fourth (with a just tuning of 512/405), which 53-EDO also tunes to 18 steps. I don't think so. I think it's pretty obvious that Saba exists because someone played both m3 and M3 on an instrument, maybe one that had markers at both palces, and they likes the sound. 

Finally, let's look at intonations for jins Siga and jins Mustaar. They both outline a neutral third at 15\53. I support using whatever 9\53 and 6\53 intervals you use for Rast in Siga, e.g.

Jins Siga [6, 9] ~ (88/81 * 9/8 )

That would mean that jins Siga would outline an AsGrm3, justly tuned to 11/9. If Mustaar has the same size, then we might do

Jins Mustaar [10, 5]

~ (55/48 * 16/15)

~ (8/7 * 77/72)

The mathematician J. E. Littlewood once remarked that every positive integer was one of Srinivasa Ramanujan's personal friends. I'm no Ramanujan, but sometimes I wonder if I have too many friends who are rational numbers.

: Syrian Jewish Maqamat

Braunstein gives his Maqamat in terms of pitches and jins annotations, and the jins annotations occasionally have 53-EDO steps, but not always. I think I'm going to trust that his pitches match his tetrachords, and I'll just share his maqamat in terms of its tonic + jins structure, unless perhaps it's a maqam that we haven't seen before.

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