Uhhh, this is your Captain speaking. I don't know about you folks, but me and the rest of your crew here on Delta flight 11-36 have been getting pretty bored with the classic six translational and rotational dimensions of rigid body motion. Bored, bored, bored. Uhhhh. We talked it over good and long up here. At first we thought about spicing things up with a longitudinal cabin separation. But that doesn't leave much chance for arriving at O'Hare on time, and we're sure not lookin to inconvenience nobody. Scotty said we should do one of those, quote, "sick ass twisty optimus prime transformer changes". Don't worry, folks, I talked him down. No telling which of us would end up in the pilot seat in that scenario, and not all of us can fly as well as I do when we're this hammered. Ultimately we decided a nice little Chiral Flip would be just the thing to make this flight a memorable one. Now, I'm pretty sure I see a toggle here in front of me that would do the trick. No idea what else it could be for. So we're just, uh, just gonna try it. Please remain seated, hold on to something sturdy, and don't be alarmed in a moment if your heart is beating on th'other side of your chest. All according to plan. I'd also like to say, on behalf of Delta Airlines, we thank you for flying with us and we hope to see you again soon. If this works, we might even flip you back next time. Here we go!
Rule Of The Octave In Rast
In middle eastern music, a maqam is a scale with a little extra structure. The structure tells you to play melodic phrases within certain subscales that mostly span a range of a perfect fourth, to ascend and descend at certain times, to dwell on certain notes, and to change certain scale degrees for flavor or to play them differently ascending and descending. The structure might also tell you when it's appropriate to modulate to another scale or scale fragment, which modulations are available to you, how to end a melodic phrases, which stock melodic phrases and rhythms are good to incorporate into your compositions, and other things like that. There's a lot of structure in a maqam, and a lot of it is fuzzy things you pick up by listening to songs written in that maqam, so it's easy to just pretend that a maqam is a scale or a scale and it's subscale structure, but that's not really correct. A maqam has a scale, but it is more than a scale.
The fundamental maqam of Arabic music is called maqam Rast. It has two microtones that can sound a little exotic to the western ear. And it's usually played monophonically (or in in octave in an ensemble, but still having a monophonic texture) or with a very simple harmony consisting of a drone against a monophonic texture.
Middle eastern music that is based on scales like the scale of maqam Rast don't have much microtonal polyphony and I want to do something about it - I want to figure out a way to make beautiful exotic microtonal polyphony. Admittedly, some turkish music has microtonal polyphony, but the dominant pedagogical paradigm for Turkish music is basically 5-limit just intonation, which is barely microtonal. Some Turkish music might be more microtonal than that, but it's hard to find sources about it from which to learn. Byzantine Liturgical chant, that was influenced by early Turkish/Ottoman music, also has microtonal polyphony, but no one seems to know a ton about it - I certainly don't - and that's a topic for a future post. What I want to do here is figure out how to harmonize music in the Arabic maqam Rast. I expect a lot of this work will translate to other Arabic maqamat.
Maqamat have highly variable intonation by region, time period, performer, and sometimes even by performance if the performer isn't that precise. As much as there is a standard intonation for maqam Rast, it's probably found on vynil records from the golden age of Egyptian music and cinema, centered on Cairo, Egypt between 1930 and 1970. There might be a somewhat precise intonation available if you do measurements of those records, but also the Cairo Congress of Arab Music in 1932 couldn't agree on any notational standard for intonation that was more precise than 24-EDO, so while there might be (or might have been) a precise intonation in practice, we can say that there is no theoretical, written pedagogical intonation with a precision below 50 cents.
All of that is just to say that 24-EDO might not be right, but it's hard for anyone to agree on anything better, and I won't feel too bad using 24-EDO intonation in this post. Let's use 24-EDO pitch notation for maqam Rast and see what chords we can build on it.
Here's our scale ascending:
[C3, D3, Ed3, F3, G3, A3, Bd3, C4]
The "d" accidental is a backward flat, which indicates a lowering by one step of 24-EDO. The chromatic pitches traditionally are considered to have a Pythagorean intonation, although the difference between Pythagorean 3-limit and just 5-limit intonation disappears in 24-EDO since that tuning system tempers out the acute unison. The "d" accidental is called a "half flat", and one step of 24-EDO is called a "quarter tone" since four of them make a "whole tone", i.e. a major second. I'll say that again: a half flat lowers a tuned pitch by a quarter tone. One music educator I like a lot on youtube is constantly saying "half flat or quarter flat" and, uh, those aren't the same thing, and it took me a long time to realize he was just using the wrong terms instead of talking about 48-EDO or 53-EDO or something similar that does have quarter flats. In addition to the half-flat accidental "d", there's also a half-sharp accidental "t", which raises the tuning of tuned pitches by one step of 24-EDO.
To start, let's look at which diatonic triads are available for harmonizing maqam Rast. On the first scale degree, ^1 at C natural, I think our best options are
[C, F, A] _ F.maj
[C, G, A] _ C.maj6(no 3), which could also be called A.m7(no 5).
These are not very good chords for a tonic, but they're what we have. I'd really like the tonic pitch of the scale to have a chord that is rooted on the tonic pitch, so I'm leaning toward C.maj6(no 3).
Scale degree two could be:
[D, F, A] _ D.m
or maybe
[D, F, G] _ G.7(no 3)
Scale degree three is hard. How do you harmonize the microtonal {Ed}? We've got {Bd} a perfect fifth over {Ed}, so that's a start.
[Ed, Bd] _ Ed.5
but it's not a triad, and in full generality I'd like to be able to do 4-voice and 5-voice harmony. If we want a minor triad on Ed, we need a tone that is one step of 24-EDO below {G}, i.e. {Gd}, and if we want a major triad rooted on {Ed}, then we need a tone that is one step of 24-EDO over {G}, i.e. {Gt}. But neither of these is in maqam Rast. We'll come back to it.
Scale degree four could be:
[F, A, C] _ F.maj
or maybe
[F, A, C] _ D.m
Scale degree five should probably be:
[G, D, F] _ G.7(no 3)
Scale degree six has a bunch of options:
[A, C, F] _ F.maj
[A, D, F] _ D.m
[A, C, G] _ A.m7(no 5), which could also be called C.maj6(no 3)
The {Bd} at scale degree 7 of maqam Rast only has {Ed} for an obvious harmonic friend:
[Bd, Ed] _ Ed.5 or Bd.4
which makes me a sad camper/panda.
Maqam Rast often has Bb when it descends, which gives us some interesting different options for triads, but it also makes harmonizing {Ed} more difficult. Before we get to the descending scale, let's see how we can mix microtones with chromatic tones.
If we consider Pythagorean tuning and 5-limit just intonation to be chromatic, then the first prime-limit that we could try using to build mixed microtonal+tonal chords is 7-limit. In 7-limit just intonation, the simplest frequency ratios are justly associated with intervals that have "sub-minor" and "super-major" qualities, which are respectively flatter than (5-limit or 3-limit) minor and sharper than (5-limit to 3-limit) major. This isn't a great model for middle eastern microtones, which are conventionally "neutral" in that they are tuned between minor and major intervals of the same ordinal (like a neutral third is between a minor third and a major third), but we can still do some work within the 7-limit system.
A subminor seventh over C is mapped to "Bbd" in 24-EDO, i.e. a step below Bb. If we want a 4-note chord tht has "Bd" for its 7th interval, we just have to raise our C chords up by an augmented unison and the Bbd will transform into a Bd. Here are two chordal options including {Bd}:
[C#, E#, G#, Bd] _ harmonic dominant seventh chord _ [P1, M3, P5, Sbm7]
[C#, E, G#, Bd] _ harmonic minor seventh chord _ [P1, m3, P5, Sbm7]
Now, we don't have most of those notes in Rast, but the E# is enharmonically equivalent to F, since 24-EDO tempers out the diminished second between them. F might be in Rast, but we already *had* a harmonic relationship between an {E} pitch in rast and a {B} pitch in Rast, so this isn't much progress. Still, it's good to know that C# and G# have strong relationship with Bd through 7-limit just intonation.
Another chord that sounds good in 7-limit, if not quite as good in a 24-EDO treatment of 7-limit is
[C#, Ed, G#, Bd] _ Subminor third chord with harmonic seventh _ [P1, Sbm3, P5, Sbm7]
And this nicely contains both Ed and Bd.
The analogous chords that have Ed as the pitch for the 7th interval are:
[F#, A#, C#, Ed] _ Harmonic dominant seventh
[F#, A, C#, Ed] _ Harmonic minor seventh
[F#, Ad, C#, Ed] _ Subminor third with harmonic seventh
the A# in the first chord is enharmonically equivalent to Bb in the descending form of Rast, since 24-EDO tempers out d2, and the A natural in the second chord is already in Rast. Nice.
I think it's good to have an option to harmonize the microtones of Rast with chromatic tones like F#, C#, G#, but it'll still take a little cleverness to use them since they're not in Rast. But now if we want to harmonize {Ed} and {Bd} we have options to introduce either microtonal notes like Gd and Gt or chromatic notes liek F#, C#, G#.
Another nice 7-limit chord is the subminor triad, [P1, Sbm3, P5]. We can reach our Rast microtones {Ed} and {Bd} by rooting this chord on C# and G# respectively:
[C#, Ed, G#]
[G#, Bd, D#]
And for the super-major triad, we have
[Cb, Ebt, Gb]
[Gb, Bbt, Db]
The Ebt is basically the same as Ed and Bbt is basically the same as Bd. How so? There are intervallic interpretations of 24-EDO pitch notation in which they're different - they would certainly be different in 7-limit just intonation, but if we're actually playing in 24-EDO, then they're tuned to the same same frequency ratio over C natural. These new chord pithces like D# and Gb are still not shared with the Rast scale, but they're giving us more options for harmonizing {Ed} and {Bd}.
Instead of rooting 7-limit chords on chromatic tones to hit microtones, let's root a 7-limit chord on a microtone and we'll catch a chromatic tone in the middle.
If we root, [P1, Sbm3, P5] on {Ed} we get [Ed, Gb, Bd].
If we root, [P1, SpM3, P5] on {Ed} we get [Ed, G#, Bd].
To recap: if you want to use a normal diatonic triad on Ed (like a major or minor triad) in order to reach both Ed and Bd in one chord, then you can use a microtonal third interval at Gd or Gt. And if you want to use a septimal triad rooted on Ed in order to reach Ed and Bd in one chord, then you can use a chromatic third interval at Gb or G#. Lots of options.
I'd say our best options for scale degree 3 are:
[Ed, G#, Bd] _ Ed.SpM3
[Ed, Gb, Bd] _ Ed.Sbm3
[Ed, G#, C#] _ C#.Sbm3
[Ed, G#, Bd, C#] _ C#.Sbm3,Sbm7
We'll have to think more about which of these we like.
In 18th century baroque musical practice, there was a thing called a partimento: a bass line with some extra notation about implied harmony that a student or musician could expand to make a full song, often using some partimento-specific rules for the expansion. To a first approximation, you'd harmonize the notes of the bass line according to "the rule of the octave" that describes what voiced chords work well on each bass note, ascending and descending, except in some well defined places you'd harmonize differently to make a strong, functional, chordal cadence to finish a musical phrase. Then, on top of that harmonic skeleton, you'd add melodic motives called diminutions. Now, I'm not a student of 18th century baroque practice, but I'm hoping we can do something similar to partimento practice for maqam Rast: we'll try to specify a "rule of the octave" for Rast, i.e. 3-voice or 4-voice chords for each scale degree ascending and descending, that will make for songs with good voice leading if used on top of (???normal???) bass lines. At the very least, I'm hoping that there will be good voice leading if we just play a bass line that moves up and down by 2nd intervals.
Let's go through triad options for the descending form of maqam Rast first and then we'll try to figure out which chords among those options we will actually use, and what voicings of those chords will make our chord progression sound as good/baroque as possible.
Maqam Rast often has a Bb instead of Bd "when the scale descends". This means 1) when the melodic motion played on top of the scale has an overall descending tendency, but especially this happens 2) after a song section where you had an ascending tendency, reaching a high note, at which point you emphasize that high note by playing riffs that repeat the note or dwell on the note or keep returning to the note, and then you want a contrasting musical phrase that moves down the scale. It's not that every moment you're moving up or down the scale and so you're constantly deciding between Bd and Bb - rather, the song has long broad phases, and you'll use Bb in a later phase of the song.
Here's the descending scale, but still written ascending: [C, D, Ed, F, G, A, Bb, C]
Here are some simple chord options:
^1: F.maj, D.m7, C.maj6(no 3)
^2: D.m, Bb.maj, G.m
^3: ???
^4: F.maj, D.m, Bb.maj
^5: G.m, C.maj6(no 3)
^6: F.maj, D.m, A.m7(no 5), C.maj6(no 3)
^7: G.m, Bb.maj,
We don't have {Bd} to harmonize with {Ed} any more. One option we discovered in our look at 7-limit harmony was
[F#, A#, C#, Ed] _ Harmonic dominant seventh
which has an A# that's enharmonic with Bb in 24-EDO.
if we drap the F# at just look at the top triad, that's a septimal sub-diminished chord,
[P1, m3, Sbd5]
which does indeed sound pretty good in just tuning, [1/1, 6/5, 7/5], and possibly also okay in 24-EDO. (The sub-minor sub-diminished triad, [P1, Sbm3, Sbd5] also sounds good in 7-limit, not that it gets us any closer to the Rast scale.)
So if you want to harmonize Ed in the descending form of Rast, then the best option I can see is probably [Ed, Bb, Db] which is like a Bb sub-diminished triad, although that would more properly be spelled [Bb, Db, Fbd], but we can kind of let it slide since {Fbd} and {Ed} are tuned the same by 24-EDO (and by other tuning systems that temper out d2, the diminished second).
Another option for harmonizing scale degree ^3 that we saw in the ascending form of Rast, and which is still available to us, is
[Ed, G#, C#] _ C#.Sbm3
Although this has two notes that aren't in Rast. If they were semitones below {C} and {G} of Rast, like {B} and {F#}, that feels like it would be good for voice leading, but {C#} and {G#} are kind of out of place, I'd say. You might be thinking "We can do a tritone substituton for G.7 rooted on Db which is like C#", but it doesn't work well in this case. So our best three options for harmonizing Ed in descending Rast are probably:
[Ed, F#, A#, C#] _ F#.maj3,Sbm7
[Fbd, Bb, Db] _ Bb.m3,Sbd5
[Ed, G#, C#] _ C#.Sbm3
We've got some options for chords now. I'm going to try to use these chord options to write a Rule Of The Octave for four voices that fits between [C3, E5], with the bass between C3 and C4 and the other three voices between C4 and E5. We'll see how many rules of voice leading I can follow.
...
Oh, interesting! When I listen to them, the chords I like most for harmonizing Ed and Bb ascending are just made from notes of maqam Rast
[Ed, G, Bd]
[Bd, Ed, G]
Obviously they have the same pitch classes and are inversions of the same chord, but it's a weird chord! It's not major, minor, super major, or subminor. It could be sub-major or super-minor, I guess? But actually, when I listened to the chords, I was listening to an 11-limit detempering in which the "d" accidental flattened things by 33/32 and the "t" accidental sharpens things by 33/32. So, since that chord sounds nice and is in fact closer to Arabic intonation than a septimal detempering, let's call the chord what it really is. For [Ed, G, Bd], the intervals and their just frequency ratios over the nearest C natural below are:
[DeAcM3, P5, DeAcM7] _ [27/22, 3/2, 81/44]
If we root that chord on Ed / DeAcM3 / 27/22, then we get this chord:
[P1, AsGrm3, P5] _ [1/1, 11/9, 3/2]
Rocking Deer Template
From bass to seat height = 214 pixels, and 21.4 inches in wood is a good small rocker height, so let's set our scale so that every pixel is 1/10 of an inch. Then
Legs x4:
80 pixels wide in image, or 8 inches wide in wood.
195 pixels long, or 20 inch long in wood (or 1.6 feet)
Torso x1 (or x2 or x3 for width?):
216 pixels long, or 22 inches long in wood (or 1.8 feet)
83 pixels high, or 8 inches high in wood
Rocking stand:
55 pixels high, or 6 inches in wood
393 pixels long, or 40 inches long in wood (or 3.3 feet)
Head:
...
Most of the pieces can be made from 10 inch wide boards. You'd think they could be made from 8 inch wide boards, but "8 inches wide" is a nominal dimension in lumber, and the boards of that description really measure 7.5 inches. If you want to cut a shape that's 8 inches wide, you need a 10 inch wide board.
I might make a doe or fawn at this scale and then a buck at a larger scale later.
Skeleton Jelly by Mat Brinkman
I am Skeleton Jelly. I am Skeleton Jelly. I am Skeleton Jell. I am Skeeton Jelly. I am Sketeton Jelly. I am Skeleton Jelly.
My brain! ... is made ... of tiny ... animals!
... I am Skullton Jelly. I am Skulltown Jelly? No! I am Skelleton Jelly! I am Skeleton Jelly. I am Skeleton Jelly.
Really? Somebody was just here looking for you.
Skeleton Jelly?
It said if it finds you it will tear you into pieces and eat them.
I am gettin' eaten? I am Skeleton Eating? No! I am Skeleton Jelly. I am Skeletin Jelly. I am Skeleton Jelly. I am Skeleton Jelly.
Well met! Have a drink.
Am I drinking jelly? Am I drunk on jelly? No, I am Skeleton Jelly!
You are Skeleton Jelly? I've been looking for you!
I am Squirxical Jelly. I am Squirclixal Jelly. I am Squirxical Jelly.
Where is your skeleton?
Die-jested.
Do you know where you are?
Citadel City?
Far from it. If you are not careful you will drip to the ruined Ultra Violet City.
Am I Careful Jelly?
Farther below...
Am I Dripping Jelly
Umm dripping to the ruined ultraviolet city?
Qutb al-Din al-Shirazi and the Systematists
Owen Wright is a scholar of medieval middle eastern music. In "The Modal System of Arabian and Persian Music 1250 to 1300", he writes extensively about music theorist Qutb al-Din, a prominent Systematist who wrote just after another prominent Systematist, writer Safi al-Din al-Urmawi, whose 17-tone Pythagorean gamut we've discussed before.
Qutb al-Din wrote extensively and he's a great source about medieval Persian and Arabic music of the time. In this post we'll be exploring his tetrachords (and pentachords and other ajnas) and modes, as relayed by Owen Wright.
Wright remarks that the modes of Qutb al-Din are notated twice, once in frequency ratios and once in pitches, and these are not consistent - clearly derived separately. The pitches weren't in Latin script, they were in Arabic I think, and they were a weird Pythagorean holdover notation from Qutb al-Din's predecessor Safi al-Din, but Owen Wright doesn't write the pitches in Arabic and neither will I. The fact that the frequency ratios and pitches are inconstent in Qutb al-Din's work makes it a little hard to be sure what al-Din is talking about, but it gets worse. Another complication is that the Systematists really like simple frequency ratios even when they weren't true-to-sound. It seems, from reading Wright, that they basically only use Pythagorean or super particular ratios as relative degrees in tetrachords. For example, the only super-particular frequency ratios between a just minor third 6/5 and a Pythagorean major second 9/8, are 7/6 and 8/7, and so when a Systematist needs an interval in that range, you can be pretty sure that they'll grab one of those two, regardless of whether it is sonically appropriate. There is a difference of 111 cents between 6/5 and 9/8, and if we only distinguish two ratios in that range, well, that's roughly a 37-cent granularity, which might be better than 24-EDO, but it's not amazing for nailing down intonation.
For some reason Wright shares the tetrachords in terms of cents instead of ratios, but since there aren't that many frequency ratios that are used by the Systematists, it's easy enough to figure out what arithmetic they're doing behind Wright's notation.
Here's a pentachord from Qutb al-Din as relayed by Wright. He calls it "24b shahnaz":
[G, Ad, Bb, Bd, C, Dd, D]
[139, 128, 49, 139, 128, 49] cents
The cents correspond to these relative frequency ratios:
[13/12, 14/13, 36/35, 13/12, 14/13, 36/35]
Wright points out that these frequency ratios don't form a perfect fifth, but that they should (based on the pitches and other facts, I'm sure). As another example, many ajnas have what would be a neutral third based on the pitch notation, but the frequency ratios have the third at a just major third, 5/4 at 386 cents. This is indeed lower than a Pythagorean major third and thus more in the direction of neutral. And indeed there are arguments that some middle eastern musicians have used 5/4 as a neutral third at some points in history, as many musicians currently do in Turkey. Owen Wright knows all the medieval manuscripts though and says that 5/4 doesn't make sense, and any time 5/4 is written, it should really be interpreted as a true neutral third, as the pitches indicate, i.e. more like 330 to 370 cents. So there's another case where the frequency ratios are probably not correct, and we're better off looking at the pitches, but what a shame because we'd really like a precise rational intonation.
Wright provides his own plausible ranges of cents for each scale degree of the ajnas, presented in little ruler graphics. By measuring the pixels and taking midpoints, I can tell you that this is a prototypical intonation for a medieval shahnaz pentachord according to Owen Wright:
[0, 147, 293, 348, 498, 642, 702]
And a decent representation of that might be
[1/1, 12/11, 32/27, 11/9, 4/3, 13/9 or 81/56, 3/2]
My pixel measuring process is a little bit labor intensive, so I'm not going to provide Wright's intonation everywhere just yet, but I do want to present the Systematist frequency ratios and pitch classes. Partly, these ratios are what was actually written, and I think there is some import to transmitting the history of the music theory veridically. Secondly, these frequency ratios still give us more clues about intonation than the naive 24-EDO interpretation of pitch classes, and I really want to know what the medieval modes sounded like and how they've evolved into modern ones.
...
* Zirafkand-i Kuchek (or Zirafkand, or Kuchek, or Mukhalifak).
Pitches: [G, Ad, Bb, Bd]. // G and Bd are prominent notes.
Absolute: [1/1, 13/12, 7/6, 6/5]
Relative: [13/12, 14/13, 36/35] _ [139, 128, 49]
// Given by Safi al-Din as [14/13, 13/12, 36/35].
* 'Iraq:
Pitches: [G, Ad, Bd] // G and Bd are prominent notes.
Absolute: [1/1, 10/9, 5/4]
Relative: [10/9, 9/8]
* Zawli:
Pitches: [G, A, Bd] // G and Bd are prominent notes.
Absolute: [1/1, 9/8, 5/4]
Relative: [9/8, 10/9]
* Rahawi:
Pitches: [G, Ad, Bb, B] // G is the only prominent pitch.
Absolute: : [1/1, 13/12, 7/6, 5/4]
Relative: [13/12, 14/13, 15/14] _ [139, 128, 119]
* 'Ushshaq:
Pitches: [G, A, B, C] // G is the only prominent pitch.
Absolute: [1/1, 9/8, 81/64, 4/3]
Relative: [9/8, 9/8, 256/243]
* Busalik:
Pitches: [G, Ab, Bb, C] // G is the only prominent pitch.
Absolute: [1/1, 256/243, 32/27, 4/3]
Relative: [256/243, 9/8, 9/8]
* Nawa:
Pitches: [G, A, Bb, C] // No prominent pitch listed.
Absolute: [1/1, 9/8, 32/27, 4/3]
Relative: [9/8, 256/243, 9/8]
* Rast:
[G, A, Bd, C] // G is the prominent pitch.
[1/1, 9/8, 5/4, 4/3]
[9/8, 10/9, 16/15] _ [204, 182, 112]
* Nawruz:
Pitches: [G, Ad, Bb, C] // G and C are prominent.
Absolute: [1/1, 16/15, 32/27, 4/3]
Relative: [16/15, 10/9, 9/8] _ [112, 182, 204]
* 'Iraq (or Ru-yi 'Iraq):
Pitches: [G, Ad, Bd, C] // G and C are prominent.
Absolute: [1/1, 10/9, 5/4, 4/3]
Relative: [10/9, 9/8, 16/15] _ [182, 204, 112]
* Isfahan:
Pitches: [G, Ad, Bb, B, C] // G and C are prominent.
Absolute: [1/1, 13/12, 7/6, 5/4, 4/3]
Relative: [13/12, 14/13, 15/14, 16/15] _ [139, 128, 119, 112]
Here Owen Wright stops us to say that the frequency ratios for jins Isfahan and and the related jins Rahawi are unbelievable, and that the pitch notation is more accurate. Further he notes that jiins Isfahan is clearly derived by adding a major third within jins Nawruz.
I think it's time we looked a little more closely at jins Isfahan, jins Rahawi, and jins Nawruz. From the frequency ratios
Rahawi has Bb at 7/6
Isfahan has Bb 7/6
Nawruz has Bb at 32/27
But from Owen Wright's ruler diagrams, it's clear he thinks that all three are Pythagorean on the chromatic intervals including the Bb, so Rahawi is:
[1/1, ?, 32/27, 4/3]
By eye, it's obvious that Wright's intonation on the second scale degree, the {Ad}, is not much more precise than "some kind of neutral second". I'm tempted to use 13/12, since it's the ratio of the second scale degree used by Qutb al-Din in both jins Isfahan and jins Rahawi. On the other hand, Qutb al-Din uses 16/15 for the second scale degree of Nawruz, which is quite a bit lower, and so maybe we should use 14/13 as a compromise. But I'm not really feeling that. Let's use 13/12 for all of them. Or at least for Rahawi and Isfahan.
Lots of modern middle eastern music theorists, at in the xenharmonic parts I frequent, are very pleased with the idea that Isfahan as a tetrachord is tuned to [12:13:14:15:16]. And since that's how Qutb al-Din described it, ... maybe that's a fine way to play it? I don't know for sure if it's a medieval intonation, but if someone in modern times plays Isfahan like that, I won't be upset. I don't think I've ever seen anyone extend it all the way to a pentachord as
[13/12 * 14/13 * 15/14 * 16/15 * 17/16 * 18/17]
In absolute terms that would be
[1/1, 13/12, 7/6, 5/4, 4/3, 17/12, 3/2]
Maybe no one adds in the tritone because they care more about history than about playing a harmonic series. Anyway, let's keep looking at more ajnas.
* Hijazi:
Pitches: [G, Ad, B, C] // G and C are prominent.
Absolute: [1/1, 12/11, 14/11, 4/3]
Relative: [12/11, 7/6, 22/21] _ [150, 267, 81]
Owen wright says that the major third was probably not sharper than major thirds of other genera, but otherwise he's happy with the ratios:
"This minor adjustment apart, Hijazi is one of the rare cases in which the ratios for a theoretical non-diatonic genus would seem to correspond exactly to intervals used in practice."
Super hot fire, Owen. Way to stick it to the Systematists frequency ratios. Although there are only three relative ratios in the tetrachord, and if we're changing the intonation of the 3rd scale degree, then we have to fiddle with two of them, so is this really any kind of praise? Even at his most congratulatory, Wright is basically saying "Way to get a single frequency ratio right, Qutb."
Anyway, I think this is what Owen Wright would condone for Hijazi:
[G, Ad, B, C]
[1/1, 12/11, 81/64, 4/3] _ [0, 151, 408, 498]
[12/11, 297/256, 256/243] _ [151, 257, 90]
This looks kind of weird to me as a modern intonation for jins Hijaz, but maybe it's a medieval one, sure.
Now we get some pentachords
* 'Ushshaq pentachord:
[G, A, B, C, D] // G is prominent.
[9/8, 9/8, 256/243, 9/8]
* Busalik pentachord:
[G, Ab, Bb, C, D] // G and D are prominent.
[256/243, 9/8, 9/8, 9/8]
Which just add an AcM2 onto the tetrachord of the same name. We also get a pentachord version of the Nawa tetrachord:
[G, A, Bb, C, D]
[9/8, 256/243, 9/8, 9/8]
This jins was mentioned in the "Kitab al-Adwar" by Safi al-Din but not in works by Qutb al-Din, who is normally the more comprehensive source. Apparently this jins doesn't have a historic name, but I think "Nawa Pentachord" suits it just fine. But also, who cares about pentachords that are just tetrachords with AcM2 added on the top. Boring.
* Rast pentachord:
[G, A, Bd, C, D]
Absolute: [1/1, 9/8, 5/4, 4/3]
Relative: [9/8, 10/9, 16/15, 9/8]
* Isfahan-i Asl pentachord (also called Mukhalif-i Rast):
[G, A, Bd, C, C#, D] // G and D are prominent.
Absolute: [1/1, 9/8, 39/32, 21/16, 45/32, 3/2]
Relative: [9/8, 13/12, 14/13, 15/14, 16/15]
Owen wright points that this is an Isfahan tetrachord with AcM2 added at the bottom instead of the top. Mukhalif (or mukhtalif) means "differing" in Arabic, like saying "the other/alternative Rast pentachord. It's worth noticing that these two scales having very different frequency ratios but very similar pitches. You can decide for yourself if this is another point against the frequency ratios or evidence of different intonation for the tones across different ajnas. I will say that 21/16 at 470 cents is noticeably flat of a normal C natural over G at 498 cents, and that the author might have added an accidental to the pitches to drawn attention to this 28 cent difference, which is not really a subtle thing. Although I did mention that Systematists sometimes only have like a 37-cent granularity. I still think someone would have mentioned an impure P4, since pure perfect fourths were maybe considered the highest consonance in medieval middle eastern music.
...
I'm sad and tired.
...
* Husayni pentachord
[G, Ad, Bb, C, D] # G and D are prominent notes.
[1/1, 16/15, 32/27, 4/3, 3/2]
[16/15, 10/9, 9/8, 9/8] _ [112, 182, 204, 204]
* Zirkesh Huseyni pentachord:
[G, Ad, Bb, B, C, D] # G and D are prominent notes.
[1/1, 13/12, 7/6, 5/4, 4/3, 3/2]
[13/12, 14/13, 15/14, 16/15, 9/8] _ [139, 128, 119, 112, 204]
Some 23-limit Otonal Tetrachords
I'll might write in descriptions of these at some point comparing them to ancient Greek and modern Persian/Arabic/Turkish tetrachords. But for now, here are some otonal representations of tetrachords:
[9, 10, 11, 12] [1/1, 10/9, 11/9, 4/3] [P1, M2, AsGrm3, P4]
[12, 13, 14, 16] [1/1, 13/12, 7/6, 4/3] [P1, Prm2, Sbm3, P4]
[12, 13, 15, 16] [1/1, 13/12, 5/4, 4/3] [P1, Prm2, M3, P4]
[15, 16, 18, 20] [1/1, 16/15, 6/5, 4/3] [P1, m2, m3, P4]
[15, 17, 18, 20] [1/1, 17/15, 6/5, 4/3] [P1, ExM2, m3, P4]
[18, 19, 21, 24] [1/1, 19/18, 7/6, 4/3] [P1, Lfm2, Sbm3, P4]
[18, 19, 22, 24] [1/1, 19/18, 11/9, 4/3] [P1, Lfm2, AsGrm3, P4]
[18, 19, 23, 24] [1/1, 19/18, 23/18, 4/3] [P1, Lfm2, NbM3, P4]
[18, 20, 21, 24] [1/1, 10/9, 7/6, 4/3] [P1, M2, Sbm3, P4]
[18, 20, 22, 24] [1/1, 10/9, 11/9, 4/3] [P1, M2, AsGrm3, P4]
[18, 20, 23, 24] [1/1, 10/9, 23/18, 4/3] [P1, M2, NbM3, P4]
[21, 24, 26, 28] [1/1, 8/7, 26/21, 4/3] [P1, SpM2, PrSpGrm3, P4]
[21, 24, 27, 28] [1/1, 8/7, 9/7, 4/3] [P1, SpM2, SpM3, P4]
[21, 25, 26, 28] [1/1, 25/21, 26/21, 4/3] [P1, SpA2, PrSpGrm3, P4]
[21, 25, 27, 28] [1/1, 25/21, 9/7, 4/3] [P1, SpA2, SpM3, P4]
[24, 26, 28, 32] [1/1, 13/12, 7/6, 4/3] [P1, Prm2, Sbm3, P4]
[24, 26, 30, 32] [1/1, 13/12, 5/4, 4/3] [P1, Prm2, M3, P4]
[24, 27, 28, 32] [1/1, 9/8, 7/6, 4/3] [P1, AcM2, Sbm3, P4]
[24, 27, 30, 32] [1/1, 9/8, 5/4, 4/3] [P1, AcM2, M3, P4]
[27, 28, 32, 36] [1/1, 28/27, 32/27, 4/3] [P1, Sbm2, Grm3, P4]
[27, 30, 32, 36] [1/1, 10/9, 32/27, 4/3] [P1, M2, Grm3, P4]
[27, 30, 33, 36] [1/1, 10/9, 11/9, 4/3] [P1, M2, AsGrm3, P4]
[27, 30, 34, 36] [1/1, 10/9, 34/27, 4/3] [P1, M2, ExGrM3, P4]
Maqam Sikah Baladi
Maqam Sikah Baladi is an Arab maqam (rather than Turkish or Persian) with a lot of microtones. We're going to try figuring out some things about it.
MaqamWorld decsribes an associated scale fragment, jins Sikah Baladi, as:
[Ed, Ft, G, Ad, Bd, C]
Those are the base pitch classes that would indicate 24-EDO steps, but they have some extra accidentals that I haven't transcribed.
The Ed is flatter than 24-EDO, the Ft is sharper, the Ad is flatter, the Bd is sharper, and the C is flatter.
If we ignore those extra accidentals, I would notate this in 24-EDO steps as:
[4, 3, 3, 4, 3]\24
If we include the accidentals, we'll have to commit to some kind of step size for the flattening and sharpening. Let's arbitrarily call it 0.25 steps. If it was more than 0.5 steps, then we'd be closer to the next step and the pitches would have been notated differently. With that intonation, we get this for our steps:
[4.5, 2.75, 2.75, 4.5, 2.5]\24.
MaqamWorld says that the tonic/finalis is on G, and that there is no ghammaz.
Oud player Joseph Tawadros describes maqam sikah baladi as
[C, Dd, Ed, Ft, G, Ad, Bd, C]
in a Facebook video. The jins sikah baladi from MaqamWorld is a subset of this, so that's a nice bit of agreement. In 24-EDO these pitch classes are:
[0, 3, 7, 11, 14, 17, 21, 24] // relative
[3, 4, 4, 3, 3, 4, 3] // absolute
with the initial [3, 4] being the relative intervals not accounted for in the jins. And those are the intervals of the normal jins Sikah, so everything looks good so far.
Now let's compare to maqam Sikah Baladi from MaqamWorld. They have it written descending, and I'm sure it's played in a descening way, but I like to write my scales ascending and will do so now.
The maqam starts low with part of jins Sikah baladi (starting in te middle at the tonic on G) and moving up tot that flat C like beofre:
[G, Ad, Bd, C]
Then there's a C# as part of jins "pseudo-hijazkar / suspended 5th"
The pitch classes of this are
[C#, D, Ed, Ft, G]
From the pitch classes, we'd expect this to have an 24-EDO intonation like
[2, 3, 4, 3]
Agai n this has non-24-EDO accidentals, indicating a flat Ed and a sharp Ft. If we use the 0.25 step intonation again, then we get
[2, 2.75, 4.5, 2.75]
Let's compare this jins "pseudo-hijazkar / suspended 5th" to regular jins hijazkar.
MaqamWorld presents jins Hijazkar in terms of major tones as
[3/2, 1/2, 1/2, 3/2] tones
i.e.
[6, 2, 2, 6]\24
with pitches
[Ab, B, C, Db, E, F]
and notes that the C in the middle is the tonic and there is no ghammaz. That looks absolutely nothing like pseudo-hijazkar. It doesn't even have neutral tones. I think we just have to ignore that jins label.
Let's continue on with the maqam from MaqamWorld. Overlapping with jins pseudo-hijazkar we have another jins Sikah Baladi, this time the standard one that stretches from a flat Ed up to a flat C. I will note that there are numbers 1 through 7 starting under the D and moving up to the high C, as through D is the tonic of the whole maqam and it doesn't reach the octave, and the C# in the middle is just a leading tone up to the D.
I'm tempted to ignore the low jins Sikah Baladi since
1) it doesn't give as any new information (being repeated above),
2) it messes up the intervallic structure when we have both C natural and C#, and
3) The tetrachord doesn't even present in full, only including from G up to C instead of from Ed up to C.
If we skip all the notes from the lowest jins, then our maqam Sikah Baladi loos like this:
[(C#), D, Ed, Ft, G, Ad, Bd, C]
Using the same intonation for the non-24-EDO accidentals, this would look like
[(2), 2.75, 4.5, 2.75, 2.75, 4.5, 2.5]\24.
in relative steps, which is an adjusted version of this:
[(2), 3] + [4, 3, 3, 4, 3] \24
Across the whole maqam, including the lower jins Sikah Baladi, the notes which are highlighted as special targets for tonicization and/or ghammazization are [G, Bd, D, G, Bd]. So I don't know why people ever present the scale spanning from C to C.
The maqam Sikah Baladi of Tawadros reaches the octave and has Dd instead of D, but is otherwise quite close.
If we altered the MaqamWorld version of the maqam so that we had a tonic of a 0.25-step-flattened C natural (instead of a leading tone of C#), then the maqam would be:
[4.25, 2.75, 4.5, 2.75, 2.75, 4.5, 2.5]\24.
which does reach the octave. This still differs from Tawadros's maqam in having D natural instead of Dd, but there's more agreement than disagreement.
Navid from OudForGutarists posted a piece in Sikah Baladi with key signature [Ad, Ed, Bd, Ft], which is consistent with these pitches:
[C, D, Ed, Ft, G, Ad, Bd, C]
He starts his phrases on Ed, works up to a few notes to G, and ten works down to a low G where he ends his phrases, so it's more like
[G, Ad, Bd, C, D, Ed, Ft, G]
Anyway, with two sources agreeing on D instead of Dd, I'm going to go with that.
One more data source? There are some video on youtube from user @FantasticoTube that maqamat and look like they're from a website that has gone defunct. Honestly, they look like an early version of MaqamWorld, but perhaps they're unrelated. The FantasticoTube video presents Sikah Baladi twice. The first form looks like this:
[G, Ab, B, C, D, Eb, F#, G]
[1/2, 3/2, 1/2, 1, 1/2, 3/2, 1/2] tones
with arrow accidentals indicating that Ab is played sharper, B is played flatter, Eb is played sharper, and F# is played flatter. Tetrachord annotations describe it as
[Hijaz on G + major second + Hijaz on D]
The second form looks like this:
[G, Ad, Bd, C, D, Ed, Ft, G]
[3/4, 1, 3/4, 1, 3/4, 1, 3/4] tones
It is annotated with jins as
[Sikah on G] + 3/4 + 1 + 3/4 + [Sikah on D]
This version with quarter tones and jins Sikah does indeed move the maqam in the direction indicated by the arrow accidentals from the first form.
So the idea seems to be to alter jins hijaz
[2, 6, 2]\24
by quarter tones to give
[3, 4, 3]\24
which has its first wo intervals the same as a 24-EDO jins Sikah, although this guy here is an actual tetrachord whereas the traditional jins Sikah is just a trichord.
Anyway, the second form form of maqam Sikah Baladi from FantasticoTube has the same pitch classes and arrangement as my summary of Navid's maqam Sikah Baladi ending on G:
[G, Ad, Bd, C, D, Ed, Ft, G]
So now we've got tons of agreement. Here it is in integer steps of 24 EDO:
[3, 4, 3, 4, 3, 4, 3]\24
Using the sub-quarter tone intonation inspired by notes from MaqamWorld (still with 0.25 steps unless you've got a better idea), this is our more precise intonation given this arrangement of pitch classes:
[G (2.75) Ad (4.5) Bd (2.5) C (4.25) D (2.75) Ed (4.5) Ft (2.75) G]
The 24-EDO version does indeed have a repeated structure with tetrachords that are like jins Hijaz adjusted toward jins Sikah:
[3, 4, 3] + T + [3, 4, 3]
Although the repeated structure is less exact in my intonation with the made up 0.25 tone adjustments.
[2.75, 4.5, 2.5] + [4.25] + [2.75, 4.5, 2.75]
I think this is a slight problem. If we adjust the intonation so that the lower group of three relative intervals sum a tempered P4 at 10 steps of 24-EDO, then we get C natural instead of the slightly flat C that MaqamWorld specifies. (The upper group of three relative intervals is already a true tetrachord spanning 10 steps).
I think we need more data to make more conclusions.
If we want to make a just tuning based on the 0.25 step intonation, here's one option:
[P1, Prm2, ReM3, HbAc4, P5, Prm6, ReM7, P8] # [1/1, 13/12, 16/13, 45/34, 3/2, 13/8, 24/13, 2/1] _ [0, 139, 359, 485, 702, 841, 1061, 1200] cents
[Prm2, ReReAcA2, HbPrAcm2, ExM2, Prm2, ReReAcA2, Prm2] # [13/12, 192/169, 585/544, 17/15, 13/12, 192/169, 13/12] _ [139, 221, 126, 217, 139, 221, 139] cents
It looks pretty good in absolute intervals and a little crazy in relative intervals. If we assume adjustments more like 12 cents, then this is a decent tuning:
[P1, AsGrm2, GrM3, HbAc4, P5, AsGrm6, GrM7, P8] # [1/1, 88/81, 100/81, 45/34, 3/2, 44/27, 50/27, 2/1] _ [0, 143, 365, 485, 702, 845, 1067, 1200]
[AsGrm2, DeAcA2, HbAcAcm2, ExM2, AsGrm2, DeAcA2, Acm2] # [88/81, 25/22, 729/680, 17/15, 88/81, 25/22, 27/25] _ [143, 221, 120, 217, 143, 221, 133]
Although I kind of doubt that the maker of MaqamWorld would even write a note about a difference of intonation as small as 12 cents.
We need more data to draw more conclusions.
...
OffTonic Theory! It's a website where a guy describes the use of Arabic maqamat in Syrian Jewish liturgical music. And the author of the site uses 53-EDO instead of 24 EDO. He analyzes the maqam as having a hijaz-like tetrachord at the base of either [6, 10, 6] or [7, 8, 7] relative steps. A frequency ratio between 8 and 10 steps of 53-EDO isn't all that precise - it's a 45 cent difference, but we can use this. We are not restricted to using integers. What's the intonation of Sikah Baladi? About [6.5, 9, 6.5], i.e. [147, 204, 147] cents relative or [0, 147, 351, 498] cents absolute. Those are actually surprisingly close to 24-EDO values of [0, 150, 350, 500] cents absolute or [3, 4, 3]\24 steps relative. So a 24-EDO intonation isn't too bad among Syrian Jews at least. A nice nearby just intonation for this is
[1/1, 12/11, 27/22, 4/3] absolute
[12/11, 9/8, 88/81] relative
A this one's a less simple but it's symmetric:
[1/1, 12/11, 11/9, 4/3] absolute
[12/11, 121/108, 12/11] relative
So there's another option for intonation, though I can't help but feel that the intonation I made up is better.
...
Ah! Got it.
Sami Abu Shumays gives a .scl file for a pitch set that includes Jiharkah and its modulations and says that jins Sikah Baladi is an option: https://tuning.ableton.com/arabic-maqam/jiharkah/. The tricky bit is that this Sikah Baladi has its tonic on C instead of G, so we'll have to transpose.
Here's our maqam Sikah Baladi from MaqamWorld:
[G, low Ad, high Bd, low C, D, low Ed, high Ft, G]
Move that up P4 or down P5 and we get:
... nothing. Those pitches aren't in his pitch set. We'd be a lot closer if we hadn't transposed.
Rooting the maqam on G and using the closest available pitches for modulation, we get [G, Ab, Bd, C, D, E-, F#, G] -> [0, 123, 359, 498, 707, 876, 1088, 1200]. This looks plausible as an intonation (even if the pitch names aren't all correct) everywhere except for the E-, which should instead be a low E half flat instead of a low E natural. A low E half flat should be like 310 to 340 cents over C natural / perde Rast, so like 808 to 838 cents over G.
...
Oh, oops, he wasn't saying that maqam Sikah Baladi was a modulation option, just jins Sikah Baladi. So I shouldn't be looking for the full set of tones in the maqam. His intonation for just the jins is:
...
...
I asked the xenharmonic discord about the intonation of Sikah Baladi and Margo Schulter had an interesting take.
"The traditional interpretation might be like the versions of Systematist Buzurg from around 1300"
[1/1, 14/13, 16/13, 4/3] _ [0, 128, 359, 498] cents
[14/13, 8/7, 13/12] _ [128, 231, 139] cents
or
[1/1, 13/12, 26/21, 4/3] _ [0, 139, 370, 498] cents
[13/12, 8/7, 14/13] _ [139, 231, 128] cents
Buzurg (also called Buzurk, Buzrak, and Bozorg) is an difficult and interesting thing to pin down in the history of middle eastern music, but Margo Schulter is cool, so let's try.
Buzurg is, in one sense, a pitch or a perde or a place on the neck of a lute like a tanbur or oud. It's specifically an octave above perde Sikah. Thus if perde Rast is called C, then Sikah and Buzurg are both Ed, in different octaves.
Buzurg was also a mode in medieval Persian and Arabic music. My understanding is that Safi al-Din described the mode as
[P1, GrGrGrd3, GrGrd4, P4, GrGrGrd6, P5, AcM6, GrGrd8, P8] # [1/1, 65536/59049, 8192/6561, 4/3, 262144/177147, 3/2, 27/16, 4096/2187, 2/1] _ [0, 180, 384, 498, 678, 702, 906, 1086, 1200] cents
which is ugly due to being Pythagorean, but we give it a schismastic reinterpretation as:
[P1, M2, M3, P4, Gr5, P5, AcM6, M7, P8] # [1/1, 10/9, 5/4, 4/3, 40/27, 3/2, 27/16, 15/8, 2/1]
[M2, AcM2, m2, Ac1, AcM2, M2, m2] # [10/9, 9/8, 16/15, 10/9, 81/80, 9/8, 10/9, 16/15]
This is much nicer looking, it's spelled correctly intervallically (except for having two 5th intervals), and it's aurally indistinguishable from the previous intonation.
It's also basically just a major scale (with a weirdly doubled up 5th scale degree).
Encyclopedia Iranica says that the later Qoṭb-al-Dīn Šīrāzī in his "Dorrat al-tāj" provided corrections to Safi al-Din's work and gave a jins for Bozorg as a pentachord:
Absolute: [G, Ad, B, C, C#(+), D] _ [0, 150, 417, 498, 626, 702]
Relative: [150, 267, 81, 128, 76]
which can be extended with these tones:
Absoltue: [E, Gb, G] [204, 386, 498]
Relative: [204, 182, 112] cents
To give this full scale:
Full scale:
[G, Ad, B, C, C#(+), D, E, F#, G]
[0, 150, 417, 498, 626, 702, 906, 1088, 1200]
This has a fairly obvious detempering:
Absolute: [1/1, 12/11, 14/11, 4/3, 56/39, 3/2, 27/16, 15/8, 2/1]
Relative: [12/11, 7/6, 22/21, 14/13, 117/112, 9/8, 10/9, 16/15]
Although it's not spelled correctly in my interval naming system (with the 7/6 being a 3rd interval and the 22/21 being a 1st, though we'd hope for them to both be kinds of 2nds in order to get a scale that progressed alphabetically). That's fine. Not every medieval middle eastern music theorist will use my interval naming system.
The reference for that intonation in Encyclopedia Iranica is from Owen Wright. This definitely looks closer to a distinct middle eastern mode than Safi al-Din's garbage major scale, and it's closer to Margo Schulter's jins. I think both Safi al-Din and Qutb al-Din al-Shirazi have been described as being Systematists about middle eastern modes, not that I really know what that means (although I think they're the ones who introduced a [T B J]-like notation for tetrachords, and they might have championed 1/3 tones in contrast to quarter tones, and are they're probably involved any time you see an intonation involving 8/7 or 7/6), and they both lived around 1300 AD, so we are looking at "versions of Systematist Buzurg from around 1300", if you were curious.
Encyclopedia Iranica also lists some modern things called Bozorg across various middle eastern musical traditions. It's a shashmaqam in Tajikistan and Uzbekistan, "characterized by a pentatonic structure: (C) D E (F#) G A B (C) D." I don't know exactly what they mean by that, but it sure doesn't look anything like the microtonal scale of Qutb al-Din al-Shirazi. In modern Persian music, Bozorg is a melodic motif played in Dastgah Shur that goes through these notes [C, Dp, Eb, F, G, (Ap | Ab), Bb] but in a broadly descending order. This at least has a microtone or two. And it's also some other things. I don't know how these are connected and neither does Encyclopedia Iranica. It doesn't seem to be that they all emphasis a note that's an octave and a neutral third above Rast.
In modern Turkish music, Büzürk/Büzürg is a compound maqam described in ascending order as a "Buselik pentachord on A, a Huseyni pentachord on E, and a Çargâh pentachord on G." I'm sorry to say this is just Arel-Ezgi-Uzdilek bullshit and probably it can't tell us anything about the history of Buzurk, but let's try.
Genus Buselik is jins Nahawand, i.e. [9/8, 256/243, 9/8], and we can add on one more 9/8 for a pentachord. Huseyni is also called Ussak in Turkish music theory, but in Arabic it's called Bayati and has an intonation like [13/12, 128/117, 9/8] or [88/81, 12/11, 9/8]. Add on another 9/8 to get a pentachord. Finally Çargâh is the must infuriating name in all of the AEU corpus, because it's a Persian name for a tetrachord like Hijaz but they use it for Ajam, because they wanted a historic name for the major scale and to pretend like the western major scale was ever of central importance to their music, and their solution for that was .... to ignore history and change their own historic names. They already has Acem as a perde that was cognate with 'ajam. I get so mad when I see this, Hüseyin Sadeddin Arel. I curse you in your grave.
Anyway, jins 'Ajam is [9/8, 9/8, 256/243], and we can add on 9/8 for a pentachord. This doesn't look like any other Buzurg to my eye. I don't think it really even deserves to be called a "compound" maqam. It's just a seyr.
So, Buzurg. Is it related to Sikah Baladi? Yeah. Margo Schulter's
[14/13, 8/7, 13/12] and [13/12, 8/7, 14/13]
are both tuned to [6, 10, 6] steps of 53-EDO, like one of OffTonic Theory's intonations. It definitely looks like a modified jins Hijaz, and modified in the right direction.
Unlike my detempering of Bozorg from Qoṭb-al-Dīn Šīrāzī, Margo Schulter's tetrachord is spelled by 2nd intervals, which I really like. I think I slightly prefer her intonation with a leading 13/12, just based on it's similarity to my theoretical intonations for Sikah Baladi. If we make a maqam out of it, repeating the tetrachord with a AcM2 disjunction, we get:
Absolute: [P1, Prm2, PrSpGrm3, P4, P5, Prm6, PrSpGrm7, P8] # [1/1, 13/12, 26/21, 4/3, 3/2, 13/8, 13/7, 2/1] _ [0, 139, 370, 498, 702, 841, 1072, 1200] cents
Relative: [Prm2, SpM2, ReSbAcM2, AcM2, Prm2, SpM2, ReSbAcM2] # [13/12, 8/7, 14/13, 9/8, 13/12, 8/7, 14/13] _ [139, 231, 128, 204, 139, 231, 128] cents
...