Arabic Maqamat

:: The Motivation: You Know Who Really Loves Microtonal Music?

The most widely practiced and loved microtonal music scene in the modern era is in the Middle East, the Maghreb, balkans, and the Mediterranean. Lots of musical traditions in these areas are based on basically the same microtonal modal scales. Their scales all pretty much all called some homonym or derivative of "maqam".

• Arabic-speaking nations: maqam. 

• Turkey: makam. 

• The Turkish Uyghurs in China: muqam. 

• Azerbaijan: mugham. 

• Uzbekistan and Tajikistan: shashmaqam. 

• Greek Rebetiko music, which was influenced by the music of the Ottoman empire: adromoi. 

• In the musical tradition of Nubah from Morocco, Algeria, Tunisia, and Libya, such a scale is called a tab'.

In Iran they also have modal scales called dastgahs (or dastgah-ha), some of which are related to the scales above. We'll have a chapter all about those.

These musical traditions almost never use rich harmony: a monophonic instrument wanders within one part of the scale and then to another, with expert dynamic and rhythmic expressivity, and the melodies are mostly just accompanied by percussion, or constant note drones for harmony, or by other instruments playing together in unison or at the octave.

The Turkish and the Arabic musical traditions are the best documented online, so I'll focus on those. For the Arabic scales I'll say "a maqam" or multiple "maqamat". For Turkish scales, I'll say makam and makams. The actual plural in Turkish is "makamlar", depending on the grammatical case, but Turkish people writing in English say "makams", so I will too.

Makams, maqamat, and dastgah-ha are the building blocks of the most widely practiced and loved microtonal music tradition in the world. It's a little frustrating to try to characterize makams and maqamat, since they vary by region and historic period and musician. It's a little bit like trying to construct the platonic ideal recipe for pie - not the best pie, but the one fundamental pie as it truly is, expressing itself in the recipes of all lands. You can't really do it, but you can gather lots of pie recipes and talk a little bit about the differences. That's what I'm here to do. Our first chapter will look at Arabic maqamat in 24-EDO, and a simple 11-limit just intonation that hardly sounds different from 24-EDO.

: Arabic Maqamat In 24-EDO And The 2.3.11 Just Intonation Subgroup

Arabic maqamat have a few "half-flat" notes, like "G half flat". A G half-flat note sounds somewhere between a G natural and a G flat. For notation, I'll use "d" to indicate a half-flat accidental, and "t" to indicate the a half-sharp accidental. Some other decent options in Unicode are ᵈ, as in Gᵈ, and ѣ as in Gѣ, which looks a bit like a flat symbol with a slash through it. 

In 1932, the influential Cairo Congress of Arab Music decided that maqamat should be notated in 24-EDO, if not necessarily played that way. I wish they had worked a little harder to find a more precise notation, but

• There was very little theoretical disagreement at a granularity more precise than 24-EDO

• There were some persuasive 24-EDO keyboard salsemen at the Congress

• The absence of the Congress's organizer due to poor health meant that the resolution of the congress was less academic that it might have otherwise been - more of a compromise than an agreed upon best system. 

• The most ardent critic of 24-EDO in attendance had perhaps an even worse proposal.

Now now 24-EDO is the pedological standard for Arabic maqamat and we shall learn from it what we can.

If you think of maqamat as tuned-scales within 24-EDO, then a half-flat accidental corresponds to flattening of pitch down by one step of 24-EDO, and a half-sharp means raising by one step of 24-EDO. Easy enough. While 24-EDO allows you to represent some neutral tones, it doesn't allow you to express much in the way of regional tonal variation or melodic ornamentation, which are fundamental to maqamat.

One reason that the adoption of 24-EDO is a little sad is that we have hundreds of years treatises and artefacts giving us information on historic intonations of middle eastern modal music. Like, there's a thousand year old Arabic music theory text, the Kitab al-Musiqa al-Kabir by al-Farabi, which distinguishes a lute fingering that the author geometrically constructs to have a frequency ratio of 162/149 (@ 145 cents) and another with frequency ratio 54/49 (@ 168 cents), and pretending that these are both "3 steps of 24 EDO", when we're explicitly told to treat them differently by the master who has has honed his craft until he can hear the difference and perform the difference, is ignoring what the music really is and replacing it with a fantasy. And the history goes back way farther than that: there's a Persian flute called a ney at the University of Philadelphia Museum which is estimated to be from 3000 to 2800 BC. I don't know if anyone has looked at the geometry of the finger holes to figure out the tuning inherent to the instrument, but that's the sort of scholarship that is theoretically available to us, and the sort which could supplant 24-EDO simplifications.

Unfortuantely, even the historic sources don't agree, just as the modern theorists don't agree, so 24-EDO is an okay starting point.

In our chapter "Higher Rank EDO Generators", we learned that in order to analyze 24-EDO music intervallically, we need to use at least a 4-dimensional interval space, which is justly assocaited with 7-limit frequency ratios. This is the easiest and most obnvious interpretation to make if you only know that the scales are taught in 24-EDO, but we can do better. There is fairly wide agreement that the natural intervals of maqamat mostly have a Pythagorean intonation. And for the neutral intervals, there is significant historical and contemporary support 11-limit frequency ratios, and almost none for 7-limit ratios. Other sources give 13-limit or 17-limit intonations, or more exotic things, but working in 2.3.11 just intonation is the most basic and conservative way to start looking at the just tuning of Arabic maqamat, so that's what we'll do here. The 11-limit neutral tones also hardly sound different from 24-EDO. 

: Arabic Pitch Notation

You might wonder what pitches look like in 24-EDO. In the most common system, the normal accidentals of sharp, flat, and neutral and augmented with a half-flat symbol (which either looks like a backward flat symbol or a flat symbol with a slash through it) and a half-sharp symbol (which looks like if you cut a sharp symbol down its height and took only half of the hash). In text, I'll use "d" for a backwards flat and "t" for half of a hash. Thus we have "Ed" for E half flat (which has a sound somewhere between E natural and Eb), and we have Ft for F half-sharp (which has a sound somewhere between F natural and F#). In principle we can combine these accidentals with the old ones, so that Bbd is B three-quarter flat and G#t is G three quarters sharp. These are useful for writing 24-EDO music generally, but they don't make much of an appearance in maqamat. Indeed, almost all maqamat can be characterized using just the normal western pitches plus Ad, Bd, Ed, Ft. And to give a little more sense of how many pitches the music uses, there was a famous medieval music theorist who proposed using a 17-tone scale for all maqamat that existed at that time.

Now that we have established some pitch notation, here's our first bit of data. These are my transcriptions of some Arabic maqam scales based on staff notation on Wikipedia.

Hijaz (Nahawand ending) [0, 2, 8, 10, 14, 16, 20, 24] [D, Eb, F#, G, A, Bb, C, D] # Tonal. 

Nawa Athar [0, 4, 6, 12, 14, 16, 22, 24] [C, D, Eb, F#, G, Ab, B, C] # Tonal.

Shad 'Araban [0, 2, 8, 10, 14, 16, 22, 24] [G, Ab, B, C, D, Eb, F#, G] # Tonal.

Bayati [0, 3, 6, 10, 14, 16, 20, 24] [D, Ed, F, G, A, Bb, C, D] # Has Ed.

Jiharkah [0, 4, 8, 10, 14, 18, 21, 24] [F, G, A, Bb, C, D, Ed, F] # Has Ed.

Huzam [0, 3, 7, 9, 15, 17, 21, 24] [Ed, F, G, Ab, B, C, D, Ed]. # Has Ed.

Rahat al Arwah [0, 3, 7, 9, 15, 17, 21, 24] [Bd, C, D, Eb, F#, G, A, Bd] # Has Bd.

Saba [0, 3, 6, 8, 14, 16, 20, 24] [D, Ed, F, Gb, A, Bb, C, D] # Has Ed.

Rast [0, 4, 7, 10, 14, 18, 21, 24] [C, D, Ed, F, G, A, Bd, C] # Has Ed and Bd.

Husayni 'Ushayran [0, 3, 6, 10, 13, 16, 20, 24] [A, Bd, C, D, Ed, F, G, A] # Has Bd and Ed.

On each line, I show the name of the maqam, the number of steps of 24-EDO for each scale degree relative to the tonic, the pitch classes of the maqam using "d"s as a half-flat accidental, and finally a summary comment on the presence or absence of any notes with half-flat accidentals. Wikipedia also tells us that the maqamat 'Ajam, Nahawand, and Kurd are tonal, and correspond to western Major, Minor, and Phrygian modes.

: A Undecimal Determpering

Now that we have some 24-EDO scales, we can look at just intonation, using Pythagorean natural pitches and the 11-limit commas of Ben Johnston. The ascendant unison, As1 (justly tuned to 33/32) is tuned by 24-EDO to one step, and its inverse, the descendant unison, De1 (justly tuned to 32/33) is tuned to -1 step of 24-EDO. Using only these 11-limit commas as deviations from Pythagorean intervals we can get neutral 2nds, 3rds, 6ths, and 7th with simple names and simple frequency ratios.

Step : Name :: Just frequency ratio _ Pitch over C natural

3 : AsGrm2 :: 88/81 _ Dbt

3 : DeAcM2 :: 12/11 _ Dd

7 : AsGrm3 :: 11/9 _ Ebt

7 : DeAcM3 :: 27/22 _ Ed

17 : AsGrm6 :: 44/27 _ Abt

17 : DeAcM6 :: 18/11 _ Ad

21 : AsGrm7 :: 11/6 _ Bbt

21 : DeAcM7 :: 81/44 _ Bd

We also get a few deviations from perfect intervals with simple ratios:

1 : As1 :: 33/32 _ Ct

11 : As4 :: 11/8 _ Ft

13 : De5 :: 16/11 _ Gd

23 : De8 :: 64/33 _ Cd

In this system, we get a simple interpretation of 24-EDO accidentals: the half-sharp corresponds to As1, and the half-flat corresponds to De1, and these are applied on top of Pythagorean natural intervals.

The rest of the chapter will just be notated in pitches and steps of 24-EDO, but if you want to think of the scales justly, here's an easy and I think fairly unconstroversial option.

:: 24-EDO Ajnas

Maqamat are made out of smaller scale fragments called "ajnas" in plural, the singular being "jins". They commonly consist of four notes, in which case they are called tetrachords, and tetrachords almost always span an interval of a perfect fourth. Ajnas are not just scale fragments - they are modes themselves, in which musicians produce small melodic phrases - riffs, licks, motives, figures, whatever -  before passing into other modes.

Many people will tell you that maqamat are objects somewhere between songs and scales, and this has some truth to it. Maqamat have extra structure beyond the scale. They have subscales, for exampole. Also maqamat are associated with a historical corpus of songs that suggests to a player what rhythmic and melodic choices to make within a subscale, and how to move between subscales, and how to modulate to related maqamat. 

The scale fragments are calls ajnas (in the plural) or a jins (in the singular). The nebulous paths between them are called "seyir" or "sayir". They're like the contour that a piece in a maqam should have. A given improvisation in a maqam is called a taqsim.

This extra structure is less concrete than the scales, less easy to transmit, but very real to the practitioners of middle eastern music. Still, even if maqam rast is not a scale, it has a scale and subscales, and those are the things we learn first. 

Here are some Arabic ajnas presented in steps of 24-EDO:

Sikah trichord: [3, 4] :: [0, 3, 7]

'Ajam trichord: [4, 4] :: [0, 4, 8]

Saba tetrachord: [3, 3, 2] :: [0, 3, 6, 8]

Kurd tetrachord: [2, 4, 4] :: [0, 2, 6, 10]

Hijaz tetrachord: [2, 6, 2] :: [0, 2, 8, 10]

Bayati tetrachord: [3, 3, 4] :: [0, 3, 6, 10]

Nahawand tetrachord: [4, 2, 4] :: [0, 4, 6, 10]

Rast tetrachord: [4, 3, 3] :: [0, 4, 7, 10]

Nikriz pentachord: [4, 2, 6, 2] :: [0, 4, 6, 12, 14]

The first set of bracketed numbers on each row are relative steps between scale degrees of each jins, and the second set of numbers are absolute steps.

Those ajnas are all taken from Wikipedia, although the Wikipedia page uses e.g. 1 "whole step" to decribe the size of a M2 whole tone, so I multiplied through by a factor of 4 to get 24-EDO commas. The Saba tetrachord only reaches 8 steps of 24-EDO, falling flat of the usual P4 at 10 steps of 24-EDO, but the other tetrachords reach it. The ajnas with odd-valued step sizes are microtonal, while the ajnas with all even-valued step sizes are representable in 12-EDO.

Here are a few more ajnas in 24-EDO steps, which I have taken, again with a little numerical translation of format, from "Between Theory, Representation and Practice of Maqām" by Brent Keogh:

Musta'ar: [5, 2] :: [0, 5, 7]

Jiharkah: [4, 3] :: [0, 4, 7]

Zamzama: [2, 4, 2] :: [0, 2, 6, 8]

Busalik (or 'Ushaq): [4, 2, 4] :: [0, 4, 6, 10]

Nawa Athar: [4, 2, 6, 2] :: [0, 4, 6, 12, 14]

Athar Kurd: [2, 4, 6, 2] :: [0, 2, 6, 12, 14]

The jins of Busalik (or 'Ushaq) here is the same as  jins Nahawand in the previous set. Jins Zamzama is a variation of jins Saba from the previous set. And jins Nawa Athar from this set is the  same as jins Nikriz from the previous set. Everything is like this in the study of maqam music. - many names for one things, many things for one name.

: Maqamat from MaqamWorld

MaqamWorld is a website created by Johnny Farraj. It has been my primary source for learning about Arabic maqamat. The maqamat are presented there in staff notation. I've never enjoyed sign reading, so I'm going to share text-data transcriptions of the maqamat, I have comments about the jins structure of most scales also, but some I still need to annotate.

'Ajam Family:

'Ajam (Upper Ajam Ending): [C, D, E, F, G, A, B, C] # 'Ajam pentachord [C, D, E, F, G] + Upper 'Ajam tetrachord [G, A, B, C].

'Ajam (Nahawand Ending): [C, D, E, F, G, A, Bb, C] # 'Ajam pentachord [C, D, E, F, G] + Nahawand tetrachord [G, A, Bb, C].

'Ajam 'Ushayran (descends): [Bb, A, G, F, Eb, D, C, Bb] # Written ascending: 'Ajam trichord [Bb, C, D] + Kurd tetrachord [D, Eb, F, G] + Nahawand trichord [G, A, Bb].

Shawq Afza: [C, D, E, F, G, Ab, B, C] # 'Ajam pentachord [C, D, E, F, G] + Hijaz tetrachord [G, Ab, B, C].

Bayati Family:

Bayati (Nahawand Ending): [D, Ed, F, G, A, Bb, C, D] # Bayati tetrachord [D, Ed, F, G] + Nahawand pentachord [G, A, Bb, C, D].

Bayati (Rast Ending): [D, Ed, F, G, A, Bd, C, D] # Bayati tetrachord [D, Ed, F, G] + Rast pentachord [G, A Bd, C, D].

Bayati Shuri: [D, Ed, F, G, Ab, B, C, D] # Bayati tetrachord [D, Ed, F, G] + Hijaz tetrachord [G, Ab, B, C] + T.

Husayni (ascending): [D, Ed, F, G, A, Bd, C, D] # Bayati pentachord [D, Ed, F, G, A] + Bayati tetrachord [A, Bd, C, D]

Husayni (descending): Descending: [D, Ed, F, G, A, Bb, C, D] # Bayati pentachord [D, Ed, F, G, A] + Kurd tetrachord [A, Bb, C, D]

Muhayyar: Just a more specific path through Maqam Bayati, where you ascend with Rast ending up to the octave, play jins Bayati starting on and above the octave, and then descend down however you want through normal tetrachords of maqam Bayati.

Hijaz Family:

Hijaz (Nahawand Ending): [D, Eb, F#, G, A, Bb, C, D] # Hijaz tetrachord [D, Eb, F#, G] + Nahawand pentachord [G, A, Bb, C, D].

Hijaz (Rast Ending): [D, Eb, F#, G, A, Bd, C, D] # Hijaz tetrachord [D, Eb, F#, G] + Rast pentachord [G, A, Bd, C, D].

Hijazkar (descends) (= Shadd 'Araban = Suzidil = Shahnaz): [E, Db, C, B, Ab, G, F, E, Db, C] # Written ascending this is: Hijaz tetrachord [C, Db, E, F] + Nikriz tetrachord [F, G, Ab, B] overlapping with Hijazkar pentachord [Ab, B, C, Db, E].

Zanjaran (descends): [C, Bb, A, G, F, E, Db, C] # Hijaz tetrachord [C, Db, E, F] + 'Ajam pentachord [F, G, A, Bb, C].

Kurd Family:

Kurd: [D, Eb, F, G, A, Bb, C, D] # Kurd tetrachord [D, Eb, F, G] + Nahawand pentachord [G, A, Bb, C, D].

Hijazkar Kurd (descends): [E, Db, C, B or Bb, Ab, G, F, Eb, Db, C] # This one has all kinds of annotations, but we can figure it out. Written ascending: Kurd tetrachord [C, Db, E, F] + Nahawand pentachord [F, G, Ab, Bb, C]. When you reach the octave C, you play a different jins, namely jins Hijazkar, which has its tonic in the middle of the set of pitches, namely the tonic is C in [Ab, B, C, Db, E, (F)]. So to  play the full maqam descending, you noodle around on jins HIjazkar, and then at some point when you're on C, you switch to jins Nahawand, which leads you down to jins Kurd.

Nahawand Family:

Nahawand (Hijaz Ending): [C, D, Eb, F, G, Ab, B, C] # Nahawand pentachord [C, D, Eb, F, G] + Hijaz tetrachord [G, Ab, B, C].

Nahawand (Kurd Ending): [C, D, Eb, F, G, Ab, Bb, C] # Nahawand pentachord [C, D, Eb, F, G] + Kurd tetrachord [G, Ab, Bb, C].

Farahfaza: (Nahawand transposed to start on G.)

Nahawand Murassa': [C, D, Eb, F, Gb, A, Bb, C] # Nahawand Murassa pentachord [C, D, Eb, F, Gb] overlapping with Hijaz tetrachord [F, Gb, A, Bb] + T.

'Ushaq Masri: [D, E, F, G, A, Bd, C, D] # Nahawand pentachord [D, E, F, G, A] + Bayati tetrachord [A, Bd, C, D].

Nikriz Family:

Nikriz (descends from 9 rather than octave): [D, C, Bb, A, G, F#, Eb, D, C] # Nikriz pentachord [C, D, Eb, F#, G] + Nahawand pentachord [G, A, Bb, C, D].

Nawa Athar: [C, D, Eb, F#, G, Ab, B, C] # Nikriz pentachord [C, D, Eb, F#, G]  overlapping with Hijazkar hexachord [Eb, F#, G, Ab, B, C].

Athar Kurd: [C, Db, Eb, F#, G, Ab, B, C] # Athar Kurd pentachord [C, Db, Eb, F# G] overlapping with Hijazkar hexachord [Eb, F#, G, Ab, B, C].

Rast Family:

Rast (Upper Rast ending): [C, D, Ed, F, G, A, Bd, C] # Rast pentachord [C, D, Ed, F, G] + Upper Rast tetrachord [G, A, Bd, C].

Rast (Nahawand ending): [C, D, Ed, F, G, A, Bb, C] # Rast pentachord [C, D, Ed, F, G] + Nahawand [G, A, Bb, C]. Jins Nahawand is written descending, so maybe it's more commonly used in descent.

Kirdan: (descending Rast with upper Rast ending)

Sazkar (descends): [C, Bd, A, G, F, Ed, D#, C] # Sazkar pentachord [C, D#, Ed, F, G] + Upper Rast tetrachord [G, A, Bd, C].

Suznak: [C, D, Ed, F, G, Ab, B, C] # Rast pentachord [C, D, Ed, F, G] + Hijaz tetrachord [G, Ab, B, C].

Nairuz: [C, D, Ed, F, G, Ad, Bb, C] # Rast pentachord [C, D, Ed, F, G] + Bayati tetrachord [G, Ad, Bb, C]. Modern transposed maqam Yakah.

Yakah: [G, A, Bd, C, D, Ed, F, G] # Older less common version of Nairuz.

Dalanshin (descends): [E, Db, C, Bd, A, G, F, Ed, D, C] # Rast pentachord [C, D, Ed, F, G]  + Upper Rast tetrachord [G, A, Bd, C] overlapping with Saba Dalanshin pentachord [A, Bd, C, Db, E].

Suzdalara (descends): [C, Bb, A, G, F, Ed, D, C] # Just the descending form of rast with Nahawand ending.

Mahur: [C, D, Ed, F, G, A, B, C] # Rast pentachord [C, D, Ed, F, G] + Upper 'Ajam tetrachord [G, A, B, C].

Sikah family:

Sikah: [Ed, F, G, A, Bd, C, D, Ed] # Sikah trichord [Ed, F, G] + Upper Rast tetrachord [G, A, Bd, C] + Rast trichord [C, D, Ed].

Huzam: [Ed, F, G, Ab, B, C, D, Ed] # Sikah trichord [Ed, F, G] + Hijaz tetrachord [G, Ab, B, C] + Rast trichord [C, D, Ed].

Maqam Rahat al-Arwah: (Huzzam rooted on Bd).

'Iraq: [Bd, C, D, Ed, F, G, A, Bd] # Sika trichord + Bayati tetrachord + Rast trichord

Awj ‘Iraq (descends): [D, C, Bd, A#, G, F#, Eb, D, C, Bd]. Sikah trichord [Bd, C, D] + Hijaz tetrachord [D, Eb, F#, G] + m2 up to A# + a tiny DeGrm2 up to Bd + Sikah trichord [Bd, C, D]. It's weird that this one has a note not covered by a jins.

Bastanikar: [Bd, C, D, Ed, F, Gb, A, Bb, C, Db, E, F] # Sikah trichord [Bd, C, D] + Saba pentachord [D, Ed, F, Gb, A] overlapping with Hijaz tetrachord [F, Gb, A, Bb] + Nikriz pentachord [Bb, C, Db, E, F].

Musta'ar: [Ed, F#, G, A, Bb, C, D, Ed] # Musta'ar trichord [Ed, F#, G] + Nahawand tetrachord [G, A, Bb, C] + Rast trichord [C, D, Ed].

No family:

Jiharkah: [Ed, F, G, A, Bb, C, D, Ed, F] # F is the tonic, I think, not Ed. Jiharkah hexachord [Ed, F, G, A, Bb, C] + Upper Rast tetrachord [C, D, Ed, F]. The Bb is actually notated "Bb_down", which might mean Bb or Bbd or Bd; I'm not sure of their notation. Navid Goldrick from Oud For Guitarists says that both the A and Bb are played flat (relative to 12-TET), with A about 15 cents flat and Bb about 35 to 40 cents flat. Also the Ed is 60 cents flat relative to E, rather than 50. So I've transcribed it as A and Bb, but there's a more precise intonation for you. I think he probably gives his cents relative to 12-EDO, not to Pythagorean intonation.

Lami: [D, Eb, F, G, Ab, Bb, C, D] # Lami pentachord [D, Eb, F, G, Ab] overlapped with Kurd tetrachord [G, Ab, Bb, C] + T.

Saba ('Ajam ending): [D, Ed, F, Gb, A, Bb, C, D] # Saba pentachord [D, Ed, F, Gb, A] overlapping with Hijaz tetrachord [F, Gb, A, Bb] + 'Ajam trichord [Bb, C, D].

Saba (Nikriz ending): [D, Ed, F, Gb, A, Bb, C, Db, E, F] # Saba pentachord [D, Ed, F, Gb, A] overlapping with Hijaz tetrachord [F, Gb, A, Bb] + Nikriz pentachord [Bb, C, Db, E, F].

Saba Zamzam ('Ajam ending): [D, Eb, F, Gb, A, Bb, C, D] # Saba Zamzam pentachord [D, Eb, F, Gb, A] overlapping with Hijaz tetrachord [F, Gb, A, Bb] + 'Ajam trichord [Bb, C, D].

Saba Zamzam (Nikriz ending): [D, Eb, F, Gb, A, Bb, C, Db, E, F]  Saba Zamzam pentachord [D, Eb, F, Gb, A] overlapping with Hijaz tetrachord [F, Gb, A, Bb] + Nikriz pentachord [Bb, C, Db, E, F].

Sikah Baladi (descends): [C, Bd, Ad, G, Ft, Ed, D, C#, C, Bd, Ad, G] # Sikah Baladi tetrachord [G, Ad, Bd, C] + augmented unison up to C# + pseudo-Hijazkar / suspended 5th pentachord [C#, D, Ed, Ft, G] overlapping with Sikah Baladi hexachord [Ed, Ft, G, Ad, Bd, C].

Nice. Although I think Saba and Saba Zamzam and Bastanikar obviously form a family, and SIkah Baladi should be with regular maqam Sikah and maqam Huzam. Also maqam Lami should be in the Kurd family.

: All The Maqamat In 24-EDO

We've got a bunch of scales that span an octave. Those are easy:

'Ajam 'Ushayran (descends): [0, 4, 8, 10, 14, 18, 22, 24]

'Ajam (Nahawand Ending): [0, 4, 8, 10, 14, 18, 20, 24]

'Ajam (Upper Ajam Ending): [0, 4, 8, 10, 14, 18, 22, 24]

'Iraq: [0, 3, 7, 10, 13, 17, 21, 24]

'Ushaq Masri: [0, 4, 6, 10, 14, 17, 20, 24]

Athar Kurd: [0, 2, 6, 12, 14, 16, 22, 24]

Awj ‘Iraq (descends): [0, 3, 7, 9, 15, 17, 23, 24]

Bayati (Nahawand Ending): [0, 3, 6, 10, 14, 16, 20, 24]

Bayati (Rast Ending): [0, 3, 6, 10, 14, 17, 20, 24]

Bayati Shuri: [0, 3, 6, 10, 12, 18, 20, 24]

Dalanshin (descends): [0, 4, 7, 10, 14, 18, 21, 24]

Hijaz (Nahawand Ending): [0, 2, 8, 10, 14, 16, 20, 24]

Hijaz (Rast Ending): [0, 2, 8, 10, 14, 17, 20, 24]

Hijazkar (or Shadd 'Araban) (descends) : [0, 2, 8, 10, 14, 16, 22, 24]

Husayni 'Ushayran: [0, 3, 6, 10, 13, 16, 20, 24]

Husayni (Descending): [0, 3, 6, 10, 14, 16, 20, 24]

Husayni (ascending): [0, 3, 6, 10, 14, 17, 20, 24]

Huzam: [0, 3, 7, 9, 15, 17, 21, 24]

Jiharkah: [0, 4, 8, 10, 14, 18, 21, 24]

Kurd: [0, 2, 6, 10, 14, 16, 20, 24]

Lami: [0, 2, 6, 10, 12, 16, 20, 24]

Mahur: [0, 4, 7, 10, 14, 18, 22, 24]

Musta'ar: [0, 5, 7, 11, 13, 17, 21, 24]

Nahawand (Hijaz Ending): [0, 4, 6, 10, 14, 16, 22, 24]

Nahawand (Kurd Ending): [0, 4, 6, 10, 14, 16, 20, 24]

Nahawand Murassa': [0, 4, 6, 10, 12, 18, 20, 24]

Nairuz: [0, 4, 7, 10, 14, 17, 20, 24]

Nawa Athar: [0, 4, 6, 12, 14, 16, 22, 24]

Nikriz (descends): [0, 4, 6, 12, 14, 18, 20, 24]

Rahat al-Arwah: [0, 3, 7, 9, 15, 17, 21, 24]

Rast (Nahawand ending): [0, 4, 7, 10, 14, 18, 20, 24]

Rast (Upper Rast ending): [0, 4, 7, 10, 14, 18, 21, 24]

Saba ('Ajam ending): [0, 3, 6, 8, 14, 16, 20, 24]

Saba Zamzam ('Ajam ending): [0, 2, 6, 8, 14, 16, 20, 24]

Sazkar (descends): [0, 6, 7, 10, 14, 18, 21, 24]

Shad Araban: [0, 2, 8, 10, 14, 16, 22, 24]

Shawq Afza: [0, 4, 8, 10, 14, 16, 22, 24]

Sikah Baladi (descends): [0, 3, 7, 10, 12, 14, 17, 21, 24]

Sikah: [0, 3, 7, 11, 14, 17, 21, 24]

Suzdalara (descends): [0, 4, 7, 10, 14, 18, 20, 24]

Suznak: [0, 4, 7, 10, 14, 16, 22, 24]

Yakah: [0, 4, 7, 10, 14, 17, 20, 24]

Zanjaran (descends): [0, 2, 8, 10, 14, 18, 20, 24]

We've also got four scales that span more than an octave: Hijazkar Kurd and three variants of Saba, namely Bastanikar, Saba (Nikriz ending), and Saba Zamzam (Nikriz ending). Here they are in 24 EDO:

Hijazkar Kurd (descends): []

Bastanikar: [0, 3, 4, 6, 10, 12, 18, 20, 24, 26, 32, 34]

Saba (Nikriz ending): [0, 3, 6, 8, 14, 16, 20, 22, 28, 30]

Saba Zamzam (Nikriz ending): [0, 2, 6, 8, 14, 16, 20, 22, 28, 30]

Nice.

: 24 EDO Ajnas From Maqam World

MaqamWorld had some ajnas we hadn't seen before. Let's go over them in families

The 'Ajam ajnas:

'Ajam trichord : [0, 4, 8] :: [4, 4]

'Ajam tetrachord : [0, 4, 8, 10] :: [4, 4, 2]

'Ajam pentachord : [0, 4, 8, 10, 14] :: [4, 4, 2, 4]

The Nahawand ajnas:

Nahawand trichord : [0, 4, 6] :: [4, 2]

Nahawand tetrachord: [0, 4, 6, 10] :: [4, 2, 4]

Nahawand pentachord : [0, 4, 6, 10, 14] :: [4, 2, 4, 4]

Nahawand Murassa pentachord : [0, 4, 6, 10, 12] :: [4, 2, 4, 2]

The Nikriz ajnas:

Nikriz tetrachord : [0, 4, 6, 12] :: [4, 2, 6]

Nikriz pentachord : [0, 4, 6, 12, 14] :: [4, 2, 6, 2]

The Kurd ajnas:

Kurd tetrachord : [0, 2, 6, 10] :: [2, 4, 4]

Lami pentachord : [0, 2, 6, 10, 12] ;: [2, 4, 4, 2]

Athar Kurd pentachord : [0, 2, 6, 12, 14] :: [2, 4, 6, 2]

The Rast ajnas:

Rast trichord : [0, 4, 7] :: [4, 3]

Rast tetrachord : [0, 4, 7, 10] :: [4, 3, 3]

Rast pentachord : [0, 4, 7, 10, 14] :: [4, 3, 3, 4]

Musta'ar trichord : [0, 5, 7] :: [5, 2]

The Bayati ajnas:

Bayati tetrachord : [0, 3, 6, 10] :: [3, 3, 4]

Bayati pentachord : [0, 3, 6, 10, 14] :: [3, 3, 4, 4]

The Saba ajnas:

Saba pentachord : [0, 3, 6, 8, 14] :: [3, 3, 2, 6]

Saba Zamzam pentachord : [0, 2, 6, 8, 14] :: [2, 4, 2, 6]

There was also a "Saba Dalanshin pentachord", but it turns out to have the same 24-EDO tuning as the regular Saba pentachord.

The Sikah ajnas:

Sikah trichord : [0, 3, 7] :: [3, 4]

Sikah Baladi tetrachord : [0, 3, 7, 10] :: [3, 4, 3]

Sikah Baladi hexachord : [0, 4, 7, 10, 14, 17] :: [4, 3, 3, 4, 3]

You can see here that the Sikah Baladi hexachord adds two notes below the tonic. You migth call them approach notes or some other kind of ornament.

The Sazkar and Hijazkar ajnas look related:

Sazkar pentachord : [0, 6, 7, 10, 14] :: [6, 1, 3, 4]

Hijazkar pentachord : [0, 6, 8, 10, 16] :: [6, 2, 2, 6]

Hijazkar hexachord : [0, 6, 8, 10, 16, 18] :: [6, 2, 2, 6, 2]

Although "jins pseudo-Hijazkar" is nothing like them:

pseudo-Hijazkar / suspended 5th pentachord : [0, 2, 5, 9, 12] :: [2, 3, 4, 3]

This one is more like a variation on a jins fromt he Kurd family, e.g. we could see it as jins Lami with 3rd and 4th degrees flattened by a step each.

Also I don't know where to put regular Hijaz:

Hijaz tetrachord : [0, 2, 8, 10] :: [2, 6, 2]

I had thought it would go with Hijazkar based on the name. And if we reversed the first two relative intervals, it would obviously go there. But I'm putting it on its own.

Finally jins Jiharkah is all on its own:

Jiharkah hexachord : [0, 3, 7, 11, 13, 17] :: [3, 4, 4, 2, 4]

though it starts like jins Sikah and it's a little bit like an altered jins Bayati.

Your homework is to look back in the chapter at the 24-EDO ajnas from Wikipedia and Brent Keogh. Compare and contrast them with the current set. What's different? Are any of them here under a different name? Et cetera.