The Huygens-Fokker Foundation has a webpage where they share some scales and modes and things. I kind of hate it, because the scales aren't really associated with authors or publication dates or research or anything that would help you to sort out their credibility. They're usually just random numbers and names, like a set og integers that adds up to 29 is called xarbo-29 para lydian or some nonsense like that. Unfortunately, I like microtonal music and I want to learn more about it, and sometimes this means leafing through and analyzing garbage. Today we'll be looking at some middle eastern scales or modes from the Huygens-Fokker Foundation (HFF) and hoping that they're good.
HFF gives a bunch of Arabic maqamat, mostly attributed to Safi al-Din, in Pythagorean tunings. The scales are all drawn from this 17-tone collection of Pythagorean frequency ratios: "1/1 256/243 65536/59049 9/8 32/27 8192/6561 81/64 4/3 1024/729 262144/177147 3/2 128/81 32768/19683 27/16 16/9 4096/2187 1048576/531441 2/1".
I usually like to work in rank-3 interval space or higher, in which the intervals that are justly tuned to Pythagorean ratios, like 1048576/531441, often have fairly complicated names, like that one is GrGrGrd9. I stand by this choice: that's a complicated ratio and it deserves a complicated name. However, long names and long ratios make it harder to read these things, so sometimes in a purely Pythagorean context I'll use rank-2 interval names, which you can derive from rank-3 intervals by removing any Grave and Acute qualities.
Here are rank-2 interval names for the Arabic maqamat of HFF in a Pythagorean intonation.
All of these maqam intonations are attributed to Safi al-Din:
Ussaq: [P1, M2, M3, P4, P5, M6, m7, P8] :: [1, 9/8, 81/64, 4/3, 3/2, 27/16, 16/9, 2]
Nawa: [P1, M2, m3, P4, P5, m6, m7, P8] :: [1, 9/8, 32/27, 4/3, 3/2, 128/81, 16/9, 2]
Abu Salik: [P1, m2, m3, P4, d5, m6, m7, P8] :: [1, 256/243, 32/27, 4/3, 1024/729, 128/81, 16/9, 2]
Rast: [P1, M2, d4, P4, P5, d7, m7, P8] :: [1, 9/8, 8192/6561, 4/3, 3/2, 32768/19683, 16/9, 2]
Iraq: [P1, d3, d4, P4, d6, d7, m7, d9, P8] :: [1, 65536/59049, 8192/6561, 4/3, 262144/177147, 32768/19683, 16/9, 1048576/531441, 2]
Isfahan: [P1, M2, d4, P4, P5, d7, m7, d9, P8] :: [1, 9/8, 8192/6561, 4/3, 3/2, 32768/19683, 16/9, 1048576/531441, 2]
Zirafkand: [P1, d3, m3, P4, d6, m6, d7, d8, P8] :: [1, 65536/59049, 32/27, 4/3, 262144/177147, 128/81, 32768/19683, 4096/2187, 2]
Buzurg: [P1, d3, d4, P4, d6, P5, M6, d8, P8] :: [1, 65536/59049, 8192/6561, 4/3, 262144/177147, 3/2, 27/16, 4096/2187, 2]
Zangulah: [P1, M2, d4, P4, d6, d7, m7, P8] :: [1, 9/8, 8192/6561, 4/3, 262144/177147, 32768/19683, 16/9, 2]
Rahawi: [P1, d3, d4, P4, d6, m6, m7, P8] :: [1, 65536/59049, 8192/6561, 4/3, 262144/177147, 128/81, 16/9, 2]
Husaini: [P1, d3, m3, P4, d6, m6, m7, P8] :: [1, 65536/59049, 32/27, 4/3, 262144/177147, 128/81, 16/9, 2]
Higazi: [P1, d3, m3, P4, d6, d7, m7, P8] :: [1, 65536/59049, 32/27, 4/3, 262144/177147, 32768/19683, 16/9, 2]
HFF also givess two more Arabic modes with Pythagorean intonation, drawn from the same 17-tone collection as Safi al-Din's maqamat. These are:
al-Kindi's mode: [P1, m2, M2, m3, d4, M3, P4, d5, P5, m6, d7, M6, m7, d8, P8] :: [1, 256/243, 9/8, 32/27, 8192/6561, 81/64, 4/3, 1024/729, 3/2, 128/81, 32768/19683, 27/16, 16/9, 4096/2187, 2]
Ishaq al-Mausili's mode: [P1, m2, M2, m3, M3, P4, d5, P5, m6, M6, m7, P8] :: [1, 256/243, 9/8, 32/27, 81/64, 4/3, 1024/729, 3/2, 128/81, 27/16, 16/9, 2]
You can see that al-Kindi's mode has 14 tones. Pretty crazy. All of Safi al-Din's maqamat had just 7 tones.
HFF presents these things with indices into the 17-tone collection, but relative indices from the last scale tone instead of absolute indices, so that a scale looks like this:
3 3 1 3 3 1 3 Safi al-Din's maqam `Ussaq
And you have to keep a running sum of indices to figure out the next scale tone. That's a compressed representation, but it doesn't let me directly see the intervals or frequency ratios and isn't very useful to me, which is part of why I'm writing this post.
I don't know if these scales can rightly be attributed to Safi al-Din, but it's nice to have some data if not any kind of attributable or followable source. Let's do a few more.
HFF presents some scales as "24-tone modes" without any specification of just frequency ratios, so they're probably intended to be read as 24-EDO. This list has some maqamat (presumably Arabic maqamat and not Turkish) and some Persian dastgah. If we accumulate relative steps, we get these scales:
Maqam 'Ushshaq Turki, Urfa, Isfahan, Dastgah-e Shur: [0, 3, 6, 10, 14, 16, 20, 24]
Maqam Bayati: [0, 3, 6, 10, 14, 16, 17, 20, 24]
Maqam Nahfat: [0, 3, 6, 10, 14, 18, 20, 24]
Maqam Saba: [0, 3, 6, 8, 14, 16, 20, 22, 24]
Maqam Sabr Jadid: [0, 3, 6, 8, 14, 16, 22, 24]
Maqam Mansuri: [0, 3, 6, 8, 10, 14, 17, 20, 24]
Maqam Suznak (Soznak): [0, 4, 7, 10, 14, 16, 22, 24]
Maqam Rast, Dilkashidah, Dilnishin: [0, 4, 7, 10, 14, 18, 20, 21, 24]
Maqam Mahur: [0, 4, 7, 10, 14, 18, 22, 24]
Maqam Yakah: [0, 4, 7, 8, 10, 11, 14, 18, 20, 21, 24]
Maqam Suzidil 'ara: [0, 4, 7, 8, 10, 14, 18, 20, 24]
Maqam Qarjighar, Bayati Shuri: [0, 3, 6, 10, 12, 18, 20, 24]
Maqam Huzzam: [0, 3, 7, 9, 11, 13, 15, 17, 21, 24]
Maqam Hizam (Huzzam, El Houzam), Rahat al Arouah: [0, 3, 7, 9, 15, 17, 21, 24]
Maqam Rahat al-Arwah: [0, 3, 7, 9, 15, 17, 21, 23, 24]
Maqam Iraq: [0, 3, 7, 10, 13, 17, 21, 23, 24]
Maqam Hijaz: [0, 2, 8, 10, 14, 16, 17, 20, 24]
Maqam Musta'ar: [0, 3, 7, 11, 13, 14, 17, 21, 24]
Maqam Farahnak: [0, 3, 7, 11, 15, 17, 21, 23, 24]
Maqam Bastanikar, Tarz Nuin (Tarznauyn): [0, 3, 7, 10, 13, 15, 21, 23, 24]
Maqam Farah Faza, Maqam Nakriz: [0, 4, 6, 12, 14, 18, 20, 21, 24]
Maqam Hayyan: [0, 4, 6, 7, 10, 12, 14, 16, 18, 21, 22, 24]
Maqam Basandida: [0, 4, 6, 7, 10, 12, 14, 18, 20, 21, 24]
Maqam Shawq Afza: [0, 4, 8, 10, 11, 14, 16, 18, 22, 24]
Maqam Shawq Tarab: [0, 2, 3, 6, 8, 10, 14, 16, 20, 22, 24]
Maqam Jabburi: [0, 3, 4, 6, 10, 14, 16, 20, 24]
Maqam Nawa: [0, 2, 6, 10, 14, 17, 20, 24]
Maqam Higaz-kar: [0, 2, 7, 10, 14, 16, 21, 24]
Maqam Su'ar, Naghmeh Abuata, Naghmeh Afshari: [0, 3, 7, 11, 13, 17, 21, 24]
Maqam Jahargah (Jiharkah), Naghmeh Bayat-e Tork, Naghmeh Dashti: [0, 4, 8, 10, 14, 18, 21, 24]
Maqam 'Ajam Murassah, Ioniolydian: [0, 4, 8, 11, 14, 18, 22, 24]
Dastgah-e Homayun: [0, 3, 8, 10, 14, 16, 20, 24]
Naghmeh Esfahan: [0, 4, 6, 10, 14, 17, 22, 24]
Maqam 'Awg 'ara (Aug-ara): [0, 3, 9, 10, 15, 17, 23, 24]
Maqam Buselik: [0, 4, 5, 10, 14, 16, 22, 24]
Maqam Neuter: [0, 4, 6, 12, 14, 16, 21, 24]
I suppose I could show some detemperings of these scales. For example, frequency ratios in the 2.3.11 just intonation subgroup are an easy way to understand 24-EDO that also have moderate historical support in describing middle eastern scales. But I think that's for a different post. This post is just for re-representing some ugly data.
The next middle eastern scales that interest me from this page are descriptions of Persian dastgah in 36 EDO. I've spent a long time learning about dastgah and I think I've figured out their spelling and intonations very well, but I haven't see them in 36-EDO, so let's see how that looks:
Dastgah-e Shur : [0, 4, 9, 15, 19, 21, 24, 25, 30, 36]
Dastgah-e Abuata : [0, 4, 9, 15, 21, 24, 25, 30, 36]
Dastgah-e Dashti : [0, 3, 4, 9, 15, 19, 21, 24, 25, 30, 36]
Dastgah-e Bayat-e Tork : [0, 3, 6, 12, 15, 21, 27, 31, 36]
Dastgah-e Afshari : [0, 6, 10, 15, 21, 25, 27, 30, 31, 36]
Dastgah-e Segah : [0, 5, 11, 15, 20, 21, 26, 32, 36]
Dastgah-e Chahargah : [0, 4, 12, 15, 21, 25, 33, 36]
Dastgah-e Homayun : [0, 4, 12, 15, 21, 24, 25, 30, 36]
Dastgah-e Bayat-e Esfahan : [0, 6, 9, 15, 21, 25, 31, 36]
Dastgah-e Nava : [0, 6, 9, 15, 21, 25, 30, 36]
Dastgah-e Mahur, Rast (Rast Panjgah) : [0, 6, 12, 15, 21, 27, 30, 33, 36]
It might be fun to sink my teeth into these some time.
Next HFF shows some Turkish makams in 53-EDO:
Makam Rast: [0, 9, 17, 22, 31, 40, 44, 48, 53]
Makam Nihavend, Muberka, Fifty-three tone Minor: [0, 9, 13, 22, 31, 35, 44, 53]
Makam Yegah: [0, 9, 17, 22, 31, 39, 40, 44, 48, 53]
Makam Sazkar: [0, 9, 17, 22, 31, 40, 48, 53]
Makam Sultaniyegah, Ruhnevaz, Ferahfeza (Farahfaza): [0, 9, 13, 22, 31, 35, 44, 48, 53]
Makam Ferahnuma, Askefza, Acem Kurdi: [0, 4, 13, 22, 31, 35, 44, 53]
Makam Sedaraban: [0, 5, 17, 22, 31, 36, 44, 48, 53]
Makam Huseyniasiran: [0, 8, 13, 22, 30, 35, 44, 53]
Makam Suzidil: [0, 5, 17, 22, 31, 35, 39, 44, 48, 53]
Makam Acemasiran: [0, 9, 18, 22, 26, 31, 40, 49, 53]
Makam Sevkefza: [0, 9, 14, 18, 22, 26, 31, 36, 49, 53]
Makam Iraq: [0, 5, 14, 22, 27, 36, 45, 49, 53]
Makam Evic, Segah: [0, 5, 14, 22, 27, 31, 36, 45, 49, 53]
Makam Ferahnak: [0, 5, 14, 22, 23, 27, 31, 36, 45, 49, 53]
Makam Evcara (Evicara): [0, 5, 18, 22, 31, 36, 49, 53]
Makam Mahur: [0, 9, 18, 22, 31, 40, 44, 49, 53]
Makam Suzidilara: [0, 9, 14, 18, 22, 26, 31, 40, 44, 49, 53]
Makam Buzurk: [0, 9, 18, 22, 26, 31, 40, 44, 48, 53]
Makam Suzinak: [0, 5, 9, 13, 17, 22, 31, 35, 44, 53]
Makam Zirguleli Suzinak: [0, 5, 17, 22, 27, 31, 35, 39, 44, 53]
Makam Hicazkar: [0, 5, 17, 22, 31, 36, 39, 44, 48, 53]
Makam Kurdilihicazkar: [0, 4, 5, 9, 13, 17, 22, 31, 35, 39, 44, 53]
Makam Nihavend (Nihavent): [0, 9, 13, 22, 27, 31, 35, 40, 48, 53]
Makam Neveser: [0, 9, 14, 26, 31, 36, 48, 53]
Makam Nikriz: [0, 9, 14, 26, 31, 40, 44, 48, 53]
Makam Huseyni, Muhayyer, Neva, Gerdaniye, Tahir: [0, 8, 13, 22, 31, 35, 39, 44, 53]
Makam Muhayyer Kurdi: [0, 4, 8, 13, 22, 31, 35, 39, 44, 53]
Makam Tahir Buselik: [0, 8, 9, 13, 22, 31, 39, 44, 48, 53]
Makam Gulizar, Beyati (Bayati), Karcigar: [0, 8, 13, 22, 27, 31, 35, 39, 44, 53]
Makam Ussak, Acem, Arazbar: [0, 8, 13, 22, 31, 35, 44, 53]
Makam Isfahan: [0, 8, 9, 13, 17, 22, 31, 35, 44, 53]
Makam Kurdi: [0, 4, 8, 9, 13, 22, 26, 31, 35, 44, 53]
Makam Buselik (Puselik): [0, 9, 13, 22, 27, 31, 35, 39, 44, 48, 53]
Makam Sehnaz Buselik: [0, 9, 13, 22, 31, 35, 48, 53]
Makam Arazbar: [0, 8, 13, 22, 27, 30, 31, 35, 39, 44, 53]
Makam Hicaz, Uzzal, Humayun: [0, 5, 17, 22, 31, 35, 39, 44, 53]
Makam Zirgule (Zengule): [0, 5, 17, 22, 31, 35, 36, 44, 48, 53]
Makam Zirguleli Hicaz: [0, 5, 17, 22, 31, 35, 48, 53]
Makam Sehnaz: [0, 5, 17, 22, 31, 35, 36, 39, 44, 48, 53]
Makam Saba, Sunbule: [0, 8, 13, 18, 31, 35, 44, 53]
Makam Saba Zemzeme: [0, 8, 13, 18, 31, 35, 44, 49, 53]
Makam Kucek: [0, 8, 13, 18, 31, 35, 39, 44, 49, 53]
Makam Eski Sipihr: [0, 8, 13, 18, 22, 31, 35, 39, 44, 48, 53]
Makam Dugah: [0, 4, 8, 13, 17, 18, 31, 35, 44, 53]
Makam Hisar: [0, 8, 13, 22, 26, 31, 35, 36, 44, 48, 53]
Makam Hisar Buselik: [0, 4, 13, 17, 22, 30, 31, 35, 44, 48, 53]
Makam Yeni Sipihr: [0, 5, 8, 13, 17, 22, 26, 31, 35, 36, 39, 44, 48, 53]
Makam Nisaburek: [0, 9, 17, 22, 31, 36, 44, 53]
Makam Huzzam: [0, 5, 14, 20, 31, 36, 45, 49, 53]
Makam Mustear: [0, 9, 14, 22, 31, 36, 45, 49, 53]
Makam Maye (Yeni Maye): [0, 5, 14, 22, 23, 27, 36, 45, 53]
Makam Vechi Arazbar: [0, 1, 5, 14, 22, 27, 36, 45, 48, 53]
Makam Nisabur: [0, 8, 13, 22, 26, 35, 44, 48, 53]
Makam Cargah I: [0, 5, 18, 22, 31, 36, 48, 53]
Makam Cargah II, Dastgah-e Mahur: [0, 9, 18, 22, 31, 40, 49, 53]
Makam Araban: [0, 5, 13, 26, 31, 36, 44, 48, 53]
Makam Urmawi: [0, 9, 17, 22, 31, 40, 45, 53]
Makam Rengidil: [0, 9, 13, 26, 31, 35, 48, 53]
Makam Arak: [0, 5, 14, 22, 27, 36, 45, 53]
Makam Necid Huseyni, Huzi: [0, 7, 8, 13, 22, 31, 35, 44, 53]
A 53-EDO intonation is the standard modern presentation of Turkish makams, so that makes good sense. I confess I've never heard of at least four of these makams. I'm really curious where these scales come from. I hope they're correct.
HFF gives us a 53-EDO intonation of the Persian dastgah:
Dastgah-e Shur: [0, 6, 13, 22, 28, 31, 35, 37, 44, 53]
Dastgah-e Abuata: [0, 6, 13, 22, 31, 35, 37, 44, 53]
Dastgah-e Dashti: [0, 4, 6, 13, 22, 28, 31, 35, 37, 44, 53]
Dastgah-e Bayat-e Tork: [0, 6, 9, 18, 22, 31, 40, 46, 53]
Dastgah-e Afshari: [0, 9, 15, 22, 31, 37, 40, 44, 46, 53]
Dastgah-e Homayun: [0, 6, 18, 22, 31, 35, 37, 44, 53]
Dastgah-e Mahur, Rast (Rast Panjgah): [0, 9, 18, 22, 31, 40, 44, 49, 53]
Naghmeh Abuata, Naghmeh Afshari: [0, 6, 15, 25, 28, 37, 46, 53]
Naghmeh Bayat-e Tork, Naghmeh Dashti: [0, 9, 18, 22, 31, 40, 46, 53]
Naghmeh Esfahan: [0, 9, 13, 22, 31, 37, 49, 53]
Dastgah-e Sehgah: [0, 6, 15, 22, 28, 37, 46, 53]
Dastgah-e Mokhalif, Bayat-e Esfahan: [0, 9, 13, 22, 31, 37, 46, 53]
Dastgah-e Chahargah: [0, 6, 18, 22, 31, 37, 49, 53]
Dastgah-e Nava: [0, 9, 13, 22, 31, 37, 44, 53]
I've never seen 53-EDO used for Persian dastgah before. This by itself, its existence, is moderately interesting. If we were feeling sassy, we could combine the 24-EDO and 53-EDO intonations for a simultaneous / twice-constrained de-tempering.
Finally HFF gives us a just intonation of the Persian dastgah. They use a 5-limit intonation, which was amazing to me because I had discovered a 5-limit intonation for Persian music independently. Their scales draw from this 17-tone collection: "1/1 256/243 27/25 9/8 32/27 243/200 81/64 4/3 25/18 36/25 3/2 128/81 81/50 27/16 16/9 729/400 243/128 2/1". I think these scales in this intonation come from Dariush Anooshfar, who is a random and hard to track down guy who once posted on a tuning theory message group, but still that's some kind of attribution.
Here are the rank-3 intervallic interpretations and 5-limit tunings of Persian modes according to Dariush Anooshfar:
Dastgah-e Mahur, Rast Panjgah: [P1, AcM2, AcM3, P4, P5, AcM6, AcM7, P8] # 1/1, 9/8, 81/64, 4/3, 3/2, 27/16, 243/128, 2/1
Dastgah-e Shur: [P1, Acm2, Grm3, P4, P5, Grm6, Grm7, P8] # 1/1, 27/25, 32/27, 4/3, 3/2, 128/81, 16/9, 2/1
Naghmeh Abuata, Naghmeh Afshari: [P1, Acm2, Acm3, A4, d5, Acm6, Acm7, P8] # 1/1, 27/25, 243/200, 25/18, 36/25, 81/50, 729/400, 2/1
Naghmeh Bayat-e Tork, Naghmeh Dashti: [P1, AcM2, AcM3, P4, P5, AcM6, Acm7, P8] # 1/1, 9/8, 81/64, 4/3, 3/2, 27/16, 729/400, 2/1
Dastgah-e Homayun: [P1, Acm2, AcM3, P4, P5, Grm6, Grm7, P8] # 1/1, 27/25, 81/64, 4/3, 3/2, 128/81, 16/9, 2/1
Naghmeh Esfahan: [P1, AcM2, Grm3, P4, P5, Acm6, AcM7, P8] # 1/1, 9/8, 32/27, 4/3, 3/2, 81/50, 243/128, 2/1
Dastgah-e Sehgah: [P1, Acm2, Acm3, P4, d5, Acm6, Acm7, P8] # 1/1, 27/25, 243/200, 4/3, 36/25, 81/50, 729/400, 2/1
Dastgah-e Mokhalif, Bayat-e Esfahan: [P1, AcM2, Grm3, P4, P5, Acm6, Acm7, P8] # 1/1, 9/8, 32/27, 4/3, 3/2, 81/50, 729/400, 2/1
Dastgah-e Chahargah: [P1, Acm2, AcM3, P4, P5, Acm6, AcM7, P8] # 1/1, 27/25, 81/64, 4/3, 3/2, 81/50, 243/128, 2/1
Dastgah-e Nava: [P1, AcM2, Grm3, P4, P5, Acm6, Grm7, P8] # 1/1, 9/8, 32/27, 4/3, 3/2, 81/50, 16/9, 2/1
Smashing.
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