----------------------------------------------------------- The Ushshaq Masri Rotations A Constant Structure Superset of the 1-3-7-9 Hexany Modal Summary ----------------------------------------------------------- The longer paper on "The Ushshaq Masri Rotations" presents the Constant Structure resulting from the 1-3-7-9 hexany plus an added 13/8 step, and discusses the seven rotations or modes of this scale from the perspective of medieval and later Near Eastern practice and theory. This modal summary simply lists these rotations, associating them with certain Near Eastern modal categories and genera (trichords, tetrachords, or pentachords) which might fit. The term "associating" may be wise, because my associations might not be those of someone brought up in Near Eastern traditions, in the medieval era or any other! These diagrams borrow a medieval notation used by Safi al-Din al-Urmawi in the 13th century to categorize melodic intervals. In his system, the three basic symbols are these: T or _tanini_ means a whole tone, typically 9:8 (203.9 cents) B or _bakkiye_ means a limma or semitone, typically 256:243 (90.2 cents) J or _mujannab_ means a middle step somewhere between B and T Medieval usage is flexible, with T applying to either 9:8 or 8:7, and likewise B to either the usual 256:243 semitone or to smaller steps such as 27:26 (65.3 cents) or 117:112 (75.6 cents). The J symbol applies to middle second steps, broadly defined in Safi al-Din and modern Turkish theory to encompass the whole range between around 16:15 (111.7 cents) and 10:9 (182.4 cents), and including the spectrum of neutral seconds at around 125-170 cents. In this heptatonic Constant Structure, where there are five diatonic step sizes, Safi al-Din's categories of T, B, and J map like this: T or _tanini_ at 9:8 (203.9 cents) or 8:7 (231.2 cents) B or _bakiyye_ at 28:27 (63.0 cents) J or _mujannab_ at 14:13 (128.3 cents) or 13:12 (138.6 cents) Ushshaq Masri: Rotation 0 |-------------------------------------------|------------------------------| | T B T T | J J T | |___________________________________________|______________________________| | | | | | | | | | 9:8 |28:27| 9:8 | 8:7 | 13:12 | 14:13 | 8:7 | |___________|_____|___________|_____________|________|_______|_____________| 1/1 9/8 7/6 21/16 3/2 13/8 7/4 2/1 |-------------------------------------------|------------------------------| | Busalik | Bayyati | |-------------------------------------------|------------------------------| Rotation 1: Kurdi + Bayyati |-------------------------------|------------------------------|-----------| | B T T | J J T | T | |_______________________________|______________________________|___________| | | | | | | | | |28:27| 9:8 | 8:7 | 13:12 | 14:13 | 8:7 | 9:8 | |_____|___________|_____________|________|_______|_____________|___________| 1/1 28/27 7/6 4/3 13/9 14/9 16/9 2/1 |-------------------------------|------------------------------|-----------| | Kurdi | Bayyati | tone | |-------------------------------|------------------------------|-----------| Rotation 2: Maqam `Ajam Murassa |------------------------------------------|-------------------------------| | T T J J | T T B | |__________________________________________|_______________________________| | | | | | | | | | 9:8 | 8:7 | 13:12 | 14:13 | 8:7 | 9:8 |28:27| |___________|_____________|________|_______|_____________|___________|_____| 1/1 9/8 9/7 39/28 3/2 12/7 27/14 2/1 |------------------------------------------|-------------------------------| | Najdi | `Ajam | |------------------------------------------|-------------------------------| Rotation 3: Septimal Rast + Septimal `Ajam |------------------------------|-------------------------------|-----------| | T J J | T T B | T | |______________________________|_______________________________|___________| | | | | | | | | | 8:7 | 13:12 | 14:13 | 8:7 | 9:8 |28:27| 9:8 | |_____________|________|_______|_____________|___________|_____|___________| 1/1 8/7 26/21 4/3 32/21 12/7 16/9 2/1 |------------------------------|-------------------------------|-----------| | Septimal Rast | Septimal `Ajam | tone | |------------------------------|-------------------------------|-----------| Rotation 4: Arab Bayyati or Persian Shur |------------------------------|-----------------------------|-------------| | J J T | T B T | T | |______________________________|_____________________________|_____________| | | | | | | | | | 13:12 | 14:13 | 8:7 | 9:8 |28:27| 9:8 | 8:7 | |________|_______|_____________|___________|_____|___________|_____________| 1/1 13/12 7/6 4/3 3/2 14/9 7/4 2/1 |------------------------------|-----------------------------|-------------| | Bayyati | Nahawand | tone | |------------------------------|-----------------------------|----------=--| Rotation 5: A Buzurg Variant |---------------------|-----------------------------|----------------------| | J T | T B T | T J | |_____________________|_____________________________|______________________| | | | | | | | | | 14:13 | 8:7 | 9:8 |28:27| 9:8 | 8:7 | 13:12 | |_______|_____________|___________|_____|___________|_____________|________| 1/1 14/13 16/13 18/13 56/39 21/13 24/13 2/1 |---------------------|-----------------------------|----------------------| | Buzurg | Nahawand | Rast | |---------------------|-----------------------------|----------------------| Rotation 6: A Harmonic Maqam Jaharkah |-------------------------------|-----------|------------------------------| | T T B | T | T J J | |_______________________________|___________|______________________________| | | | | | | | | | 8:7 | 9:8 |28:27| 9:8 | 8:7 | 13:12 | 14:13 | |_____________|___________|_____|___________|_____________|________|_______| 1/1 8/7 9/7 4/3 3/2 12/7 13/7 2/1 |-------------------------------|-----------|------------------------------| | `Ajam | tone | Rast | |-------------------------------|-----------|------------------------------| Peace and love, Margo Schulter mschulter@calweb.com