| Christopher's Persian Classical Music Intervals Page | Back to Christopher's Music Page | 23 May 2002 |
Here's some information I originally compiled for an article I posted to The Alternate Tunings Mailing List:
OK, first a disclaimer: the easiest way to get two Persian music theorists in an argument is to ask them what the actual intervals of Persian music are. :-)
I think one of the things that strongly influences the placement of frets for Persian music is that in the course of playing a Dastgah one modulates through many subsidiary Gusheh-ha by changing tonics. So, the ability to change keys is a major factor. I think it was partly for this reason that Vaziri was such a big fan of 24 tET -- since then one can change to any key and still play all the intervals consistently. The other two groups of fixed tunings that seem to be popular are tunings built up of fifths (as promoted by theorists such as Barkechli) or of fifths and thirds (based on observations by Farhat, et al).
Despite the above, most of what I have heard and read from Persian musicians (as opposed to Persian music theorists) is that the ideal intervals for all the Gusheh-ha of all the Dastgah-ha can not be reduced to a fixed set, which is why there are moveable gut frets on those Persian lutes which are not fretless. The musicians adjust their frets depending on the sequence of Gusheh-ha they are about to play.
A note about the following notation ("p" & ">"):
This is an ASCII-ified version of the symbols Vaziri introduced to allow Persian classical music to be written in western classical notation.
| interval | ratio | cents | note name | description |
|---|---|---|---|---|
| 0 | 1/1 | 0.000 | C | unison, perfect prime |
| 1 | 256/243 | 90.225 | Db | Pythagorean limma |
| 2 | 2187/2048 | 113.685 | Dp | apotome |
| 3 | 9/8 | 203.910 | D | major whole tone |
| 4 | 32/27 | 294.135 | Eb | Pythagorean minor third |
| 5 | 19683/16384 | 317.595 | Ep | Pythagorean augmented second |
| 6 | 81/64 | 407.820 | E | Pythagorean major third |
| 7 | 4/3 | 498.045 | F | perfect fourth |
| 8 | 1024/729 | 588.270 | F> | Pythagorean diminished fifth |
| 9 | 729/512 | 611.730 | Gp | Pythagorean tritone |
| 10 | 3/2 | 701.955 | G | perfect fifth |
| 11 | 128/81 | 792.180 | Ab | Pythagorean minor sixth |
| 12 | 6561/4096 | 815.640 | Ap | Pythagorean augmented fifth |
| 13 | 27/16 | 905.865 | A | Pythagorean major sixth |
| 14 | 16/9 | 996.090 | Bb | Pythagorean minor seventh |
| 15 | 59049/32768 | 1019.550 | Bp | Pythagorean augmented sixth |
| 16 | 243/128 | 1109.775 | B | Pythagorean major seventh |
| 17 | 2/1 | 1200.000 | C | octave |
Farhat, in his doctoral thesis, gives the following as the average of several observed tar and sehtar tunings:
| interval | cents | note name |
|---|---|---|
| 0 | 0.000 | C |
| 1 | 90.000 | Db |
| 2 | 135.000 | Dp |
| 3 | 205.000 | D |
| 4 | 295.000 | Eb |
| 5 | 340.000 | Ep |
| 6 | 410.000 | E |
| 7 | 500.000 | F |
| 8 | 565.000 | F> |
| 9 | 630.000 | Gp |
| 10 | 700.000 | G |
| 11 | 790.000 | Ab |
| 12 | 835.000 | Ap |
| 13 | 905.000 | A |
| 14 | 995.000 | Bb |
| 15 | 1040.000 | Bp |
| 16 | 1110.000 | B |
| 17 | 1200.000 | C |
The following (PERSIAN.SCL from Scala) is similar to Farhat's observed tuning and can be thought of as being built up of fifths and thirds.
Another way of thinking of it is to build it up from fifths and syntonic commas:
| interval | ratio | cents | note name | description |
|---|---|---|---|---|
| 0 | 1/1 | 0.000 | C | unison, perfect prime |
| 1 | 256/243 | 90.225 | Db | Pythagorean limma |
| 2 | 27/25 | 133.238 | Dp | large limma |
| 3 | 9/8 | 203.910 | D | major whole tone |
| 4 | 32/27 | 294.135 | Eb | Pythagorean minor third |
| 5 | 243/200 | 337.148 | Ep | acute minor third |
| 6 | 81/64 | 407.820 | E | Pythagorean major third |
| 7 | 4/3 | 498.045 | F | perfect fourth |
| 8 | 25/18 | 568.717 | F> | classic augmented fourth |
| 9 | 36/25 | 631.283 | Gp | classic diminished fifth |
| 10 | 3/2 | 701.955 | G | perfect fifth |
| 11 | 128/81 | 792.180 | Ab | Pythagorean minor sixth |
| 12 | 81/50 | 835.193 | Ap | acute minor sixth |
| 13 | 27/16 | 905.865 | A | Pythagorean major sixth |
| 14 | 16/9 | 996.090 | Bb | Pythagorean minor seventh |
| 15 | 729/400 | 1039.103 | Bp | acute minor seventh |
| 16 | 243/128 | 1109.775 | B | Pythagorean major seventh |
| 17 | 2/1 | 1200.000 | C | octave |
Vaziri's scale is just a subset of 24 tET:
| interval | cents | note name |
|---|---|---|
| 0 | 0.000 | C |
| 1 | 100.000 | Db |
| 2 | 150.000 | Dp |
| 3 | 200.000 | D |
| 4 | 300.000 | Eb |
| 5 | 350.000 | Ep |
| 6 | 400.000 | E |
| 7 | 500.000 | F |
| 8 | 550.000 | F> |
| 9 | 650.000 | Gp |
| 10 | 700.000 | G |
| 11 | 800.000 | Ab |
| 12 | 850.000 | Ap |
| 13 | 900.000 | A |
| 14 | 1000.000 | Bb |
| 15 | 1050.000 | Bp |
| 16 | 1100.000 | B |
| 17 | 1200.000 | C |
I believe Vaziri actually had more than 17 frets per octave on his tar, but I can not remember if he had all 24 frets per octave or a subset that was 17 < n < 24. I will try to remember to update this page if I come across the information again.
The Dastgah concept in Persian music. Farhat, Hormoz (Los Angeles) 1966 [also:] Cambridge (England) 1990
Musique d'Iran Nelly Caron et Dariouche Safvate Paris : Buchet/Chastel 1997 [in French]
Traditional Persian art music: The Radif of Mirza Abdollah Tala'i, Dariush Costa Mesa : Mazda, 1998 [set of book + 5 CDs] [Click on the title to go to Mazda Publisher's home page for this book/CD set.]
Classical Persian music; an introduction. Zonis, Ella. Cambridge, Mass. 1973
The radif of Persian music : studies of structure and cultural context in the classical music of Iran. Nettl, Bruno, 1930- Rev. ed. Champaign, Ill. 1992