Editing Tetrachord (section)

===Persian===
[[Persian traditional music|Persian]] music divides the interval of a fourth differently than the Greek. For example, [[Al-Farabi]] describes four genres of the division of the fourth:{{sfn|Al-Farabi|2001|pp=56–57}}
* The first genre, corresponding to the Greek diatonic, is composed of a tone, a tone, and a semitone, as G–A–B–C.
* The second genre is composed of a tone, a three-quarter tone, and a three-quarter tone, as G–A–B{{music|half flat}}–C.
* The third genre has a tone and a quarter, a three-quarter tone, and a semitone, as G–A{{music|half sharp}}–B–C.
* The fourth genre, corresponding to the Greek chromatic, has a tone and a half, a semitone, and a semitone, as G–A{{music|sharp}}–B–C.
He continues with four other possible genres "dividing the tone in quarters, eighths, thirds, half thirds, quarter thirds, and combining them in diverse manners".{{sfn|Al-Farabi|2001|p=58}} Later, he presents possible positions of the frets on the lute, producing ten intervals dividing the interval of a fourth between the strings:<ref>
{{harvnb|Al-Farabi|2001|pp=165–179}}
:
{{cite book
 |first=Liberty |last=Manik
 |year=1969
 |title=Das Arabische Tonsystem im Mittelalter
 |place=Leiden, NL
 |publisher=E.J. Brill
 |page=42
}}
:
{{cite book
 |first=H.H. |last=Touma |author-link=Habib Hassan Touma
 |year=1996
 |title=The Music of the Arabs
 |translator-first=Laurie |translator-last=Schwartz
 |place=Portland, OR
 |publisher=Amadeus Press
 |ISBN=0-931340-88-8
 |page=19
}}</ref>
{| style="text-align: center; margin-left: 4em;"
|style="text-align: left; width: 6em;"| Frequency ratio:
|style="width: 3em;"| {{math|{{sfrac| 1 | 1 }} }}
|style="width: 3em;"| {{math|{{sfrac| 256 | 243 }} }}
|style="width: 3em;"| {{math|{{sfrac| 18 | 17 }} }}
|style="width: 3em;"| {{math|{{sfrac| 162 | 149 }} }}
|style="width: 3em;"| {{math|{{sfrac| 54 | 49 }} }}
|style="width: 3em;"| {{math|{{sfrac| 9 | 8 }} }}
|style="width: 3em;"| {{math|{{sfrac| 32 | 27 }} }}
|style="width: 3em;"| {{math|{{sfrac| 81 | 68 }} }}
|style="width: 3em;"| {{math|{{sfrac| 27 | 22 }} }}
|style="width: 3em;"| {{math|{{sfrac| 81 | 64 }} }}
|style="width: 3em;"| {{math|{{sfrac| 4 | 3 }} }}
|-
|style="text-align: left;"| Note name:
| C
| C{{sup|{{music|#}}{{music|-}} }}
| C{{sup|{{music|#}}{{music|17}} }}
| C{{sup|{{music|#t}}}}
| C{{sup|{{music|#t}}{{music|7}} }}
| D
| E{{sup|{{music|b}}{{music|-}} }}
| E{{sup|{{music|b}}{{music|+}} }}
| E{{sup|{{music|d}} }}
| E{{sup|{{music|-}} }}
| F
|-
|style="text-align: left;"| [[cent (music)|Cent]]s:
|   0
|  90
|  99
| 145
| 168
| 204
| 294
| 303
| 355
| 408
| 498
|}

If one considers that the interval of a fourth between the strings of the lute ([[Oud]]) corresponds to a tetrachord, and that there are two tetrachords and a [[major second|major tone]] in an octave, this would create a 25&nbsp;tone scale. A more inclusive description (where [[Turkish makam|Ottoman]], [[Persian maqam|Persian]], and [[Arabic maqam|Arabic]] overlap), of the scale divisions is that of 24&nbsp;quarter tones (see also [[Arabian maqam]]). It should be mentioned that Al-Farabi's, among other [[maqam|Islamic musical treatises]], also contained additional division schemes as well as providing a gloss of the Greek system, as Aristoxenian doctrines were often included.{{sfn|Chalmers|1993|p=20}}