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start:
09 january 2007, up-date: 09 january 2007
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| Safi al-Dîn names the intervals which he calls as "usable". He points out that the rest is recognized with their ratios. The intervals are: |
| 1. Zu'l-kul merrateyn (two octaves): The first of the intervals Safi al-Dîn names. The interval positioned between YB/C, H/B, D/A is the first level of ada'f level. Its ratio is 2/1x2/1=4/1. |
| 2. Zu'l-kul ve'l-hams (octave and pentachord): It is between YB/D, T/C, V/B. 2/1x3/2=3. |
| 3. Zu'l-kul ve'l erba' (octave and tetrachord): H/C interval is an example for this. 2/1x4/3=8/3. |
| 4. Zu'l-kul (octave): It is positioned between the intervals of YB/V, Y/h, H/D, V/C, D/B, B/A. Its value is 2/1. |
| 5. Zu'l-hams (pentachord): The first of mithl and cuz' levels. It is positioned between YB/H, T/V, V/D. Its ratio is 3/2. |
6. Zu'l-erba (tetrachord): The intervals of YB/T, H/V, D/C. The second level of mithl and cuz' at tetrachord. Its ratio is 4/3. In spite of the fact that Safi al-Dîn says the intervals mentioned above is recognized with their names and the rest is recognized with their ratios, he also points out that the interval of 9/8 is known as "tanînî (whole-tone)" and the one with 256/243 is called as "bakiyye (remnant/limma)". Among the ones he named is also an interval called "irkha" and he indicates that this is the quarter of "tanînî (9/8)". (4) |