| Safi
al-Dîn arranged tetrachords, from 5/4 to 256/243, with lahnî
intervals. And this is not more than three intervals and four notes and
called as jins (kind). |
|
| If
the ratio of the biggest of the intervals in tetrachords is bigger than
the total sum of the other two, it is called layyin (weak)
kind. The rest is called kawî (strong)
kind. In a tetrachord are three ratios bigger than the other two. These
are 5/4, 6/5, 7/6. |
| |
| Layyin
is divided into three. The one whose biggest interval is 5/4 is called râsim
(enharmonic), the one with 6/5 is lawnî
(chromatic) and the one with 7/6 is named nâzim
(chromatic). The following one will be 8/7 which is not bigger
than the other two ratios is classified in the kawî
(diatonic) kinds. |
| |
| Layyin
classes are arranged as follows; |
| Râsim
(daif/feeble) : 5/4x32/31x31/30=4/3. |
| Râsim
(eþed/firm) : 5/4x24/23x46/45=4/3. |
| Lawnî
(feeble) : 6/5x19/18x20/19=4/3. |
| Lawnî
(firm) : 6/5x15/14x28/27=4/3. |
| Nâzim
(feeble) : 7/6x16/15x15/14=4/3. |
| Nâzim
(firm) : 7/6x12/11x22/21=4/3. |
| |
| Next
comes kawî (strong) kinds: |
| |
| First
non-conjunct (feeble) : 8/7x14/13x13/12=4/3 |
| First
non-conjunct (firm) : 8/7x21/19x19/18=4/3. |
| Second
non-conjunct (feeble): 9/8x64/59x59/54=4/3. |
| Second
non-conjunct (firm) : 9/8x48/43x86/81=4/3. |
| Third
non-conjunct (feeble) : 10/9x12/11x11/10=4/3. |
| Third
non-conjunct (firm) : 10/9x9/8x16/15=4/3. |
| |
| After
that the following ones are the kinds formed
by putting the two equal ratios together. These are zü't-tadi'f
(doubling) kinds. They are arranged as three classes: |
| |
| First
doubling : 8/7x8/7x49/48=4/3 |
| Second
doubling : 9/8x9/8x256/243=4/3 |
| Third
doubling : 10/9x10/9x27/25=4/3 |
| |
| Safi
al-Dîn reminds that bakiyye interval
is named for 256/243 in "second doubling kind" and points out
that this is the mostly used and called as zü'l-müddeteyn.
|
| |
| Then
three intervals are arranged with the two ratios following each other in
a tetrachord and this kind is called muttasil (conjunct
/continuous). |
| |
| First
conjunct : 8/7x9/8x28/27=4/3 |
| Second
conjunct : 9/8x10/9x16/15=4/3 |
| Third
conjunct : 10/9x11/10x12/11=4/3 |
| |
| Following
this the kinds formed as not following each other but formed as skipping
one ratio are arranged. These kinds, which are called munfasil (disjunct),
are three parts: |
| |
| Feeble
disjunct : 8/7x10/9x21/20=4/3 |
| Medium
disjunct : 9/8x11/10x320/297=4/3 |
| Firm
disjunct :10/9x12/11x11/10=4/3. |
| |
| After
finishing the kinds he arranged the tetrachord as three intervals, Safi
al-Dîn points out that it is possible to divide tetrachord into four
intervals opposite to the general rule of "a tetrachord is composed
of three intervals". This is most conveniently classified in two ways. |
| |
| First
: 13/12x14/13x13/12x96/91=4/3. |
| Second:
13/12x14/13x15/14x16/15=4/3. |
| |
| The
second one is arranged as 24 classes and the most convenient one is the
first class (13/12, 14/13, 15/ 14, 16/15) and called as the
first single kind (Isfehân). |
| Safi
al-Dîn subtracts 16/15 from the tetrachord and names the rest
the second single kind (Râhewî). |