IV. 2) The Arrangement of

Tetrachords in

one Octave with the

Intervals at Kinds

 
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by dr. fazli arslan
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start: 09 january 2007, up-date: 09 january 2007
Safi al-Dîn arranges "munfasil al-ahad" with some of the kinds he made up in his third discourse. "Munfasil al-ahad" (C-C-B) is composed of the intervals of 4/3x4/3x9/3=2/1. He arranges the tetrachords in "munfasýl al-ahad" firstly with the intervals of "first non-conjunct kind (gayr-i muttasil)". First non-conjunct kind's intervals are 8/7x14/13x13/12=4/3. He arranges the first and the second tetrachord from these intervals and puts 9/8 at the end in order to complete the circle. Safi al-Dîn points out that he doesn't use "layyin kinds" as they are dissonant and some of the kawî kinds as they are very near in value.
 
I.Munfasil al-ahad in lower octave, is composed of these intervals as it is used with the intervals of "first non- conjunct kind/gayr-i muttasýl":
 
Octave
 
img0000000628
 
II. Munfasil al-ahad, with the intervals of "second non-conjunct". 9/8x64/59x59/49x9/8x64/59x59/54x9/8=2/1.
III. With the intervals of "third non-conjunct ";
10/9x12/11x11/10x10/9x12/11x11/10x9/8=2/1.
IV. With the intervals of "first conjunct /muttasil";
8/7x9/8x28/27x8/7x9/8x28/27x9/8=2/1.
V. With the intervals of "second conjunct ";
9/8x10/9x16/15x9/8x10/9x16/15x9/8=2/1.
VI. With the intervals of "third conjunct ";
10/9x11/10x12/11x10/9x11/10x12/11x9/8=2/1.
VII. With the intervals of "first doubling/zü't-tadî´f";
8/7x8/7x49/48x8/7x8/7x49/48x9/8=2/1.
VIII. With the intervals of "second doubling";
9/8x9/8x256/243x9/8x9/8x256/243x9/8=2/1.
IX. With the intervals of "third doubling";
10/9x10/9x27/25x10/9x10/9x27/25x9/8=2/1.
X. With the intervals of "first disjunct (feeble)/munfasil";
8/7x10/9x21/20x8/7x10/9x21/20x9/8=2/1.
XI. With the intervals of "second (medium) disjunct";
9/8x11/10x320/297x9/8x11/10x320/297x9/8=2/1.
XII. With the intervals of "third(firm) disjunct ";
10/9x12/11x11/10x10/9x12/11x11/10x9/8=2/1.