IV. 2) The Arrangement of

Tetrachords in

one Octave with the

Intervals at Kinds

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.