IV. 1) The Formation of

Two Octaves with

Tetrachords and

Tanînî Intervals

In this part Safi al-Dîn firstly arranges two octave scales with tetrachords. He calls the tetrachords in two octaves, "tabaka (layer)" and mentions about it first, second, third, fourth layers subsequently. He calls tanînî, "fâsila" in this arrangement. In this case, an octave composed of two tetrachords (tabaka) and a tone (fâsila/tanînî) and two octaves consist of four tetrachords and two tones.

He arranges the tetrachords and tanînî intervals mentioned above within two octaves as nine classes. In the first three classes "fâsýla" is at the low in pitch side, tetrachords are at the high in pitch side, in the second three classes "fâsila" is at the high in pitch side and tetrachords are at the low in pitch side, in the third three classes "fâsila intervals" are in the medium and tetrachords are at the low in pitch and high in pitch sides. Also there are two tetrachords and a tanînî in the second octave. In the second octave tanînî intervals change their position in each class and they are at the low in pitch, the high in pitch and the medium. Safi al-Dîn marked the tetrachords as "C", and the tanînî intervals as "B" and he arranged the sequences like this:

If the two "fâsila" (tanînî) are both at the low in pitch side; munfasil al-athkal,

If the two "fasila" are at the high in pitch side; munfasil al-ahad,

If the first "fasila" is at the low in pitch and the other is at the high in pitch, then a tetrachord is at the medium; muttasil,

If the two "fasila" are between the tetrachords; munfasil al-awsat or fâsilat al-wustâ.

The symbols, ratios and names of these nine classes which he arranged in two octaves with tetrachords and tanînî intervals are;

I. C-C-B C-C-B: 4/3x4/3x9/8x4/3x4/3x9/8=4/1=4: Munfasil al-ahad

Double Octave

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II. C-C-B B-C-C: 4/3x4/3x9/8x9/8x4/3x4/3=4: Munfasil al-ahad al-athkal

III. C-C-B C-B-C: 4/3x4/3x9/8x4/3x9/8x4/3=4: Munfasil al-ahad al-awsat

IV. B-C-C B-C-C: 9/8x4/3x4/3x9/8x4/3x4/3=4: Munfasil al-athkal

V. B-C-C C-C-B: 9/8x4/3x4/3x4/3x4/3x9/8=4: Munfasil al-athkal al-ahad

VI. B-C-C C-B-C: 9/8x4/3x4/3x4/3x9/8x4/3=4: Munfasil al-athkal al-awsat

VII. C-B-C C-B-C: 4/3x9/8x4/3x4/3x9/8x4/3=4: Munfasil al-awsat

VIII. C-B-C C-C-B: 4/3x9/8x4/3x4/3x4/3x9/8=4: Munfasil al-awsat al-ahad

IX. C-B-C B-C-C: 4/3x9/8x4/3x9/8x4/3x4/3=4: Munfasil al-awsat al-athkal

The two octaves are arranged by combining the tetrachords as showed above.

Al-Fârâbi called "tanînî-tetrachord-tetrachord" arrangement, "munfasýl al-athkal"; "tetrachord-tetrachord-tanînî" arrangement, "munfasýl al-ahad"; "tetrachord-tanînî-tetrachord", "munfasýl al-awsat". He made this two arrangement in two octaves and he called the arrangement of "tanînî-tetrachord-tetrachord tanînî-tetrachord-tetrachord", "munfasýl cem-i tâm", "tetrachord-tetrachord-tanînî tetrachord-tetrachord-tanînî" was called "munfasýl cem-i tâm", "tetrachord- tanînî-tetrachord tetrachord-tanînî-tetrachord" was called "cem' al-ictima". Al-Fârâbi didn't use such symbols as "C" for tetrachords and "B" for tanînîes intervals like Safi al-Dîn. (9)