Cohérence différencielle des échelles traditionnelles :

Mohajira scales and temperaments – described in the article “Differential coherence” and developped in the “Sumer” pieces in Lumières Audibles (CD by J. Dudon, Mondes Harmoniques, 1996).

A typically differentially-coherent Mohajira mediant third generator is approched by 11/9, or more precisely 1,2232849565995656, where its difference tone is in unisson, one octave higher, with four of the same generator down.

A sequence of Mohajira mediant thirds generates a Mohajira heptaphone, of typical symmetrical form   s  L  s  L  s  L  s  composed of three [s L s] tetrachords where s ~12/11 and L ~9/8, extending itself in Rast and Bayati scales, and further on in diatonic meantone scales, as any Mohajira sequence contains two interleaved Meantone sequences.

Any half of a meantone fifth can be a potential Mohajira generator, and balanced divisions of Mohajira sequences include 7, 24, 31, 55, etc. tones per octave.

The (octave-reduced) mapping of Mohajira for the first harmonics is :

h :      3    5     7    9    11    13

m^:   2    8   -11   4    5     -1

Among the commas Mohajira tempers are : 66/65, 77/76, 81/80, 96/95, 105/104, 121/120, 144/143, 176/175, 352/351

 

Tsaharuk temperamentParametric representation of Tsaharuk ribbon temperament (= 5 generators in a fifth, 6 in a 13/8, second generator = 5/4) designed for Julien Jalal Eddine Weiss’s microtonal qânuns, 3.1.2011, published and discussed in “A temperament for Maqam“, tuning list 7.7.2011.

This “parametric” version of the Tsaharuk horagram describes the resolution of some of the best edo solutions (77, 171, 94) of the temperament around pure fifths, that was the target for the qânun master’s requirements for Maqâm interpretation. Not represented are 359 edo, between 94 and 171 for even closer-to-pure fifths, nor with larger fifths 111-edo (producing the best approximation of 11/8 in 51 steps), 128-edo, etc., that will resume gradually to 17-quasi-edo solutions for the same mappings.

The idea of this temperament came after finding an extended JI version for Julien Jalal Eddine Weiss’s specially small qânun stops (15 per string), based on the harmonic suite 114:115:116:117:118:119:120, then tempering these commas. Among the schismas and commas Tsaharuk tempers are the following : 14337/14336, 5832/5831, 4096/4095, 3520/3519, 2601/2600, 2185/2184, 1521/1520, 945/944, 833/832, 768/767, 729/728, 561/560, 484/483, 385/384, 378/377, 352/351…

 

Seven-limit Slendro Mutations  – article by J.Dudon in The Journal of the Just Intonation Network, 1994, explaining how 5 types of just intonation traditional central Java Slendros (S, J, A, M, N) differ only of one note from eachother.

 

 

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Tétracorde persan médieval “Buzurg” (12:13:14:16, Safî-Al-Dîn)

Décaphone Surak-Nat Buzurg : enchevêtrement de deux slendros javanais contenant un heptaphone Buzurg et ses variantes (Estrangetés et Arabesques, Ensemble de Musique Microtonale du Thoronet, 1998)