353edo: Difference between revisions

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Using such small of a generator helps explore the 353edo's "upside down" side. In addition, every sub-pattern in a 19-note generator is actually a Hebrew makhzor, that is a mini-19edo on its own, until it is truncated to an 11-note pattern. Just as the original calendar reform consists of 18 makhzorim with 1 hendecaeteris, Hebrew[130] scale consists of a stack of naively 18 "major scales" finished with one 11-edo tetratonic.

Rectified Hebrew temperament is a 13-limit extension of the didacus. In the 13-limit, the it tempers out [[3136/3125]], [[4394/4375]], [[10985/10976]], and [[1968512/1953125]].

Rectified Hebrew temperament is a 13-limit extension of the didacus. In the 13-limit, the it tempers out [[3136/3125]], [[4394/4375]], [[10985/10976]], and [[1968512/1953125]]. 5 instances of 5/4 and two of 7/4 both amount to 30 generators (570 steps).

While the just 3/2 is on 206 in 353edo, the more rational way would be to use the perfect fifth that is provided by the 19-tone scale resulting from the generator. This produces the 353bbbbb val: [353 '''562''' 820 991 1306⟩, where the fifth is on 11*19 = 209 steps and measures about 710 cents. Such an usage of the rectified Hebrew temperament tempers out [[91/90]], [[169/168]], [[196/195]], [[625/624]], [[686/675]], [[875/864]], [[2197/2160]], and [45,-27,6,-7,1⟩.

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 Using such small of a generator helps explore the 353edo's "upside down" side. In addition, every sub-pattern in a 19-note generator is actually a Hebrew makhzor, that is a mini-19edo on its own, until it is truncated to an 11-note pattern. Just as the original calendar reform consists of 18 makhzorim with 1 hendecaeteris, Hebrew[130] scale consists of a stack of naively 18 "major scales" finished with one 11-edo tetratonic.
-Rectified Hebrew temperament is a 13-limit extension of the didacus. In the 13-limit, the it tempers out [[3136/3125]], [[4394/4375]], [[10985/10976]], and [[1968512/1953125]].
+Rectified Hebrew temperament is a 13-limit extension of the didacus. In the 13-limit, the it tempers out [[3136/3125]], [[4394/4375]], [[10985/10976]], and [[1968512/1953125]]. 5 instances of 5/4 and two of 7/4 both amount to 30 generators (570 steps).
 While the just 3/2 is on 206 in 353edo, the more rational way would be to use the perfect fifth that is provided by the 19-tone scale resulting from the generator. This produces the 353bbbbb val: [353 '''562''' 820 991 1306⟩, where the fifth is on 11*19 = 209 steps and measures about 710 cents. Such an usage of the rectified Hebrew temperament tempers out [[91/90]], [[169/168]], [[196/195]], [[625/624]], [[686/675]], [[875/864]], [[2197/2160]], and [45,-27,6,-7,1⟩.