353edo: Difference between revisions

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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]].

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⟩.

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⟩.

=== Specific chords and intervals ===

353bbbbb val offers the following resolution sequence: 7/4 D7 - 13/8 D2 - D53 - T53. This has a very pleasant sound, with 13/8 acting as a "doubled resolvant" or "resolution into resolution".

353bbbbb val offers the following resolution sequence: 7/4 D7 - 13/8 D4/3 - D53 - T53. This has a very pleasant sound, with 13/8 acting as a "doubled resolvant" or "resolution into resolution". In the patent val, 169/168 amounts to 3 steps, which is the L step of the full 93L 37s rectified Hebrew scale.

== Table of intervals ==

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 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]].
-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⟩.
+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⟩.
 === Specific chords and intervals ===
-bbbbb val offers the following resolution sequence: 7/4 D7 - 13/8 D2 - D53 - T53. This has a very pleasant sound, with 13/8 acting as a "doubled resolvant" or "resolution into resolution".
+bbbbb val offers the following resolution sequence: 7/4 D7 - 13/8 D4/3 - D53 - T53. This has a very pleasant sound, with 13/8 acting as a "doubled resolvant" or "resolution into resolution". In the patent val, 169/168 amounts to 3 steps, which is the L step of the full 93L 37s rectified Hebrew scale.
 == Table of intervals ==