353edo: Difference between revisions

Line 13:

Following this logic, a temperament can be constructed for the Rectified Hebrew calendar (see below), containing 130 notes of the 353edo scale. Hebrew[130] scale has 334\353 as its generator, which is a supermajor seventh, or alternately, 19\353, about a third-tone, since inverting the generator has no effect on the scale. 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]].

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 ===

Such a temperament gives 19edo a unique stretch: 6\19 corresponds to [[5/4]], 13\19 corresponds to [[13/8]], and 15\19 corresponds to [[7/4]]. When measured relative to the generator, the error is less than 1 in 5000.

~~If 209\353 is loosely assumed to equal 3/2, it~~ offers ~~a 710c stretched fifth, and~~ 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"~~. Such an arrangement also "tempers out" [[169/168]]~~.

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".

== Table of intervals ==

@@ Line 13: / Line 13: @@
 Following this logic, a temperament can be constructed for the Rectified Hebrew calendar (see below), containing 130 notes of the 353edo scale. Hebrew[130] scale has 334\353 as its generator, which is a supermajor seventh, or alternately, 19\353, about a third-tone, since inverting the generator has no effect on the scale. 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]].
+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 ===
 Such a temperament gives 19edo a unique stretch: 6\19 corresponds to [[5/4]], 13\19 corresponds to [[13/8]], and 15\19 corresponds to [[7/4]]. When measured relative to the generator, the error is less than 1 in 5000.
-If 209\353 is loosely assumed to equal 3/2, it offers a 710c stretched fifth, and 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". Such an arrangement also "tempers out" [[169/168]].
+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".
 == Table of intervals ==