353edo: Difference between revisions

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353bbbbb val offers the following resolution sequence:13/8 D4/3 - D7 - T53, or in steps: 247-0-38-152 - 209-323-57-152 - 0-114-209, or 0-95-209. 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.

18L 1s of Rectified Hebrew 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. 7\19 corresponds to [[13/10]] when measured using the patent val (1306 - 820 - 353 = 133), however the direct approximation using the number is 134 steps. Since patent val is used to define if a comma is "tempered out", repeatedly stacking 7\19 3 times and reducing arrives at 46\353, an approximation for [[35/32]]. The approach using 134 is inconistent by itself already, so therefore it can't be used.

18L 1s of Rectified Hebrew 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. 7\19 corresponds to [[13/10]] when measured using the patent val (1306 - 820 - 353 = 133), however the direct approximation using the number is 134 steps. Since patent val is used to define if a comma is "tempered out", repeatedly stacking 7\19 3 times and reducing arrives at 46\353, an approximation for [[35/32]]. The approach using 134 is inconistent by itself already, so therefore it can't be used. Temperance of 4394/4375 also means that two 26/25s are equated with 14/13.

Just as a large amount of [[12edo]] music can be played consistently in 19edo, it can also be played consistently in the 18L 1s subset of Rectified Hebrew.

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 bbbbb val offers the following resolution sequence:13/8 D4/3 - D7 - T53, or in steps: 247-0-38-152 - 209-323-57-152 - 0-114-209, or 0-95-209. 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.
-L 1s of Rectified Hebrew 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. 7\19 corresponds to [[13/10]] when measured using the patent val (1306 - 820 - 353 = 133), however the direct approximation using the number is 134 steps. Since patent val is used to define if a comma is "tempered out", repeatedly stacking 7\19 3 times and reducing arrives at 46\353, an approximation for [[35/32]]. The approach using 134 is inconistent by itself already, so therefore it can't be used.
+L 1s of Rectified Hebrew 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. 7\19 corresponds to [[13/10]] when measured using the patent val (1306 - 820 - 353 = 133), however the direct approximation using the number is 134 steps. Since patent val is used to define if a comma is "tempered out", repeatedly stacking 7\19 3 times and reducing arrives at 46\353, an approximation for [[35/32]]. The approach using 134 is inconistent by itself already, so therefore it can't be used. Temperance of 4394/4375 also means that two 26/25s are equated with 14/13.
 Just as a large amount of [[12edo]] music can be played consistently in 19edo, it can also be played consistently in the 18L 1s subset of Rectified Hebrew.
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