353edo: Difference between revisions
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== Theory == | == Theory == | ||
353edo is in[[consistent]] in the [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps. It is suitable for use with the 2.9.15.7.11.13.17.23.29.31.37 [[subgroup]]. This makes 353edo an "upside-down" | 353edo is in[[consistent]] in the [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps. It is suitable for use with the 2.9.15.7.11.13.17.23.29.31.37 [[subgroup]]. This makes 353edo an "upside-down" edo—poor approximation of the low harmonics, but an improvement over the high ones. Nonetheless, it provides the [[optimal patent val]] for [[didacus]], the 2.5.7 subgroup temperament tempering out [[3136/3125]]. | ||
Using the [[patent val]] nonetheless, 353edo supports [[apparatus]], [[marvo]] and [[zarvo]]. | Using the [[patent val]] nonetheless, 353edo supports [[apparatus]], [[marvo]] and [[zarvo]]. | ||
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The number 353 in this version of the Hebrew calendar must not be confused with the number of days in ''shanah chaserah'' (שנה חסרה), the deficient year. | The number 353 in this version of the Hebrew calendar must not be confused with the number of days in ''shanah chaserah'' (שנה חסרה), the deficient year. | ||
It is possible to use a superpyth-ish fifth of Rectified Hebrew fifth, 209\353, as a generator. In this case, 76 & 353 temperament is obtained. In the 2.5.7.13 subgroup, this results in the fifth being equal to 98/65 and the comma basis of 10985/10976, {{Monzo|-103 0 -38 51 0 13}}. | It is possible to use a superpyth-ish fifth of Rectified Hebrew fifth, 209\353, as a generator. In this case, {{nowrap|76 & 353}} temperament is obtained. In the 2.5.7.13 subgroup, this results in the fifth being equal to 98/65 and the comma basis of 10985/10976, {{Monzo|-103 0 -38 51 0 13}}. | ||
== Table of intervals == | == Table of intervals == | ||
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| {{monzo| 820 -353 }} | | {{monzo| 820 -353 }} | ||
| {{mapping| 353 820 }} | | {{mapping| 353 820 }} | ||
| | | −0.263 | ||
| 0.263 | | 0.263 | ||
| 7.74 | | 7.74 | ||
| Line 168: | Line 168: | ||
| 3136/3125, {{monzo| 209 -9 -67 }} | | 3136/3125, {{monzo| 209 -9 -67 }} | ||
| {{mapping| 353 820 991 }} | | {{mapping| 353 820 991 }} | ||
| | | −0.177 | ||
| 0.247 | | 0.247 | ||
| 7.26 | | 7.26 | ||
| Line 175: | Line 175: | ||
| 3136/3125, 5767168/5764801, {{monzo| -20 -6 1 9 }} | | 3136/3125, 5767168/5764801, {{monzo| -20 -6 1 9 }} | ||
| {{mapping| 353 820 991 1221 }} | | {{mapping| 353 820 991 1221 }} | ||
| | | −0.089 | ||
| 0.263 | | 0.263 | ||
| 7.73 | | 7.73 | ||
| Line 182: | Line 182: | ||
| 3136/3125, 4394/4375, 6656/6655, 5767168/5764801 | | 3136/3125, 4394/4375, 6656/6655, 5767168/5764801 | ||
| {{mapping| 353 820 991 1221 1306 }} | | {{mapping| 353 820 991 1221 1306 }} | ||
| | | −0.024 | ||
| 0.268 | | 0.268 | ||
| 7.89 | | 7.89 | ||
| Line 189: | Line 189: | ||
| 3136/3125, 4394/4375, 7744/7735, 60112/60025, 64141/64000 | | 3136/3125, 4394/4375, 7744/7735, 60112/60025, 64141/64000 | ||
| {{mapping| 353 820 991 1221 1306 1443 }} | | {{mapping| 353 820 991 1221 1306 1443 }} | ||
| | | −0.037 | ||
| 0.247 | | 0.247 | ||
| 7.26 | | 7.26 | ||
| Line 225: | Line 225: | ||
== Scales == | == Scales == | ||
* RectifiedHebrew[19] | * RectifiedHebrew[19] – 18L 1s | ||
* RectifiedHebrew[130] | * RectifiedHebrew[130] – 93L 37s | ||
* Austro-Hungarian Minor[9] | * Austro-Hungarian Minor[9] – 57 38 38 38 38 38 38 38 30 | ||
== See also == | == See also == | ||
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== Music == | == Music == | ||
; [[Eliora]] | ; [[Eliora]] | ||
* [https://www.youtube.com/watch?v=JrSEGE6_oys ''Snow On My City''] (2022) | * [https://www.youtube.com/watch?v=JrSEGE6_oys ''Snow On My City''] (2022) – cover of [[wikipedia:Naomi Shemer|Naomi Shemer]] in Rectified Hebrew and apparatus | ||
; [[Mercury Amalgam]] | ; [[Mercury Amalgam]] | ||
* [https://www.youtube.com/watch?v=z-SxvrnkTzU ''Bottom Text''] (2022) in Rectified Hebrew | * [https://www.youtube.com/watch?v=z-SxvrnkTzU ''Bottom Text''] (2022) in Rectified Hebrew | ||