353edo: Difference between revisions
-redundant categories. This is irrelevant to jewish music |
Cleanup; clarify the title row of the rank-2 temp table |
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== Theory == | == Theory == | ||
From the prime number standpoint, 353edo is suitable for use with 2.7.11.17.23.29.31.37 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]]. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|353}} | {{Harmonics in equal|353}} | ||
353edo is the 71st [[prime | === Subsets and supersets === | ||
353edo is the 71st [[prime edo]]. | |||
=== Relation to a calendar reform === | === Relation to a calendar reform === | ||
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Assuming 353edo is treated as the 2.5.7.11.13.17 subgroup temperament. | Assuming 353edo is treated as the 2.5.7.11.13.17 subgroup temperament. | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" |[[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Comma list|Comma List]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" |Optimal | ! rowspan="2" | Optimal<br>8ve Stretch (¢) | ||
8ve | ! colspan="2" | Tuning Error | ||
! colspan="2" |Tuning | |||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
|2.5 | | 2.5 | ||
|{{monzo|820 -353}} | | {{monzo| 820 -353 }} | ||
| | | {{mapping| 353 820 }} | ||
| -0.263 | | -0.263 | ||
|0.263 | | 0.263 | ||
|7.74 | | 7.74 | ||
|- | |- | ||
|2.5.7 | | 2.5.7 | ||
|3136/3125, {{monzo|209 -9 -67}} | | 3136/3125, {{monzo| 209 -9 -67 }} | ||
| | | {{mapping| 353 820 991 }} | ||
| -0.177 | | -0.177 | ||
|0.247 | | 0.247 | ||
|7.26 | | 7.26 | ||
|- | |- | ||
|2.5.7.11 | | 2.5.7.11 | ||
|3136/3125, 5767168/5764801, {{monzo|-20 -6 1 9}} | | 3136/3125, 5767168/5764801, {{monzo| -20 -6 1 9 }} | ||
| | | {{mapping| 353 820 991 1221 }} | ||
| -0.089 | | -0.089 | ||
|0.263 | | 0.263 | ||
|7.73 | | 7.73 | ||
|- | |- | ||
|2.5.7.11.13 | | 2.5.7.11.13 | ||
|3136/3125, 4394/4375, 6656/6655, 5767168/5764801 | | 3136/3125, 4394/4375, 6656/6655, 5767168/5764801 | ||
| | | {{mapping| 353 820 991 1221 1306 }} | ||
| -0.024 | | -0.024 | ||
|0.268 | | 0.268 | ||
|7.89 | | 7.89 | ||
|- | |- | ||
|2.5.7.11.13.17 | | 2.5.7.11.13.17 | ||
|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 }} | ||
| -0.037 | | -0.037 | ||
|0.247 | | 0.247 | ||
|7.26 | | 7.26 | ||
|} | |} | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
!Periods | ! Periods<br>per 8ve | ||
per | ! Generator* | ||
!Generator | ! Cents* | ||
! Associated<br>Ratio* | |||
!Cents | ! Temperaments | ||
!Associated | |||
!Temperaments | |||
|- | |- | ||
|1 | | 1 | ||
|19\353 | | 19\353 | ||
|64.59 | | 64.59 | ||
|26/25 | | 26/25 | ||
|[[ | | [[Rectified hebrew]] | ||
|- | |- | ||
|1 | | 1 | ||
|34\353 | | 34\353 | ||
|115.58 | | 115.58 | ||
|77/72 | | 77/72 | ||
|[[Subgroup temperaments#Apparatus|Apparatus]] | | [[Subgroup temperaments#Apparatus|Apparatus]] | ||
|- | |- | ||
|1 | | 1 | ||
|152\353 | | 152\353 | ||
|516.71 | | 516.71 | ||
|27/20 | | 27/20 | ||
|[[Marvo]] (353c) / [[zarvo]] (353cd) | | [[Marvo]] (353c) / [[zarvo]] (353cd) | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
== Scales == | == Scales == | ||
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== Music == | == Music == | ||
; [[Mercury Amalgam]] | |||
* [https://www.youtube.com/watch?v=z-SxvrnkTzU ''Bottom Text''] (2022) | |||
== External links == | |||
= | |||
* [http://individual.utoronto.ca/kalendis/hebrew/rect.htm Rectified Hebrew Calendar] | * [http://individual.utoronto.ca/kalendis/hebrew/rect.htm Rectified Hebrew Calendar] | ||