353edo: Difference between revisions
fifths |
regular temp properties |
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== Theory == | == Theory == | ||
{{ | {{Harmonics in equal|353}} | ||
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]]. | 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]]. | ||
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|+ | |+ | ||
!Step | !Step | ||
! | !Note name | ||
<small>(diatonic Hebrew[19] version</small>) | <small>(diatonic Hebrew[19] version</small>) | ||
!Associated ratio | !Associated ratio | ||
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|} | |} | ||
== Rank | == Regular temperament properties == | ||
Assuming 353edo is treated as the 2.5.7.11.13.17 subgroup temperament. | |||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" |[[Subgroup]] | |||
! rowspan="2" |[[Comma list|Comma List]] | |||
! rowspan="2" |[[Mapping]] | |||
! rowspan="2" |Optimal | |||
8ve stretch (¢) | |||
! colspan="2" |Tuning error | |||
|- | |||
![[TE error|Absolute]] (¢) | |||
![[TE simple badness|Relative]] (%) | |||
|- | |||
|2.5 | |||
|820 -353 | |||
|[{{val|353 820}}] | |||
| -0.263 | |||
|0.263 | |||
|7.74 | |||
|- | |||
|2.5.7 | |||
|3136/3125, 209 -9 -67 | |||
|[{{val|353 820 991}}] | |||
| -0.177 | |||
|0.247 | |||
|7.26 | |||
|- | |||
|2.5.7.11 | |||
|3136/3125, 5767168/5764801, -20 -6 1 9 | |||
|[{{val|353 820 991 1221}}] | |||
| -0.089 | |||
|0.263 | |||
|7.73 | |||
|- | |||
|2.5.7.11.13 | |||
|3136/3125, 4394/4375, 6656/6655, 5767168/5764801 | |||
|[{{val|353 820 991 1221 1306}}] | |||
| -0.024 | |||
|0.268 | |||
|7.89 | |||
|- | |||
|2.5.7.11.13.17 | |||
|3136/3125, 4394/4375, 7744/7735, 60112/60025, 64141/64000 | |||
|[{{val|353 820 991 1221 1306 1443}}] | |||
| -0.037 | |||
|0.247 | |||
|7.26 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
!Periods | !Periods | ||