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== Theory ==
== Theory ==
358et is consistent to the [[7-odd-limit]] and the [[harmonic]] 3 is about halfway its steps. It is suitable for use with the 2.9.5.7.11.17.23.29.37.41 [[subgroup]]. Using the patent val, it tempers out 283115520/282475249, 26873856/26796875, 48828125/48771072, [[2100875/2097152]] and 200120949/200000000 in the 7-limit; 20155392/20131375, 234375/234256, 29296875/29218112, 46656/46585, 1953125/1951488, 226492416/226474325, [[540/539]], 107495424/107421875, 5788125/5767168, 5767168/5764801, 1375/1372, [[3025/3024]], 766656/765625, 4108797/4096000 and 644204/643125 in the 11-limit. It [[support]]s [[hypnos]] and [[lee]].
358edo is [[consistent]] to the [[7-odd-limit]], but the [[harmonic]] [[3/1|3]] is about halfway its steps. It is suitable for use with the 2.9.5.7.13 [[subgroup]] or even better the 2.9.15.7.13 subgroup.  
 
In the 2.9.5.7.13 subgroup, the equal temperament [[tempering out|tempers out]] [[4096/4095]], 13720/13689, 59150/59049, 60025/59904, 142884/142805, and [[390625/388962]].
 
The [[patent val]] [[support]]s [[hypnos]] in the 11-limit and [[lee]] in the 2.3.7 subgroup.


=== Odd harmonics ===
=== Odd harmonics ===
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== Regular temperament properties ==
== Regular temperament properties ==
{| 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<br>8ve Stretch (¢)
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
! colspan="2" | Tuning Error
|-
|-
![[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
! [[TE simple badness|Relative]] (%)
|-
|-
|2.9
| 2.9
|{{monzo|1135 -358}}
| {{monzo| 1135 -358 }}
|{{mapping|358 1135}}
| {{mapping| 358 1135 }}
| -0.0882
| -0.0882
| 0.0882
| 0.0882
| 2.63
| 2.63
|-
|-
|2.9.5
| 2.9.5
|{{monzo|3 -9 11}}, {{monzo|-98 17 19}}
| {{monzo| 3 -9 11 }}, {{monzo| -98 17 19 }}
|{{mapping|358 1135 831}}
| {{mapping| 358 1135 831 }}
| +0.0616
| +0.0616
| 0.2238
| 0.2238
| 6.68
| 6.68
|-
|-
|2.9.5.7
| 2.9.5.7
|390625/388962, 4802000/4782969, 2100875/2097152
| 390625/388962, 2100875/2097152, 4802000/4782969
|{{mapping|358 1135 831 1005}}
| {{mapping| 358 1135 831 1005 }}
| +0.0561
| +0.0561
| 0.1941
| 0.1941
| 5.79
| 5.79
|}
|}
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