323edo: Difference between revisions

Eliora (talk | contribs)
Theory: add a fact and corresponding mappings
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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]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal 8ve <br>stretch (¢)
! rowspan="2" | Optimal 8ve <br>Stretch (¢)
! colspan="2" | Tuning error
! colspan="2" | Tuning Error
|-
|-
! [[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
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| 3.14
| 3.14
|-
|-
| 2.3.5.7.11
| 2.3.5.7.13
| 540/539, 4375/4374, 12005/11979, 16384/16335
| 676/675, 4375/4374, 4096/4095, 65000/64827
| [{{val| 323 512 750 907 1118 }}] (323e)
| [{{val| 323 512 750 907 1195}}]
| -0.2213
| -0.0431
| 0.2375
| 0.1770
| 6.39
| 4.76
|-
|-
| 2.3.5.7.11
| 2.3.5.7.13.17
| 1375/1372, 4375/4374, 5632/5625, 14641/14580
| 442/441, 1275/1274, 2500/2499, 4375/4374, 4096/4095
| [{{val| 323 512 750 907 1117 }}] (323)
| [{{val| 323 512 750 907 1195 1320}}]
| -0.0066
| +0.0020
| 0.2399
| 0.1905
| 6.46
| 5.13
|-
|-
|2.3.5.7.13
| style="border-top: double;" | 2.3.5.7.11
|676/675, 4375/4374, 4096/4095, 65000/64827
| style="border-top: double;" | 540/539, 4375/4374, 12005/11979, 16384/16335
|[{{val| 323 512 750 907 1195}}]
| style="border-top: double;" | [{{val| 323 512 750 907 1118 }}] (323e)
|<nowiki>-0.0431</nowiki>
| style="border-top: double;" | -0.2213
|0.1770
| style="border-top: double;" | 0.2375
|4.76
| style="border-top: double;" | 6.39
|-
|-
|2.3.5.7.13.17
| style="border-top: double;" | 2.3.5.7.11
|442/441, 1275/1274, 2500/2499, 4375/4374, 4096/4095
| style="border-top: double;" | 1375/1372, 4375/4374, 5632/5625, 14641/14580
|[{{val| 323 512 750 907 1195 1320}}]
| style="border-top: double;" | [{{val| 323 512 750 907 1117 }}] (323)
| +0.0020
| style="border-top: double;" | -0.0066
|0.1905
| style="border-top: double;" | 0.2399
|5.13
| style="border-top: double;" | 6.46
|}
|}


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{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
|+Table of rank-2 temperaments by generator
! Periods<br>per octave
! Periods<br>per 8ve
! Generator<br>(reduced)
! Generator<br>(Reduced)
! Cents<br>(reduced)
! Cents<br>(Reduced)
! Associated<br>ratio
! Associated<br>Ratio
! Temperaments
! Temperaments
|-
|-