742edo: Difference between revisions
→Regular temperament properties: corrections; cleanup; style |
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742et has a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any previous equal temperaments. It is only bettered by [[1178edo|1178et]]. | 742et has a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any previous equal temperaments. It is only bettered by [[1178edo|1178et]]. | ||
{| 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 | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
8ve stretch (¢) | ! colspan="2" | Tuning error | ||
! colspan="2" |Tuning error | |||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
| | | {{monzo| 23 6 -14 }}, {{monzo| -84 53 }} | ||
|[{{val|742 1176 1723}}] | | [{{val| 742 1176 1723 }}] | ||
| | | -0.0157 | ||
|0. | | 0.0555 | ||
|3.43 | | 3.43 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|2401/2400, 14348907/14336000, | | 2401/2400, 14348907/14336000, {{monzo| 23 6 -14 }} | ||
|[{{val|742 1176 1723 2083}}] | | [{{val| 742 1176 1723 2083 }}] | ||
| -0. | | -0.0035 | ||
|0. | | 0.0525 | ||
|3.24 | | 3.24 | ||
|- | |- | ||
|2.3.5.7.11 | | 2.3.5.7.11 | ||
|9801/9800 | | 2401/2400, 9801/9800, 172032/171875, 1240029/1239040 | ||
|[{{val|742 1176 1723 2083 2567}}] | | [{{val| 742 1176 1723 2083 2567 }}] | ||
| -0. | | -0.0123 | ||
|0. | | 0.0501 | ||
|3.10 | | 3.10 | ||
|- | |- | ||
|2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
|4096/4095, 9801/9800, | | 2401/2400, 4096/4095, 6656/6655, 9801/9800, 39366/39325 | ||
|[{{val|742 1176 1723 2083 2567 2746}}] | | [{{val| 742 1176 1723 2083 2567 2746 }}] | ||
| -0. | | -0.0302 | ||
|0. | | 0.0608 | ||
|3.76 | | 3.76 | ||
|- | |- | ||
|2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
|1701/1700, 2058/2057, 2601/2600, | | 1701/1700, 2058/2057, 2401/2400, 2601/2600, 4096/4095, 6656/6655 | ||
|[{{val|742 1176 1723 2083 2567 2746 3033}}] | | [{{val| 742 1176 1723 2083 2567 2746 3033 }}] | ||
| | | -0.0317 | ||
|0. | | 0.0564 | ||
|3.49 | | 3.49 | ||
|} | |} | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
| Line 78: | Line 78: | ||
| [[Fortune]] | | [[Fortune]] | ||
|- | |- | ||
|1 | | 1 | ||
| | | 303\742 | ||
| | | 490.026 | ||
|675 | | 896/675 | ||
|[[Surmarvelpyth]] | | [[Surmarvelpyth]] | ||
|- | |- | ||
| 2 | | 2 | ||