270edo: Difference between revisions
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=== 23-odd-limit interval mappings === | === 23-odd-limit interval mappings === | ||
{{15-odd-limit|270|23}} | {{15-odd-limit|270|23}} | ||
=== Zeta peak index === | |||
{| class="wikitable center-all" | |||
|- | |||
! colspan="3" | Tuning | |||
! colspan="3" | Strength | |||
! colspan="2" | Closest edo | |||
! colspan="2" | Integer limit | |||
|- | |||
! ZPI | |||
! Steps per octave | |||
! Step size (cents) | |||
! Height | |||
! Integral | |||
! Gap | |||
! Edo | |||
! Octave (cents) | |||
! Consistent | |||
! Distinct | |||
|- | |||
| [[1936zpi]] | |||
| 270.017794631965 | |||
| 4.44415154799558 | |||
| 13.370691 | |||
| 1.998595 | |||
| 22.286976 | |||
| 270edo | |||
| 1199.92091795881 | |||
| 22 | |||
| 22 | |||
|} | |||
== Regular temperament properties == | == Regular temperament properties == | ||
| Line 40: | Line 71: | ||
! rowspan="2" | [[Comma list]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
! colspan="2" | Tuning error | ! colspan="2" | Tuning error | ||
|- | |- | ||
| Line 110: | Line 141: | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods<br | ! Periods<br>per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br | ! Associated<br>ratio* | ||
! Temperament | ! Temperament | ||
|- | |- | ||
| Line 189: | Line 220: | ||
|- | |- | ||
| 2 | | 2 | ||
| 131\270<br | | 131\270<br>(4\270) | ||
| 582.22<br | | 582.22<br>(17.78) | ||
| 7/5<br | | 7/5<br>(99/98) | ||
| [[Quarvish]] | | [[Quarvish]] | ||
|- | |- | ||
| Line 207: | Line 238: | ||
|- | |- | ||
| 5 | | 5 | ||
| 83\270<br | | 83\270<br>(25\270) | ||
| 368.89<br | | 368.89<br>(111.11) | ||
| 1024/891<br | | 1024/891<br>(16/15) | ||
| [[Quintosec]] | | [[Quintosec]] | ||
|- | |- | ||
| 6 | | 6 | ||
| 112\270<br | | 112\270<br>(4\270) | ||
| 497.78<br | | 497.78<br>(97.78) | ||
| 4/3<br | | 4/3<br>(128/121) | ||
| [[Sextile]] | | [[Sextile]] | ||
|- | |- | ||
| 9 | | 9 | ||
| 71\270<br | | 71\270<br>(11\270) | ||
| 315.56<br | | 315.56<br>(48.89) | ||
| 6/5<br | | 6/5<br>(36/35) | ||
| [[Ennealimmal]] / ennealimmia | | [[Ennealimmal]] / ennealimmia | ||
|- | |- | ||
| 10 | | 10 | ||
| 16\270<br | | 16\270<br>(11\270) | ||
| 71.11<br | | 71.11<br>(48.89) | ||
| 25/24<br | | 25/24<br>(36/35) | ||
| [[Decavish]] | | [[Decavish]] | ||
|- | |- | ||
| 10 | | 10 | ||
| 56\270<br | | 56\270<br>(2\270) | ||
| 248.89<br | | 248.89<br>(8.89) | ||
| 15/13<br | | 15/13<br>(176/175) | ||
| [[Decoid]] | | [[Decoid]] | ||
|- | |- | ||
| 10 | | 10 | ||
| 71\270<br | | 71\270<br>(10\270) | ||
| 315.56<br | | 315.56<br>(44.44) | ||
| 6/5<br | | 6/5<br>(40/39) | ||
| [[Deca]] | | [[Deca]] | ||
|- | |- | ||
| 18 | | 18 | ||
| 71\270<br | | 71\270<br>(4\270) | ||
| 248.89<br | | 248.89<br>(17.78) | ||
| 15/13<br | | 15/13<br>(99/98) | ||
| [[Hemiennealimmal]] | | [[Hemiennealimmal]] | ||
|- | |- | ||
| 18 | | 18 | ||
| 71\270<br | | 71\270<br>(2\270) | ||
| 475.56<br | | 475.56<br>(8.89) | ||
| 1053/800<br | | 1053/800<br>(1287/1280) | ||
| [[Semihemiennealimmal]] | | [[Semihemiennealimmal]] | ||
|- | |- | ||
| 27 | | 27 | ||
| 61\270<br | | 61\270<br>(1\270) | ||
| 271.11<br | | 271.11<br>(4.44) | ||
| 1375/1176<br | | 1375/1176<br>(385/384) | ||
| [[Trinealimmal]] | | [[Trinealimmal]] | ||
|- | |- | ||
| 30 | | 30 | ||
| 82\270<br | | 82\270<br>(1\270) | ||
| 364.44<br | | 364.44<br>(4.44) | ||
| 216/175<br | | 216/175<br>(385/384) | ||
| [[Zinc]] | | [[Zinc]] | ||
|- | |- | ||
| 45 | | 45 | ||
| 59\270<br | | 59\270<br>(1\270) | ||
| 262.22<br | | 262.22<br>(4.44) | ||
| 64/55<br | | 64/55<br>(385/384) | ||
| [[Rhodium]] | | [[Rhodium]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | <nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
== External links == | == External links == | ||