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 />8ve stretch (¢)
! 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 />per 8ve
! Periods<br>per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br />ratio*
! Associated<br>ratio*
! Temperament
! Temperament
|-
|-
Line 189: Line 220:
|-
|-
| 2
| 2
| 131\270<br />(4\270)
| 131\270<br>(4\270)
| 582.22<br />(17.78)
| 582.22<br>(17.78)
| 7/5<br />(99/98)
| 7/5<br>(99/98)
| [[Quarvish]]
| [[Quarvish]]
|-
|-
Line 207: Line 238:
|-
|-
| 5
| 5
| 83\270<br />(25\270)
| 83\270<br>(25\270)
| 368.89<br />(111.11)
| 368.89<br>(111.11)
| 1024/891<br />(16/15)
| 1024/891<br>(16/15)
| [[Quintosec]]
| [[Quintosec]]
|-
|-
| 6
| 6
| 112\270<br />(4\270)
| 112\270<br>(4\270)
| 497.78<br />(97.78)
| 497.78<br>(97.78)
| 4/3<br />(128/121)
| 4/3<br>(128/121)
| [[Sextile]]
| [[Sextile]]
|-
|-
| 9
| 9
| 71\270<br />(11\270)
| 71\270<br>(11\270)
| 315.56<br />(48.89)
| 315.56<br>(48.89)
| 6/5<br />(36/35)
| 6/5<br>(36/35)
| [[Ennealimmal]] / ennealimmia
| [[Ennealimmal]] / ennealimmia
|-
|-
| 10
| 10
| 16\270<br />(11\270)
| 16\270<br>(11\270)
| 71.11<br />(48.89)
| 71.11<br>(48.89)
| 25/24<br />(36/35)
| 25/24<br>(36/35)
| [[Decavish]]
| [[Decavish]]
|-
|-
| 10
| 10
| 56\270<br />(2\270)
| 56\270<br>(2\270)
| 248.89<br />(8.89)
| 248.89<br>(8.89)
| 15/13<br />(176/175)
| 15/13<br>(176/175)
| [[Decoid]]
| [[Decoid]]
|-
|-
| 10
| 10
| 71\270<br />(10\270)
| 71\270<br>(10\270)
| 315.56<br />(44.44)
| 315.56<br>(44.44)
| 6/5<br />(40/39)
| 6/5<br>(40/39)
| [[Deca]]
| [[Deca]]
|-
|-
| 18
| 18
| 71\270<br />(4\270)
| 71\270<br>(4\270)
| 248.89<br />(17.78)
| 248.89<br>(17.78)
| 15/13<br />(99/98)
| 15/13<br>(99/98)
| [[Hemiennealimmal]]
| [[Hemiennealimmal]]
|-
|-
| 18
| 18
| 71\270<br />(2\270)
| 71\270<br>(2\270)
| 475.56<br />(8.89)
| 475.56<br>(8.89)
| 1053/800<br />(1287/1280)
| 1053/800<br>(1287/1280)
| [[Semihemiennealimmal]]
| [[Semihemiennealimmal]]
|-
|-
| 27
| 27
| 61\270<br />(1\270)
| 61\270<br>(1\270)
| 271.11<br />(4.44)
| 271.11<br>(4.44)
| 1375/1176<br />(385/384)
| 1375/1176<br>(385/384)
| [[Trinealimmal]]
| [[Trinealimmal]]
|-
|-
| 30
| 30
| 82\270<br />(1\270)
| 82\270<br>(1\270)
| 364.44<br />(4.44)
| 364.44<br>(4.44)
| 216/175<br />(385/384)
| 216/175<br>(385/384)
| [[Zinc]]
| [[Zinc]]
|-
|-
| 45
| 45
| 59\270<br />(1\270)
| 59\270<br>(1\270)
| 262.22<br />(4.44)
| 262.22<br>(4.44)
| 64/55<br />(385/384)
| 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
 
== Zeta properties ==
=== Zeta peak index ===
{| class="wikitable"
|-
! 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
|}


== External links ==
== External links ==