183edo: Difference between revisions

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=== Subsets and supersets ===
=== Subsets and supersets ===
Since 183 factors into 3 × 61, 183edo contains [[3edo]] and [[61edo]] as its subsets.
Since 183 factors into 3 × 61, 183edo contains [[3edo]] and [[61edo]] as its subsets.
== Approximation to JI ==
=== 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
|-
| [[1210zpi]]
| 182.999728466810
| 6.55738677895164
| 11.020824
| 1.643410
| 19.731996
| 183edo
| 1200.00178054815
| 18
| 18
|}


== Regular temperament properties ==
== Regular temperament properties ==
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! 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
|-
|-
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|+ 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*
! Temperaments
! Temperaments
|-
|-
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|-
|-
| 3
| 3
| 38\183<br />(23\183)
| 38\183<br>(23\183)
| 249.18<br />(150.82)
| 249.18<br>(150.82)
| 15/13<br />(12/11)
| 15/13<br>(12/11)
| [[Hemiterm]]
| [[Hemiterm]]
|-
|-
| 3
| 3
| 76\183<br />(15\183)
| 76\183<br>(15\183)
| 498.36<br />(98.36)
| 498.36<br>(98.36)
| 4/3<br />(200/189)
| 4/3<br>(200/189)
| [[Term]] / terminator
| [[Term]] / terminator
|-
|-
| 61
| 61
| 38\183<br />(2\183)
| 38\183<br>(2\183)
| 249.18<br />(13.11)
| 249.18<br>(13.11)
| 13750/11907<br />(?)
| 13750/11907<br>(?)
| [[Promethium]]
| [[Promethium]]
|}
|}
<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
|-
| [[1210zpi]]
| 182.999728466810
| 6.55738677895164
| 11.020824
| 1.643410
| 19.731996
| 183edo
| 1200.00178054815
| 18
| 18
|}


== Music ==
== Music ==