39edo: Difference between revisions

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| 1
| 2/1
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== 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
|-
| [[173zpi]]
| 39.1237487937926
| 30.6719073963176
| 5.593908
| 0.926356
| 14.714802
| 39edo
| 1196.20438845639
| 7
| 7
|}
|}


Line 730: Line 762:
! 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*
! Temperament
! Temperament
! MOS Scales
! MOS scales
|-
|-
| 1
| 1
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|-
|-
| 3
| 3
| 8\39<br />(5\39)
| 8\39<br>(5\39)
| 246.2<br />(153.8)
| 246.2<br>(153.8)
| [[Triforce]] (39)
| [[Triforce]] (39)
| [[3L&nbsp;3s]], [[6L&nbsp;3s]], [[9L&nbsp;6s]], [[15L&nbsp;9s]]
| [[3L&nbsp;3s]], [[6L&nbsp;3s]], [[9L&nbsp;6s]], [[15L&nbsp;9s]]
|-
|-
| 3
| 3
| 16\39<br />(3\39)
| 16\39<br>(3\39)
| 492.3<br />(92.3)
| 492.3<br>(92.3)
| [[Augene]] (39d)
| [[Augene]] (39d)
| [[3L&nbsp;3s]], [[3L&nbsp;6s]], [[3L&nbsp;9s]], [[12L&nbsp;3s]], [[12L&nbsp;15s]]
| [[3L&nbsp;3s]], [[3L&nbsp;6s]], [[3L&nbsp;9s]], [[12L&nbsp;3s]], [[12L&nbsp;15s]]
|-
|-
| 3
| 3
| 17\39<br />(4\39)
| 17\39<br>(4\39)
| 523.1<br />(123.0)
| 523.1<br>(123.0)
| [[Deflated]] (39bd)
| [[Deflated]] (39bd)
| [[3L&nbsp;3s]], [[3L&nbsp;6s]], [[9L&nbsp;3s]], [[9L&nbsp;12s]], [[9L&nbsp;21s]]
| [[3L&nbsp;3s]], [[3L&nbsp;6s]], [[9L&nbsp;3s]], [[9L&nbsp;12s]], [[9L&nbsp;21s]]
|-
|-
| 13
| 13
| 16\39<br />(1\39)
| 16\39<br>(1\39)
| 492.3<br />(30.8)
| 492.3<br>(30.8)
| [[Tridecatonic]]
| [[Tridecatonic]]
| [[13L&nbsp;13s]]
| [[13L&nbsp;13s]]
|}
|}
<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
|-
| [[173zpi]]
| 39.1237487937926
| 30.6719073963176
| 5.593908
| 0.926356
| 14.714802
| 39edo
| 1196.20438845639
| 7
| 7
|}


== 39edo and world music ==
== 39edo and world music ==