87edo: Difference between revisions

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=== Interval mappings ===
=== Interval mappings ===
{{Q-odd-limit intervals|87}}
{{Q-odd-limit intervals|87}}
=== 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
|-
| [[483zpi]]
| 87.0139255957575
| 13.7908960178956
| 8.869041
| 1.439474
| 18.061741
| 87edo
| 1199.80795355692
| 16
| 14
|}


== Regular temperament properties ==
== Regular temperament properties ==
Line 354: Line 385:
! 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*
! Temperament
! Temperament
|-
|-
Line 477: Line 508:
|-
|-
| 3
| 3
| 18\87<br />(11\87)
| 18\87<br>(11\87)
| 248.276<br />(151.724)
| 248.276<br>(151.724)
| 15/13<br />(12/11)
| 15/13<br>(12/11)
| [[Hemimist]]
| [[Hemimist]]
|-
|-
| 3
| 3
| 23\87<br />(6\87)
| 23\87<br>(6\87)
| 317.241<br />(82.759)
| 317.241<br>(82.759)
| 6/5<br />(21/20)
| 6/5<br>(21/20)
| [[Tritikleismic]]
| [[Tritikleismic]]
|-
|-
| 3
| 3
| 28\87<br />(1\87)
| 28\87<br>(1\87)
| 386.207<br />(13.793)
| 386.207<br>(13.793)
| 5/4<br />(126/125)
| 5/4<br>(126/125)
| [[Mutt]]
| [[Mutt]]
|-
|-
| 3
| 3
| 36\87<br />(7\87)
| 36\87<br>(7\87)
| 496.552<br />(96.552)
| 496.552<br>(96.552)
| 4/3<br />(18/17~19/18)
| 4/3<br>(18/17~19/18)
| [[Misty]]
| [[Misty]]
|-
|-
| 29
| 29
| 28\87<br />(1\87)
| 28\87<br>(1\87)
| 386.207<br />(13.793)
| 386.207<br>(13.793)
| 5/4<br />(121/120)
| 5/4<br>(121/120)
| [[Mystery]]
| [[Mystery]]
|}
|}
<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
 
87 can serve as a MOS in these:


* [[Avicenna (temperament)|Avicenna]] ([[Breed|87 &amp; 270]]) {{multival| 24 -9 -66 12 27 … }}
87 can serve as a mos in these:
* [[Breed|87 &amp; 494]] {{multival| 51 -1 -133 11 32 … }}


== Zeta properties ==
* [[Avicenna (temperament)|Avicenna]] ([[Breed|87 & 270]]) {{multival| 24 -9 -66 12 27 … }}
=== Zeta peak index ===
* [[Breed|87 & 494]] {{multival| 51 -1 -133 11 32 … }}
{| 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
|-
| [[483zpi]]
| 87.0139255957575
| 13.7908960178956
| 8.869041
| 1.439474
| 18.061741
| 87edo
| 1199.80795355692
| 16
| 14
|}


== Scales ==
== Scales ==
=== MOS scales ===
=== Mos scales ===
{{main|List of MOS scales in 87edo}}
{{main|List of MOS scales in 87edo}}