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91edo: Difference between revisions

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The [[concoctic scale]] for 91edo is 27 steps, where two concoctic neutral thirds make a sharp fifth of 54\91, representing 3/2 in the 91b val.
The [[concoctic scale]] for 91edo is 27 steps, where two concoctic neutral thirds make a sharp fifth of 54\91, representing 3/2 in the 91b val.


== Regular temperament properties ==
== Intervals ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| -144 91 }}
| {{mapping| 91 144 }}
| +0.963
| 0.964
| 7.31
|-
| 2.3.5
| 15625/15552, 43046721/41943040
| {{mapping| 91 144 211 }}
| +1.202
| 0.857
| 6.49
|-
| 2.3.5.7
| 225/224, 4375/4374, 50421/50000
| {{mapping| 91 144 211 255 }}
| +1.453
| 0.860
| 6.51
|}
 
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br />per 8ve
! Generator*
! Cents*
! Associated<br />ratio*
! Temperament
|-
| 1
| 2\91
| 26.37
| 49/48
| [[Sfourth]]
|-
| 1
| 4\91
| 52.75
| 33/32
| [[Quartkeenlig]] (91f)
|-
| 1
| 11\91
| 145.05
| 49/45
| [[Swetneus]] (91ef)
|-
| 1
| 19\91
| 250.55
| 1240029/1048576
| ''[[Semaphore]] variant'' (24 &amp; 91)**
|-
| 1
| 20\91
| 263.74
| 7/6
| [[Septimin]] (91)
|-
| 1
| 24\91
| 316.48
| 6/5
| [[Catakleismic]] (91f)
|-
| 1
| 33\91
| 435.16
| 9/7
| [[Supermajor]]
|-
| 1
| 34\91
| 448.35
| 35/27
| [[Semidimfourth]]
|-
| 1
| 38\91
| 501.10
| 4/3
| [[Python]]
|-
| 1
| 44\91
| 580.22
| 7/5
| [[Tritonic]]
|-
| 7
| 38\91<br />(1\91)
| 501.10<br />(13.19)
| 4/3<br />(81/80)
| [[Absurdity]]
|-
| 13
| 38\91<br />(1\91)
| 501.10<br />(13.19)
| 4/3<br />(265/252)
| [[Trideci]] (91)<br />[[Aluminium]] (91c)
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 
<nowiki />** Derived from scales in the Scales section, official name not decided upon yet.
 
== Interval table ==
{{Interval table}}
{{Interval table}}


== Notation ==
== Notation ==
=== Ups and downs notation ===
=== Ups and downs notation ===
91edo can be notated using [[ups and downs notation|ups and downs]]. Trup is equivalent to quudsharp, trudsharp is equivalent to quup, etc.
91edo can be notated using [[ups and downs notation|ups and downs]]. Trup is equivalent to quudsharp, trudsharp is equivalent to quup, etc.
{{Sharpness-sharp7a}}
{{Sharpness-sharp7a}}
Line 476: Line 355:
| [[2/1]] exact
| [[2/1]] exact
|}
|}
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{Monzo| -144 91 }}
| {{Mapping| 91 144 }}
| +0.963
| 0.964
| 7.31
|-
| 2.3.5
| 15625/15552, 43046721/41943040
| {{Mapping| 91 144 211 }}
| +1.202
| 0.857
| 6.49
|-
| 2.3.5.7
| 225/224, 4375/4374, 50421/50000
| {{Mapping| 91 144 211 255 }}
| +1.453
| 0.860
| 6.51
|}
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>ratio*
! Temperament
|-
| 1
| 2\91
| 26.37
| 49/48
| [[Sfourth]]
|-
| 1
| 4\91
| 52.75
| 33/32
| [[Quartkeenlig]] (91f)
|-
| 1
| 11\91
| 145.05
| 49/45
| [[Swetneus]] (91ef)
|-
| 1
| 19\91
| 250.55
| 1240029/1048576
| ''[[Semaphore]] variant'' (24 & 91)**
|-
| 1
| 20\91
| 263.74
| 7/6
| [[Septimin]] (91)
|-
| 1
| 24\91
| 316.48
| 6/5
| [[Catakleismic]] (91f)
|-
| 1
| 33\91
| 435.16
| 9/7
| [[Supermajor]]
|-
| 1
| 34\91
| 448.35
| 35/27
| [[Semidimfourth]]
|-
| 1
| 38\91
| 501.10
| 4/3
| [[Python]]
|-
| 1
| 44\91
| 580.22
| 7/5
| [[Tritonic]]
|-
| 7
| 38\91<br>(1\91)
| 501.10<br>(13.19)
| 4/3<br>(81/80)
| [[Absurdity]]
|-
| 13
| 38\91<br>(1\91)
| 501.10<br>(13.19)
| 4/3<br>(265/252)
| [[Trideci]] (91)<br>[[Aluminium]] (91c)
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[normal lists|minimal form]] in parentheses if distinct
<nowiki/>** Derived from scales in the Scales section, official name not decided upon yet.


== Scales ==
== Scales ==
Retrieved from "https://en.xen.wiki/w/91edo"