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=== Subsets and supersets ===
=== Subsets and supersets ===
Since 94 factors into primes as {{nowrap| 2 × 47 }}, 94edo contains [[2edo]] and [[47edo]] as subset edos. It can be thought of as two sets of 47edo offset by one step of 94edo. It inherits from 47edo's good approximations of primes 5, 7, 13, and 17, while dramatically improving on prime 3, as well as primes 11, 19, and 23 to a lesser degree.
Since 94 factors into primes as {{nowrap| 2 × 47 }}, 94edo contains [[2edo]] and [[47edo]] as subset edos. It can be thought of as two sets of 47edo offset by one step of 94edo. It inherits from 47edo's good approximations of primes 5, 7, 13, and 17, while dramatically improving on prime 3, as well as primes 11, 19, and 23 to a lesser degree. Tripling 94edo yields [[282edo]], which converts flat-tending harmonics to sharp, so as to achieve distinct consistency through the 23-limit and consistency through the 29-limit.


== Intervals ==
== Intervals ==
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! 13-limit
! 13-limit
! 23-limit
! 23-limit
![[Ups and downs notation|Ups and downs]]
! [[Ups and downs notation|Ups and downs]]
! Short-form [[SKULO interval names#WOFED interval names|WOFED]]
! Short-form [[SKULO interval names#WOFED interval names|WOFED]]
! Long-form WOFED
! Long-form WOFED
Line 910: Line 910:


=== Sagittal ===
=== Sagittal ===
94edo can be notated in [[Sagittal notation|Sagittal]] using the [[Sagittal_notation#Athenian_extension_single-shaft|Athenian extension]], with the apotome equal to 9 edosteps and the limma to 7 edosteps.  
94edo can be notated in [[Sagittal notation|Sagittal]] using the [[Sagittal_notation#Athenian|Athenian set]], with the apotome equal to 9 edosteps and the limma to 7 edosteps.  
{| class="wikitable" style="text-align: center;"
{| class="wikitable" style="text-align: center;"
! colspan="2" |Steps
! colspan="2" |Steps
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| rowspan="2" |<big>{{sagittal|(|(}}</big>
| rowspan="2" |<big>{{sagittal|(|(}}</big>
| rowspan="2" |<big>{{sagittal|/|\}}</big>
| rowspan="2" |<big>{{sagittal|/|\}}</big>
|<small>{{sagittal|#}}{{sagittal|\!/}}</small>
| rowspan="2" |<big>{{sagittal|(|)}}</big>
|<small>{{sagittal|#}}{{sagittal|(!(}}</small>
|{{sagittal|(!(}}{{sagittal|#}}
|<small>{{sagittal|#}}{{sagittal|\!}}</small>
|{{sagittal|\!}}{{sagittal|#}}
|<small>{{sagittal|#}}{{sagittal|~!(}}</small>
|{{sagittal|~!(}}{{sagittal|#}}
|<small>{{sagittal|#}}</small>
|{{sagittal|#}}
|-
|-
!Revo
!Revo
|<big>{{sagittal|(|)}}</big>
|<big>{{sagittal|~||(}}</big>
|<big>{{sagittal|~||(}}</big>
|<big>{{sagittal|||\}}</big>
|<big>{{sagittal|||\}}</big>
Line 1,117: Line 1,116:


Temperaments to which 94et can be detempered:  
Temperaments to which 94et can be detempered:  
* [[Satin]] ({{nowrap|94 & 217}})  
* [[Satin]] ({{nowrap| 94 & 217 }})  
* [[Gariwizmic]] (94 & 176)  
* [[Gariwizmic]] ({{nowrap| 94 & 176 }})  
* 94 & 130
* {{nowrap| 94 & 422 }}  
* {{nowrap|94 & 422}}  
* 94 & 130 & 176


=== Commas ===
=== Commas ===
94et [[Tempering out|tempers out]] the following [[Comma|commas]] using its 23-limit patent [[val]], ⟨94 149 218 264 325 348 384 399 425].
94et [[tempering out|tempers out]] the following [[comma]]s using its 23-limit patent [[val]], {{val| 94 149 218 264 325 348 384 399 425 }}.
 
{| class="commatable wikitable center-1 center-2 right-3 center-6"
{| class="commatable wikitable center-1 center-2 right-3 center-6"
! [[Harmonic limit|Prime<br>mit]]
! [[Harmonic limit|Prime<br>limit]]
! [[Ratio]]<ref>Ratios with more than 8 digits are presented by placeholders with informative hints</ref>
! [[Ratio]]<ref>Ratios with more than 8 digits are presented by placeholders with informative hints</ref>
! [[Cents]]
! [[Cents]]
Line 1,136: Line 1,134:
| <abbr title="36893488147419103232/36472996377170786403">(90 digits)</abbr>
| <abbr title="36893488147419103232/36472996377170786403">(90 digits)</abbr>
| 16.22
| 16.22
| {{monzo| 149 -94 }}
| {{Monzo| 149 -94 }}
| Wa-94
| Wa-94
| 94-edo
| 94-edo
Line 1,212: Line 1,210:
| 1urry
| 1urry
| Swetisma
| Swetisma
|-
| 11
| [[4225/4224]]
| 0.41
| {{Monzo| -7 -1 2 0 -1 2 }}
| Thotholuyoyo
| 3oo1uyy
| Leprechaun comma
|-
|-
| 11
| 11
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| s3urg
| s3urg
| Minisma
| Minisma
|-
| 13
| [[4225/4224]]
| 0.41
| {{Monzo| -7 -1 2 0 -1 2 }}
| Thotholuyoyo
| 3oo1uyy
| Leprechaun comma
|-
|-
| 17
| 17
| [[289/288]]
| [[289/288]]
| 6.00
| 6.00
| 2.3.17 {{Monzo| 5 -2 2 }}
| {{Monzo| 5 -2 0 0 0 0 2 }}
| Soso
| Soso
| 17oo
| 17oo
Line 1,320: Line 1,318:
| [[361/360]]
| [[361/360]]
| 4.80
| 4.80
| 2.3.5.19 {{Monzo| -3 -2 -1 2 }}
| {{Monzo| -3 -2 -1 0 0 0 0 2 }}
| Nonogu
| Nonogu
| 19oog2
| 19oog2
Line 1,328: Line 1,326:
| [[513/512]]
| [[513/512]]
| 3.38
| 3.38
| 2.3.19 {{Monzo| -9 3 1 }}
| {{Monzo| -9 3 0 0 0 0 0 1 }}
| Lano
| Lano
| L19o
| L19o
Line 1,336: Line 1,334:
| [[1216/1215]]
| [[1216/1215]]
| 1.42
| 1.42
| 2.3.5.19 {{Monzo| 6 -5 -1 1 }}
| {{Monzo| 6 -5 -1 0 0 0 0 1 }}
| Sanogu
| Sanogu
| s19og
| s19og
| Eratosthenes' comma
| Eratosthenes' comma
|-
|-
|19
| 19
|[[11859211/11859210|(16 digits)]]
| [[11859211/11859210|(16 digits)]]
|0.00
| 0.00
|{{Monzo|-1 -4 -1 1 -4 1 0 4}}
| {{Monzo| -1 -4 -1 1 -4 1 0 4 }}
|<small>Quadno-athoquadlu-azogu</small>
| <small>Quadno-athoquadlu-azogu</small>
|<small>9o<sup>4</sup>3o1u<sup>4</sup>zg</small>
| <small>9o<sup>4</sup>3o1u<sup>4</sup>zg</small>
|Tredekisma
| Tredekisma
|-
|-
|23
| 23
|[[300/299]]
| [[300/299]]
|5.78
| 5.78
|2.3.5.13.23 {{Monzo|2 1 2 -1 -1}}
| {{Monzo| 2 1 2 0 0 -1 0 0 -1 }}
|Twethuthuyoyo
| Twethuthuyoyo
|23u3uyy
| 23u3uyy
|Major naiadvicema
| Major naiadvicema
|-
|-
|23
| 23
|[[323/322]]
| [[323/322]]
|5.37
| 5.37
|2.7.17.19.23 {{Monzo|-1 -1 1 1 -1}}
| {{Monzo| -1 0 0 -1 0 0 1 1 -1 }}
|Twethunosoru
| Twethunosoru
|23u19o17or
| 23u19o17or
|Major semivicema
| Major semivicema
|-
|-
|23
| 23
|[[391/390]]
| [[391/390]]
|4.43
| 4.43
|{{Monzo|-1 -1 -1 0 0 -1 1 0 1}}
| {{Monzo| -1 -1 -1 0 0 -1 1 0 1 }}
|Twethosothugu
| Twethosothugu
|23o17o3ug
| 23o17o3ug
|Minor naiadvicema
| Minor naiadvicema
|-
|-
|23
| 23
|[[460/459]]
| [[460/459]]
|3.77
| 3.77
|2.3.5.17.23 {{Monzo|2 -3 1 -1 1}}
| {{Monzo| 2 -3 1 0 0 0 -1 0 1 }}
|Twethosuyo
| Twethosuyo
|23o17uy
| 23o17uy
|Scanisma, vicewolf comma
| Scanisma, vicewolf comma
|-
|-
|23
| 23
|[[484/483]]
| [[484/483]]
|3.58
| 3.58
|{{Monzo|2 -1 0 -1 2 0 0 0 -1}}
| {{Monzo| 2 -1 0 -1 2 0 0 0 -1 }}
|Twethuloloru
| Twethuloloru
|23u1oor
| 23u1oor
|Pittsburghisma
| Pittsburghisma
|}
|}


Retrieved from "https://en.xen.wiki/w/94edo"