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In the [[5-limit]] it tempers out the [[ennealimma]], {{monzo| 1 -27 18 }}, the [[vulture comma]], {{monzo| 24 -21 4 }}, and the [[vishnuzma]], {{monzo| 23 6 -14 }}.  
In the [[5-limit]] it tempers out the [[ennealimma]], {{monzo| 1 -27 18 }}, the [[vulture comma]], {{monzo| 24 -21 4 }}, and the [[vishnuzma]], {{monzo| 23 6 -14 }}.  


In the [[7-limit]] it tempers out the [[2401/2400|breedsma]] (2401/2400), the [[4375/4374|ragisma]] (4375/4374), and by extension the [[wizma]] (420175/419904), and the [[landscape comma]] (250047/250000) so that it [[support]]s [[ennealimmal]] temperament. It also tempers out the [[quasiorwellisma]] (29360128/29296875) and the [[garischisma]] (33554432/33480783).  
In the [[7-limit]] it tempers out the [[breedsma]] (2401/2400), the [[ragisma]] (4375/4374), and by extension the [[wizma]] (420175/419904), and the [[landscape comma]] (250047/250000) so that it [[support]]s [[ennealimmal]] temperament. It also tempers out the [[quasiorwellisma]] (29360128/29296875) and the [[septischisma]] (33554432/33480783).  


In the [[11-limit]], it tempers out the lehmerisma ([[3025/3024]]), the vishdel comma ([[5632/5625]]), the kalisma ([[9801/9800]]), the [[symbiotic comma]] (19712/19683), the [[nexus comma]] (1771561/1769472), and the [[quartisma]] (117440512/117406179). Notably, it is consistent to distance 3 in the [[11-odd-limit]], and almost to distance 4 ((11/10)<sup>4</sup> and (20/11)<sup>4</sup> are a hair off, 50.4%).
In the [[11-limit]], it tempers out the [[lehmerisma]] (3025/3024), the [[vishdelisma]] (5632/5625), the [[kalisma]] (9801/9800), the [[symbiotic comma]] (19712/19683), the [[nexus comma]] (1771561/1769472), and the [[quartisma]] (117440512/117406179). It is almost consistent to distance 3 in the [[11-odd-limit]], only barely missing [[11/9]] (off by 16.68%).  


Finally, in the [[13-limit]] it is slightly worse but still excellent. It tempers out [[676/675]], [[1001/1000]], [[1716/1715]], and [[2080/2079]], making it an [[The Archipelago|archipelago]] tuning, and the [[optimal patent val]] for some of the archipelago temperaments such as [[hemiennealimmal]], [[vulture]], [[eagle]], and [[avicenna (temperament)|avicenna]].   
Finally, in the [[13-limit]] it is slightly worse but still excellent. It tempers out [[676/675]], [[1001/1000]], [[1716/1715]], and [[2080/2079]], making it an [[The Archipelago|archipelago]] tuning, and the [[optimal patent val]] for some of the archipelago temperaments such as [[hemiennealimmal]], [[vulture]], [[eagle]], and [[avicenna (temperament)|avicenna]].   
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=== Sagittal notation ===
=== Sagittal notation ===
<span data-darkreader-inline-color="">The</span> [[Sagittal notation]] <span data-darkreader-inline-color="">for 270edo uses alterations of the Promethian set. Since the apotome can be split in two, a SZ half-sharp and a half-flat may be used.</span>  
<span data-darkreader-inline-color="">The</span> [[Sagittal notation]] <span data-darkreader-inline-color="">for 270edo uses symbols from the Promethean set. Since the apotome can be split in two, the Stein-Zimmermann half-sharp and half-flat may be used.</span>  
{| class="wikitable center-all" data-darkreader-inline-color=""
{| class="wikitable center-all" data-darkreader-inline-color=""
! colspan="2" |+ edosteps
! colspan="2" |+ edosteps
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|-
|-
! rowspan="3" |Symbol
! rowspan="3" |Symbol
!SZ
!Evo-SZ
| rowspan="3" |<big>{{sagittal||(}}</big>
| rowspan="3" |<big>{{sagittal||(}}</big>
| rowspan="3" |<big>{{sagittal|)|(}}</big>
| rowspan="3" |<big>{{sagittal|)|(}}</big>
| rowspan="3" |<big>{{sagittal|)~|}}</big>
| rowspan="3" |<big>{{Sagittal|~|(}}</big>
| rowspan="3" |<big>{{Sagittal|~|(}}</big>
| rowspan="3" |<big>{{Sagittal|~~|}}</big>
| rowspan="3" |<big>{{Sagittal|/|}}</big>
| rowspan="3" |<big>{{Sagittal|/|}}</big>
| rowspan="3" |<big>{{Sagittal||)}}</big>
| rowspan="3" |<big>{{Sagittal||)}}</big>
| rowspan="3" |<big>{{sagittal||\}}</big>
| rowspan="3" |<big>{{sagittal||\}}</big>
| rowspan="3" |<big>{{sagittal|(|}}</big>
| rowspan="3" |<big>{{sagittal|~|)}}</big>
| rowspan="3" |<big>{{sagittal|(|(}}</big>
| rowspan="3" |<big>{{sagittal|(|(}}</big>
| rowspan="3" |<big>{{sagittal|//|}}</big>
| rowspan="3" |<big>{{sagittal|//|}}</big>
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| rowspan="3" |<big>{{Sagittal|/|\}}</big>
| rowspan="3" |<big>{{Sagittal|/|\}}</big>
|<big>{{Sagittal|t}}</big>
|<big>{{Sagittal|t}}</big>
|<small>{{Sagittal||(}}{{sagittal|t}}</small>
|{{Sagittal||(}}{{sagittal|t}}
|<small>{{Sagittal|)|(}}{{sagittal|t}}</small>
|{{Sagittal|)|(}}{{sagittal|t}}
|<small>{{Sagittal|)~|}}{{sagittal|t}}</small>
| rowspan="2" |{{sagittal|\\!}}{{sagittal|#}}
|<small>{{Sagittal|~|(}}{{sagittal|t}}</small>
| rowspan="2" |{{sagittal|(!(}}{{sagittal|#}}
|<small>{{Sagittal|/|}}{{sagittal|t}}</small>
| rowspan="2" |{{sagittal|~!)}}{{sagittal|#}}
|<small>{{Sagittal||)}}{{sagittal|t}}</small>
| rowspan="2" |{{sagittal|!/}}{{sagittal|#}}
|<small>{{Sagittal||\}}{{sagittal|t}}</small>
| rowspan="2" |{{sagittal|!)}}{{sagittal|#}}
|<small>{{Sagittal|(|}}{{sagittal|t}}</small>
| rowspan="2" |{{sagittal|\!}}{{sagittal|#}}
|<small>{{Sagittal|(|(}}{{sagittal|t}}</small>
| rowspan="2" |{{sagittal|~~!}}{{sagittal|#}}
|<small>{{Sagittal|//|}}{{sagittal|t}}</small>
| rowspan="2" |{{sagittal|~!(}}{{sagittal|#}}
|<small>{{Sagittal|/|)}}{{sagittal|t}}</small>
| rowspan="2" |{{sagittal|)!(}}{{sagittal|#}}
|<small>{{Sagittal|/|\}}{{sagittal|t}}</small>
| rowspan="2" |{{sagittal|!(}}{{sagittal|#}}
| rowspan="2" |<big>{{Sagittal|#}}</big>
| rowspan="2" |<big>{{Sagittal|#}}</big>
|-
|-
!Evo
!Evo
| rowspan="2" |<big>{{sagittal|)/|\}}</big>
| rowspan="2" |<big>{{sagittal|)/|\}}</big>
|<small>{{sagittal|\!/}}{{sagittal|#}}</small>
| rowspan="2" |<big>{{Sagittal|(|)}}</big>
|<small>{{sagittal|\!)}}{{sagittal|#}}</small>
| rowspan="2" |<big>{{sagittal|(|\}}</big>
|<small>{{sagittal|\\!}}{{sagittal|#}}</small>
|<small>{{sagittal|(!(}}{{sagittal|#}}</small>
|<small>{{sagittal|(!}}{{sagittal|#}}</small>
|<small>{{sagittal|!/}}{{sagittal|#}}</small>
|<small>{{sagittal|!)}}{{sagittal|#}}</small>
|<small>{{sagittal|\!}}{{sagittal|#}}</small>
|<small>{{sagittal|~!(}}{{sagittal|#}}</small>
|<small>{{sagittal|)~!}}{{sagittal|#}}</small>
|<small>{{sagittal|)!(}}{{sagittal|#}}</small>
|<small>{{sagittal|!(}}{{sagittal|#}}</small>
|-
|-
!Revo
!Revo
|<big>{{Sagittal|(|)}}</big>
|<big>{{sagittal|(|\}}</big>
|<big>{{sagittal|)||(}}</big>
|<big>{{sagittal|)||(}}</big>
|<big>{{sagittal|~||(}}</big>
|<big>{{sagittal|~||(}}</big>
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|<big>{{Sagittal|||)}}</big>
|<big>{{Sagittal|||)}}</big>
|<big>{{Sagittal|||\}}</big>
|<big>{{Sagittal|||\}}</big>
|<big>{{sagittal|~||)}}</big>
|<big>{{sagittal|(||(}}</big>
|<big>{{sagittal|(||(}}</big>
|<big>{{sagittal|~||\}}</big>
|<big>{{sagittal|//||}}</big>
|<big>{{sagittal|//||}}</big>
|<big>{{sagittal|/||)}}</big>
|<big>{{sagittal|/||)}}</big>
|<big>{{Sagittal|/||\}}</big>
|<big>{{Sagittal|/||\}}</big>
|}
|}
Note that the Revo notation has matching flag sequences between the double-shaft symbols and a subsequence of the single-shaft symbols.
<span data-darkreader-inline-color="">Alternate spellings in the Promethean set (comma tempered out):</span>  
<span data-darkreader-inline-color="">Alternate spellings in the Promethean set (comma tempered out):</span>  


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|-
|-
| 5
| 5
| [[Vishnuzma|(20 digits)]]
| [[Vishnu comma|(20 digits)]]
| 3.34
| 3.34
| {{Monzo| 23 6 -14 }}
| {{Monzo| 23 6 -14 }}
| Sasepbigu
| Sasepbigu
| sg<sup>14</sup>
| sg<sup>14</sup>
| Vishnuzma
| Vishnu comma
|-
|-
| 7
| 7
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| Sasaru
| Sasaru
| ssr
| ssr
| Garischisma
| Septischisma
|-
| 7
| [[Quasiorwellisma|(16 digits)]]
| 3.73
| {{Monzo| 22 -1 -10 1 }}
| Sazoquinbigu
| szg<sup>10</sup>
| Quasiorwellisma
|-
|-
| 7
| 7
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| zy<sup>4</sup>
| zy<sup>4</sup>
| Ragisma
| Ragisma
|-
| 7
| [[Quasiorwellisma|(16 digits)]]
| 3.73
| {{Monzo| 22 -1 -10 1 }}
| Sazoquinbigu
| szg<sup>10</sup>
| Quasiorwellisma
|-
|-
| 11
| 11
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| Saloquagu
| Saloquagu
| s1og<sup>4</sup>
| s1og<sup>4</sup>
| Vishdel comma
| Vishdelisma
|-
|-
| 11
| 11
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| Minisma
| Minisma
|-
|-
|17
| 17
| [[12376/12375]]
| [[12376/12375]]
| 0.14
| 0.14
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| Password, Eratosthenes' comma
| Password, 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
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| 25/19
| 25/19
| [[Vulture]]
| [[Vulture]]
|-
| 2
| 4\270
| 17.{{overline|7}}
| 99/98
| [[Quarvish]]
|-
|-
| 2
| 2
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| 71.{{overline|1}}
| 71.{{overline|1}}
| 25/24
| 25/24
| [[Vishnu]] / ananta / acyuta
| [[Vishnu]] / acyuta / ananta
|-
|-
| 2
| 2
| 112\270<br>(23\270)
| 23\270
| 497.{{overline|7}}<br>(102.{{overline|2}})
| 102.{{overline|2}}
| 4/3<br>(35/33)
| 35/33
| [[Gariwizmic]]
| [[Gariwizmic]]
|-
|-
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| 8/7
| 8/7
| [[Orga]]
| [[Orga]]
|-
| 2
| 131\270<br>(4\270)
| 582.{{overline|2}}<br>(17.{{overline|7}})
| 7/5<br>(99/98)
| [[Quarvish]]
|-
|-
| 3
| 3
Line 512: Line 502:
|-
|-
| 5
| 5
| 83\270<br>(25\270)
| 25\270
| 368.{{overline|8}}<br>(111.{{overline|1}})
| 111.{{overline|1}}
| 1024/891<br>(16/15)
| 16/15
| [[Quintosec]]
| [[Quintosec]]
|-
|-
| 6
| 6
| 112\270<br>(4\270)
| 16\270
| 497.{{overline|7}}<br>(97.{{overline|7}})
| 71.{{overline|1}}
| 4/3<br>(128/121)
| 25/24
| [[Trivish]]
|-
| 6
| 22\270
| 97.{{overline|7}}
| 128/121
| [[Sextile]]
| [[Sextile]]
|-
|-
| 9
| 9
| 71\270<br>(11\270)
| 11\270
| 315.{{overline|5}}<br>(48.{{overline|8}})
| 48.{{overline|8}}
| 6/5<br>(36/35)
| 36/35
| [[Ennealimmal]] / enneabiotic / ennealympic
| [[Ennealimmal]] / enneabiotic / ennealympic
|-
|-
| 10
| 10
| 16\270<br>(11\270)
| 2\270
| 71.{{overline|1}}<br>(48.{{overline|8}})
| 8.{{overline|8}}
| 25/24<br>(36/35)
| 196/195
| [[Decavish]]
| [[Decoid]]
|-
|-
| 10
| 10
| 56\270<br>(2\270)
| 10\270
| 248.{{overline|8}}<br>(8.{{overline|8}})
| 44.{{overline|4}}
| 15/13<br>(176/175)
| 40/39
| [[Decoid]]
| [[Deca]]
|-
|-
| 10
| 10
| 71\270<br>(10\270)
| 11\270
| 315.{{overline|5}}<br>(44.{{overline|4}})
| 48.{{overline|8}}
| 6/5<br>(40/39)
| 36/35
| [[Deca]]
| [[Decavish]]
|-
|-
| 18
| 18
| 71\270<br>(4\270)
| 2\270
| 248.{{overline|8}}<br>(17.{{overline|7}})
| 8.{{overline|8}}
| 15/13<br>(99/98)
| 1287/1280
| [[Hemiennealimmal]]
| [[Semihemiennealimmal]]
|-
|-
| 18
| 18
| 71\270<br>(2\270)
| 4\270
| 475.{{overline|5}}<br>(8.{{overline|8}})
| 17.{{overline|7}}
| 1053/800<br>(1287/1280)
| 99/98
| [[Semihemiennealimmal]]
| [[Hemiennealimmal]]
|-
|-
| 27
| 27
| 61\270<br>(1\270)
| 1\270
| 271.{{overline|1}}<br>(4.{{overline|4}})
| 4.{{overline|4}}
| 1375/1176<br>(385/384)
| 385/384
| [[Trinealimmal]]
| [[Trinealimmal]]
|-
|-
| 30
| 30
| 82\270<br>(1\270)
| 1\270
| 364.{{overline|4}}<br>(4.{{overline|4}})
| 4.{{overline|4}}
| 216/175<br>(385/384)
| 385/384
| [[Zinc]]
| [[Zinc]]
|-
| 30
| 2\270
| 8.{{overline|8}}
| 196/195
| [[Triacontoid]]
|-
|-
| 45
| 45
| 59\270<br>(1\270)
| 1\270
| 262.{{overline|2}}<br>(4.{{overline|4}})
| 4.{{overline|4}}
| 64/55<br>(385/384)
| 385/384
| [[Rhodium]]
| [[Rhodium]]
|}
|}
<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
<nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]]


== Scales ==
== Scales ==
Retrieved from "https://en.xen.wiki/w/270edo"