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Added notation section in Sagittal, Ups-and-downs, and 31edo-based notation
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| [[Birds]]
| [[Birds]]
|}
|}
<nowiki />* [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 
== Notation ==
 
=== Sagittal ===
217edo can be written in Sagittal using almost the entire Athenian extension (except for {{sagittal|(|}} {{sagittal|(!}} {{sagittal|)||~}} {{sagittal|)!!~}} since it tempers 1240029/1239040), by virtue of its apotome being equal to 21 edosteps, which is the maximum equal division of the apotome (eda) supported by Athenian<ref name=":0">[[Ragismic microtemperaments#Brahmagupta]]</ref>.
{| class="wikitable mw-collapsible mw-collapsed"
|+Sagittal notation
!217edosteps
!-21
!-20
!-19
!-18
!-17
!-16
!-15
!-14
!-13
!-12
!-11
!-10
!-9
!-8
!-7
!-6
!-5
!-4
!-3
!-2
!-1
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!11
!12
!13
!14
!15
!16
!17
!18
!19
!20
!21
|-
|Revo
|{{sagittal|\!!/}}
|{{sagittal|\!!)}}
|{{sagittal|\\!!}}
|{{sagittal|(!!(}}
|{{sagittal|!!/}}
|{{sagittal|!!)}}
|{{sagittal|\!!}}
|{{sagittal|~!!(}}
|{{sagittal|)!!(}}
|{{sagittal|(!/}}
|{{sagittal|(!)}}
| rowspan="2" |{{sagittal|\!/}}
| rowspan="2" |{{sagittal|\!)}}
| rowspan="2" |{{sagittal|\\!}}
| rowspan="2" |{{sagittal|(!(}}
| rowspan="2" |{{sagittal|!/}}
| rowspan="2" |{{sagittal|!)}}
| rowspan="2" |{{sagittal|\!}}
| rowspan="2" |{{sagittal|~!(}}
| rowspan="2" |{{sagittal|)!(}}
| rowspan="2" |{{sagittal|!(}}
| rowspan="2" |{{sagittal||//|}}
| rowspan="2" |{{sagittal||(}}
| rowspan="2" |{{sagittal|)|(}}
| rowspan="2" |{{sagittal|~|(}}
| rowspan="2" |{{sagittal|/|}}
| rowspan="2" |{{sagittal||)}}
| rowspan="2" |{{sagittal||\}}
| rowspan="2" |{{sagittal|(|(}}
| rowspan="2" |{{sagittal|//|}}
| rowspan="2" |{{sagittal|/|)}}
| rowspan="2" |{{sagittal|/|\}}
|{{sagittal|(|)}}
|{{sagittal|(|\}}
|{{sagittal|)||(}}
|{{sagittal|~||(}}
|{{sagittal|/||}}
|{{sagittal|||)}}
|{{sagittal|||\}}
|{{sagittal|(||(}}
|{{sagittal|//||}}
|{{sagittal|/||)}}
|{{sagittal|/||\}}
|-
|Evo
|{{sagittal|b}}
|{{sagittal|b}}{{sagittal||(}}
|{{sagittal|b}}{{sagittal|)|(}}
|{{sagittal|b}}{{sagittal|~|(}}
|{{sagittal|b}}{{sagittal|/|}}
|{{sagittal|b}}{{sagittal||)}}
|{{sagittal|b}}{{sagittal||\}}
|{{sagittal|b}}{{sagittal|(|(}}
|{{sagittal|b}}{{sagittal|//|}}
|{{sagittal|b}}{{sagittal|/|)}}
|{{sagittal|b}}{{sagittal|/|\}}
|{{sagittal|#}}{{sagittal|\!/}}
|{{sagittal|#}}{{sagittal|\!)}}
|{{sagittal|#}}{{sagittal|\\!}}
|{{sagittal|#}}{{sagittal|(!(}}
|{{sagittal|#}}{{sagittal|!/}}
|{{sagittal|#}}{{sagittal|!)}}
|{{sagittal|#}}{{sagittal|\!}}
|{{sagittal|#}}{{sagittal|~!(}}
|{{sagittal|#}}{{sagittal|)!(}}
|{{sagittal|#}}{{sagittal|!(}}
|{{sagittal|#}}
|}
 
=== Ups-and-downs notation ===
The 5-up (quup) alteration neatly maps to the pythagorean/septimal comma.
{| class="wikitable mw-collapsible mw-collapsed" style="text-align:center;"
|+Ups-and-downs notation
! rowspan="3" |217edosteps
!-21
!-20
!-19
!-18
!-17
!-16
!-15
!-14
!-13
!-12
!-11
!-10
!-9
!-8
!-7
!-6
!-5
!-4
!-3
!-2
!-1
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!11
!12
!13
!14
!15
!16
!17
!18
!19
!20
!21
|-
| rowspan="2" |b
|<<<<
|^<<<<
|vvv<<<
|vv<<<
|v<<<
|<<<
|^<<<
|vvv<<
|vv<<
|v<<
|<<
|^<<
|vvv<
|vv<
|v<
|<
|^<
|vvv
|vv
|v
| rowspan="2" |h
|^
|^^
|^^^
|v>
|>
|^>
|^^>
|^^^>
|v>>
|>>
|^>>
|^^>>
|^^^>>
|v>>>
|>>>
|^>>>
|^^>>>
|^^^>>>
|v>>>>
|>>>>
| rowspan="2" |#
|-
|^b
|^^b
|^^^b
|v>b
|>b
|^>b
|^^>b
|^^^>b
|v>>b
|>>b
|^>>b
|^^>>b
|^^^>>b
|v>>>b
|>>>b
|^>>>b
|^^>>>b
|^^^>>>b
|v>>>>b
|>>>>b
|<<<<#
|^<<<<#
|vvv<<<#
|vv<<<#
|v<<<#
|<<<#
|^<<<#
|vvv<<#
|vv<<#
|v<<#
|<<#
|^<<#
|vvv<#
|vv<#
|v<#
|<#
|^<#
|vvv#
|vv#
|v#
|}
 
=== 31edo-based notation ===
Since 217edo is 31*7, one ''could'' base the notation on its inherited meantone fifth 126\217 (18\31) instead of its best fifth.
 
This could be useful when [[31edo]] as a base tuning, where the whole palette of 217edo is only used to provide subtle inflections of the [[31edo]] pitches, similar to how one might use [[159edo]] to provide subtle corrections of [[53edo]] pitches.
{| class="wikitable mw-collapsible mw-collapsed"
|+Alternative 31edo-based notation
!-14
!-13
!-12
!-11
!-10
!-9
!-8
!-7
!-6
!-5
!-4
!-3
!-2
!-1
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!11
!12
!13
!14
|-
|b
|^b
|^^b
|^^^b
|vvvd
|vvd
|vd
|d
|d^
|d^^
|d^^^
| rowspan="2" |vvv
| rowspan="2" |vv
| rowspan="2" |v
| rowspan="2" |h
| rowspan="2" |^
| rowspan="2" |^^
| rowspan="2" |^^^
|vvv‡
|vv‡
|v‡
|‡
|^‡
|^^‡
|^^^‡
|v#
|vv#
|vvv#
|#
|-
|^<<<
|vvv<<
|vv<<
|v<<
|<<
|^<<
|vvv<
|vv<
|v<
|<
|^<
|v>
|>
|^>
|^^>
|^^^>
|v>>
|>>
|^>>
|^^>>
|^^^>>
|v>>>
|}


== Scales ==
== Scales ==
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</syntaxhighlight>
</syntaxhighlight>


== References ==
<ref name=":0" /> [[Ragismic microtemperaments#Brahmagupta]]
[[Category:Arch]]
[[Category:Arch]]
[[Category:Birds]]
[[Category:Birds]]
[[Category:Cotoneum]]
[[Category:Cotoneum]]
Retrieved from "https://en.xen.wiki/w/217edo"