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<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 out [[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. It is identical to [[224edo]]'s Sagittal notation, but it uses the 11/7C for the +6/-6 alteration instead of 55C.<ref name=":1">[[George Secor|George D. Secor]] and [[David Keenan|David C. Keenan]], [https://sagittal.org/sagittal.pdf ''Sagittal – A Microtonal Notation System''], p. 11.</ref>
 
It shares the same exact symbol system as the Athenian notation for just intonation or ''Medium-precision JI notation.''<ref name=":1"/>
 
{| class="wikitable center-all"
|+Sagittal notation
! colspan="2" | Steps
| 1
| 2
| 3
| 4
| 5
| 6
| 7
| 8
| 9
| 10
| 11
| 12
| 13
| 14
| 15
| 16
| 17
| 18
| 19
| 20
| 21
|-
! rowspan="2" | Symbol
! Evo
| 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|#}}{{sagittal| !) }}
| {{Sagittal|#}}{{sagittal| \! }}
| {{Sagittal|#}}{{sagittal| ~!( }}
| {{Sagittal|#}}{{sagittal| )!( }}
| {{Sagittal|#}}{{sagittal| !( }}
| {{Sagittal|#}}
|-
! Revo
| {{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 center-all"
|+Ups-and-downs notation
! Steps
| 1
| 2
| 3
| 4
| 5
| 6
| 7
| 8
| 9
| 10
|-
! rowspan="2" | Symbol
| ^
| ^^
| ^^^
| v>
| >
| ^>
| ^^>
| ^^^>
| v>>
| >>
|-
| <<<<#
| ^<<<<#
| vvv<<<#
| vv<<<#
| v<<<#
| <<<#
| ^<<<#
| vvv<<#
| vv<<#
| v<<#
|-
! Steps
| 11
| 12
| 13
| 14
| 15
| 16
| 17
| 18
| 19
| 20
| 21
|-
! rowspan="2" | Symbol
| ^>>
| ^^>>
| ^^^>>
| v>>>
| >>>
| ^>>>
| ^^>>>
| ^^^>>>
| v>>>>
| >>>>
| rowspan="2" | #
|-
| <<#
| ^<<#
| vvv<#
| vv<#
| v<#
| <#
| ^<#
| vvv#
| vv#
| v#
|}
 
=== 31edo-based notation ===
Since {{nowrap| 217 {{=}} 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]] is used 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 center-all"
|+Alternative 31edo-based notation
|-
! Steps
| 1
| 2
| 3
| 4
| 5
| 6
| 7
| 8
| 9
| 10
| 11
| 12
| 13
| 14
|-
! rowspan="2" | Symbol
| rowspan="2" | ^
| rowspan="2" | ^^
| rowspan="2" | ^^^
| vvvt
| vvt
| vt
| t
| ^t
| ^^t
| ^^^t
| v#
| vv#
| vvv#
| #
|-
| 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"