Xenharmonic Wiki

217edo: Difference between revisions

← Older edit
VisualWikitext
Eufalesio (talk | contribs)
24 edits
m sagittal was not displaying evo compound accidentals
Tristanbay (talk | contribs)
457 edits
Tags: Mobile edit Mobile web edit
 
(3 intermediate revisions by 2 users not shown)
Line 177: Line 177:


== Notation ==
== 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>


=== Sagittal ===
It shares the same exact symbol system as the Athenian notation for just intonation or ''Medium-precision JI notation.''<ref name=":1"/>
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>. 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">https://sagittal.org/sagittal.pdf 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"
{| class="wikitable"
|+Sagittal notation
|+Sagittal notation
!217edosteps
! colspan="2" | Steps
!-21
| 1
!-20
| 2
!-19
| 3
!-18
| 4
!-17
| 5
!-16
| 6
!-15
| 7
!-14
| 8
!-13
| 9
!-12
| 10
!-11
| 11
!-10
| 12
!-9
| 13
!-8
| 14
!-7
| 15
!-6
| 16
!-5
| 17
!-4
| 18
!-3
| 19
!-2
| 20
!-1
| 21
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!11
!12
!13
!14
!15
!16
!17
!18
!19
!20
!21
|-
|-
|Revo
! rowspan="2" | Symbol
|{{sagittal|\!!/}}
! Evo
|{{sagittal|\!!)}}
| rowspan="2" | {{Sagittal| |( }}
|{{sagittal|\\!!}}
| rowspan="2" | {{Sagittal| )|( }}
|{{sagittal|(!!(}}
| rowspan="2" | {{Sagittal| ~|( }}
|{{sagittal|!!/}}
| rowspan="2" | {{Sagittal| /| }}
|{{sagittal|!!)}}
| rowspan="2" | {{Sagittal| |) }}
|{{sagittal|)!!~}}
| rowspan="2" | {{Sagittal| (| }}
|{{sagittal|~!!(}}
| rowspan="2" | {{Sagittal| (|( }}
|{{sagittal|)!!(}}
| rowspan="2" | {{Sagittal| //| }}
|{{sagittal|(!/}}
| rowspan="2" | {{Sagittal| /|) }}
|{{sagittal|(!)}}
| rowspan="2" | {{Sagittal| /|\ }}
| rowspan="2" |{{sagittal|\!/}}
| {{Sagittal|#}}{{sagittal| \!/ }}
| rowspan="2" |{{sagittal|\!)}}
| {{Sagittal|#}}{{sagittal| \!) }}
| rowspan="2" |{{sagittal|\\!}}
| {{Sagittal|#}}{{sagittal| \\! }}
| rowspan="2" |{{sagittal|(!(}}
| {{Sagittal|#}}{{sagittal| (!( }}
| rowspan="2" |{{sagittal|(!}}
| {{Sagittal|#}}{{sagittal| (! }}
| rowspan="2" |{{sagittal|!)}}
| {{Sagittal|#}}{{sagittal| !) }}
| rowspan="2" |{{sagittal|\!}}
| {{Sagittal|#}}{{sagittal| \! }}
| rowspan="2" |{{sagittal|~!(}}
| {{Sagittal|#}}{{sagittal| ~!( }}
| rowspan="2" |{{sagittal|)!(}}
| {{Sagittal|#}}{{sagittal| )!( }}
| rowspan="2" |{{sagittal|!(}}
| {{Sagittal|#}}{{sagittal| !( }}
| rowspan="2" |{{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|/|\}}
|{{sagittal|(|)}}
|{{sagittal|(|\}}
|{{sagittal|)||(}}
|{{sagittal|~||(}}
|{{sagittal|)||~}}
|{{sagittal|||)}}
|{{sagittal|||\}}
|{{sagittal|(||(}}
|{{sagittal|//||}}
|{{sagittal|/||)}}
|{{sagittal|/||\}}
|-
|-
|Evo
! Revo
|{{sagittal|b}}
| {{Sagittal| (|) }}
|{{sagittal|b}}{{sagittal||(}}
| {{Sagittal| (|\ }}
|{{sagittal|b}}{{sagittal|)|(}}
| {{Sagittal| )||( }}
|{{sagittal|b}}{{sagittal|~|(}}
| {{Sagittal| ~||( }}
|{{sagittal|b}}{{sagittal|/|}}
| {{Sagittal| )||~ }}
|{{sagittal|b}}{{sagittal||)}}
| {{Sagittal| ||) }}
|{{sagittal|b}}{{sagittal|(|}}
| {{Sagittal| ||\ }}
|{{sagittal|b}}{{sagittal|(|(}}
| {{Sagittal| (||( }}
|{{sagittal|b}}{{sagittal|//|}}
| {{Sagittal| //|| }}
|{{sagittal|b}}{{sagittal|/|)}}
| {{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|!(}}
|{{sagittal|#}}
|}
|}


=== Ups-and-downs notation ===
=== Ups-and-downs notation ===
The 5-up (quup) alteration neatly maps to the pythagorean-septimal comma.
The 5-up (quup) alteration neatly maps to the pythagorean-septimal comma.
{| class="wikitable" style="text-align:center;"
 
{| class="wikitable center-all"
|+Ups-and-downs notation
|+Ups-and-downs notation
! rowspan="3" |217edosteps
! Steps
!-21
| 1
!-20
| 2
!-19
| 3
!-18
| 4
!-17
| 5
!-16
| 6
!-15
| 7
!-14
| 8
!-13
| 9
!-12
| 10
!-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
! rowspan="2" | Symbol
|<<<<
| ^
|^<<<<
| ^^
|vvv<<<
| ^^^
|vv<<<
| v>
|v<<<
| >
|<<<
| ^>
|^<<<
| ^^>
|vvv<<
| ^^^>
|vv<<
| v>>
|v<<
| >>
|<<
|^<<
|vvv<
|vv<
|v<
|<
|^<
|vvv
|vv
|v
| rowspan="2" |h
|^
|^^
|^^^
|v>
|>
|^>
|^^>
|^^^>
|v>>
|>>
|^>>
|^^>>
|^^^>>
|v>>>
|>>>
|^>>>
|^^>>>
|^^^>>>
|v>>>>
|>>>>
| rowspan="2" |#
|-
|-
|^b
| <<<<#
|^^b
| ^<<<<#
|^^^b
| vvv<<<#
|v>b
| vv<<<#
|>b
| v<<<#
|^>b
| <<<#
|^^>b
| ^<<<#
|^^^>b
| vvv<<#
|v>>b
| vv<<#
|>>b
| v<<#
|^>>b
|-
|^^>>b
! Steps
|^^^>>b
| 11
|v>>>b
| 12
|>>>b
| 13
|^>>>b
| 14
|^^>>>b
| 15
|^^^>>>b
| 16
|v>>>>b
| 17
|>>>>b
| 18
|<<<<#
| 19
|^<<<<#
| 20
|vvv<<<#
| 21
|vv<<<#
|-
|v<<<#
! rowspan="2" | Symbol
|<<<#
| ^>>
|^<<<#
| ^^>>
|vvv<<#
| ^^^>>
|vv<<#
| v>>>
|v<<#
| >>>
|<<#
| ^>>>
|^<<#
| ^^>>>
|vvv<#
| ^^^>>>
|vv<#
| v>>>>
|v<#
| >>>>
|<#
| rowspan="2" | #
|^<#
|-
|vvv#
| <<#
|vv#
| ^<<#
|v#
| vvv<#
| vv<#
| v<#
| <#
| ^<#
| vvv#
| vv#
| v#
|}
|}


=== 31edo-based notation ===
=== 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.  
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.


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 center-all"
{| class="wikitable"
|+Alternative 31edo-based notation
|+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
! Steps
|^b
| 1
|^^b
| 2
|^^^b
| 3
|vvvd
| 4
|vvd
| 5
|vd
| 6
|d
| 7
|d^
| 8
|d^^
| 9
|d^^^
| 10
| rowspan="2" |vvv
| 11
| rowspan="2" |vv
| 12
| rowspan="2" |v
| 13
| rowspan="2" |h
| 14
| rowspan="2" |^
|-
| rowspan="2" |^^
! rowspan="2" | Symbol
| rowspan="2" |^^^
| rowspan="2" | ^
|vvv‡
| rowspan="2" | ^^
|vv‡
| rowspan="2" | ^^^
|v‡
| vvvt
|‡
| vvt
|^‡
| vt
|^^‡
| t
|^^^‡
| ^t
|v#
| ^^t
|vv#
| ^^^t
|vvv#
| v#
|#
| vv#
| vvv#
| #
|-
|-
|^<<<
| v>
|vvv<<
| >
|vv<<
| ^>
|v<<
| ^^>
|<<
| ^^^>
|^<<
| v>>
|vvv<
| >>
|vv<
| ^>>
|v<
| ^^>>
|<
| ^^^>>
|^<
| v>>>
|v>
|>
|^>
|^^>
|^^^>
|v>>
|>>
|^>>
|^^>>
|^^^>>
|v>>>
|}
|}


Retrieved from "https://en.xen.wiki/w/217edo"