217edo: Difference between revisions

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== 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>~~. 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>

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" />

It shares the same exact symbol system as the Athenian notation for just intonation or ''Medium-precision JI notation.''<ref name=":1"/>

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=== 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]] 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]] 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.

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@@ Line 178: / Line 178: @@
 == Notation ==
 === Sagittal ===
-edo 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>
+edo 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" />
+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"
@@ Line 324: / Line 324: @@
 === 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]] 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]] 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"