User:Eufalesio/Mappings of edos - Revision history

FloraC: Apply proper linking

2026-05-27T10:49:03Z

Apply proper linking

← Older revision		Revision as of 10:49, 27 May 2026
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	== Comptons ==		== Comptons ==
	Edos that temper out the [[poma]]. Not using up/down in 24edo because up/down differ too much in size from 72 and 84. The mapping of up/down is obviously fractions of 1\12.		Edos that temper out the [[Pythagorean comma\|poma]]. Not using up/down in 24edo because up/down differ too much in size from 72 and 84. The mapping of up/down is obviously fractions of 1\12.

	* 72edo has an astounding 11-limit, usable in the 19-limit.		* 72edo has an astounding 11-limit, usable in the 19-limit.

Eufalesio at 17:09, 26 May 2026

2026-05-26T17:09:18Z

← Older revision		Revision as of 17:09, 26 May 2026
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	Different ways edos I deem important map intervals, made mostly for myself for notekeeping but may be useful to you. Nomenclature is a mix of my [[User:Eufalesio/Holopyth and Hemipyth\|Holopyth and Hemipyth]] and [[Kite's ups and downs notation]], but resumed: sub/super/hypo/hyper add -1/+1/-2/+2 mapped pythagorean commas, up/down add edosteps.		Different ways edos I deem important map intervals, made mostly for myself for notekeeping but may be useful to you. Nomenclature is a mix of my [[User:Eufalesio/Holopyth and Hemipyth\|Holopyth and Hemipyth]] and [[Kite's ups and downs notation]], but resumed: sub/super/hypo/hyper add -1/+1/-2/+2 mapped pythagorean commas, up/down add edosteps.

	== ~~Meantonoid edos~~ ==		Before going into the tables: edos listed here are
	Edos that temper the syntonic comma in the golden series. Up/down can be used for diesis halves.
			== Meantonoids* ==
			Edos that temper the syntonic comma '''in the golden series'''. Up/down can be used for diesis halves.

	* 19edo is coarse, decent 5-limit.		* 19edo is coarse, decent 5-limit.
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	\|4:2		\|4:2
	\|}		\|}
	Treating super/sub as meantone dieses (d2) not pythagorean commas.		<nowiki>*</nowiki>Treating super/sub as meantone dieses (d2) not pythagorean commas.

	== ~~Compton edos~~ ==		== Comptons ==
	Edos that temper the ~~pythagorean comma~~. Not using up/down in 24edo because up/down differ too much in size from 72 and 84.		Edos that temper out the [[poma]]. Not using up/down in 24edo because up/down differ too much in size from 72 and 84. The mapping of up/down is obviously fractions of 1\12.

	* 72edo has an astounding 11-limit, usable in the 19-limit.		* 72edo has an astounding 11-limit, usable in the 19-limit.
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	\|}		\|}

	== ~~Superpythoid edos~~ ==		== Superpythoids ==
	Edos with sharp fifths. Up/down can be used for limma (halves).		Edos with sharp fifths. Up/down can be used for limma (halves).

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	\|tritone		\|tritone
	\|}		\|}
	== ~~Panschismoid edos~~ ==		== Panschismoids ==
	Edos that have very accurate fifths and temper ~~schisma-sized~~ commas.		Edos that have very accurate fifths and temper out very small or unnoticeable commas.

	* 41edo has a great 11-limit, usable no-17,23 29-limit		* 41edo has a great 11-limit, usable no-17,23 29-limit
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	=== Cassandroids ===		=== Cassandroids ===
	Have fifths close to just, ~~and are marvel systems~~. Up/down can be used for pc halves.		Have fifths close to just, supporting garibaldi. Up/down can be used for pc halves (or mercommas) in the case of 94edo.
	{\| class="wikitable"		{\| class="wikitable"
	!Edo		!Edo
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	=== Helmholtzoids ===		=== Helmholtzoids ===
	Have fifths a smidge flatter than just, along the optimal range for schismic and pontiac. Up/down can be used for pc fractions. The true mappings for 171 and 224's edostep are -53 fifths (~~transmercunison~~). 130 and 159 instead have a poma fraction as the only possible mapping.		Have fifths a smidge flatter than just, along the optimal range for schismic and pontiac. Up/down can be used for pc fractions. The true mappings for 171 and 224's edostep are -53 fifths (negative merccomma). 130 and 159 instead have a poma fraction as the only possible reasonable mapping.

	* 130 has a well rounded 13-limit with very good accuracy, usable all the way to the no-29 31-limit.		* 130 has a well rounded 13-limit with very good accuracy, usable all the way to the no-29 31-limit.
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	\|}		\|}

	=== ~~Ultimate~~ ===		=== Non-cassandroid Ultimates ===
	Have fifths a smidge sharper than just, along the optimal range for cassaschismic. Up/down can be used for pc fractions.		Have fifths a smidge sharper than just, along the optimal range for [[Cassaschismic\|cassaschismic (Ultimate)]]. Up/down can be used for pc fractions.

	{{Databox\|The true mappings of the up/down are contrived.\|41-comma (transsuperunison) for 217edo<br>53-comma - half poma (transsemisubunison) for 270edo<br>135-comma for 311edo<br>also -41 hemififths (sesquisubbarbaric) for 270edo and 311edo}}		{{Databox\|The true mappings of the up/down are contrived.\|41-comma (transsuperunison) for 217edo<br>53-comma - half poma (transsemisubunison) for 270edo<br>135-comma for 311edo<br>also -41 hemififths (sesquisubbarbaric) for 270edo and 311edo}}

Eufalesio: /* Helmholtzoids */

2026-05-26T09:55:49Z

Helmholtzoids

← Older revision		Revision as of 09:55, 26 May 2026
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	=== Helmholtzoids ===		=== Helmholtzoids ===
	Have fifths a smidge flatter than just, along the optimal range for schismic. Up/down can be used for pc fractions.		Have fifths a smidge flatter than just, along the optimal range for schismic and pontiac. Up/down can be used for pc fractions. The true mappings for 171 and 224's edostep are -53 fifths (transmercunison). 130 and 159 instead have a poma fraction as the only possible mapping.

	* 130 has a well rounded 13-limit with very good accuracy, usable all the way to the no-29 31-limit.		* 130 has a well rounded 13-limit with very good accuracy, usable all the way to the no-29 31-limit.
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	\|17:4		\|17:4
	\|duphyperfourth		\|duphyperfourth
	\|~~1/4perminor~~ third		\|upperminor third
	\|downpertritone		\|downpertritone
	\|}		\|}

	=== Ultimate ===		=== Ultimate ===
	Have fifths a smidge sharper than just, along the optimal range for cassaschismic. Up/down can be used for ~~3~5c deviations~~.		Have fifths a smidge sharper than just, along the optimal range for cassaschismic. Up/down can be used for pc fractions.

			{{Databox\|The true mappings of the up/down are contrived.\|41-comma (transsuperunison) for 217edo<br>53-comma - half poma (transsemisubunison) for 270edo<br>135-comma for 311edo<br>also -41 hemififths (sesquisubbarbaric) for 270edo and 311edo}}
	* 217 has a well rounded 31-limit with great accuracy.		* 217 has a well rounded 31-limit with great accuracy.
	* 270 has an astonishingly accurate yazalathana. Usable in higher limits.		* 270 has an astonishingly accurate yazalathana. Usable in higher limits.

Eufalesio: /* Garytonoids */

2026-05-08T09:37:15Z

Garytonoids

← Older revision		Revision as of 09:37, 8 May 2026
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	\|}		\|}

	=== ~~Garytonoids~~ ===		=== Ultimate ===
	Have fifths a smidge sharper than just, along the optimal range for cassaschismic. Up/down can be used for ~~schisma-sized steps~~.		Have fifths a smidge sharper than just, along the optimal range for cassaschismic. Up/down can be used for 3~5c deviations.

	* 217 has a well rounded 31-limit with great accuracy.		* 217 has a well rounded 31-limit with great accuracy.
	* 270 has an astonishingly accurate ~~2.3.5.7.11.13.19~~. Usable in higher limits.		* 270 has an astonishingly accurate yazalathana. Usable in higher limits.
	* 311 has a well rounded 41-limit with great accuracy.		* 311 has a well rounded 41-limit with great accuracy.

Eufalesio: Rewritten

2026-03-01T17:49:27Z

Rewritten

Show changes

Eufalesio: Superpyth add

2026-02-20T13:37:47Z

Superpyth add

@@ Line 91: / Line 91: @@
 |}
 Using aug/dim fractions because the chain of fifth is heavily enfactored.
 == Panschismoid edos ==

Eufalesio at 21:32, 19 February 2026

2026-02-19T21:32:17Z

Show changes

Eufalesio: Birth (WIP)

2026-02-19T17:47:13Z

Birth (WIP)

New page

Different ways edos I deem important map intervals, made mostly for myself for notekeeping but may be useful to you.

== Meantonoid edos ==
Edos that temper out the syntonic comma, in the golden series.
{| class="wikitable"
|+
!Prime
!5
!7
!11
!13
!17
!19
!23
!29
|-
|12edo
| rowspan="4" |major third
|minor seventh
| rowspan="2" |tritone
| rowspan="2" |minor sixth
| rowspan="3" |minor second
| rowspan="3" |minor third
|tritone
| rowspan="2" |minor seventh
|-
|19edo
| rowspan="3" |subminor seventh
| rowspan="3" |supertritone
|-
|31edo
| rowspan="2" |superfourth
|superminor sixth
|superminor seventh
|-
|50edo
|1/2perminor sixth
|1/2subminor second
|1/2subminor third
|1/2perminor seventh
|}
Treating super/sub as meantone dieses (d2) not pythagorean commas

== Schismoid edos ==
Edos that temper the schisma(s) or garischisma(c), or both(g).
{| class="wikitable"
!Prime
!5
!7
!11
!13
!17
!19
!23
!29
|-
|(g)41edo
| rowspan="6" |submajor third
| rowspan="3" |subminor seventh
| rowspan="3" |hyperfourth
| rowspan="3" |hyperminor sixth
| rowspan="2" |superminor second
| rowspan="6" |minor third
|tritone
| rowspan="2" |superminor seventh
|-
|(g)53edo
|supertritone
|-
|(g)94edo
| rowspan="2" |1/2perminor second
|1/2pertritone
|1/2perminor seventh
|-
|(s)130edo
|3/2subminor seventh
|3perfourth
|5/2perminor sixth
|supertritone
|hyperminor seventh
|-
|(s)159edo
| rowspan="2" |4/3subminor seventh
| rowspan="2" |7/3perfourth
|hyperminor sixth
| rowspan="2" |2/3perminor second
|2/3pertritone
|4/3perminor seventh
|-
|(s)171edo
|7/3perminor sixth
|supertritone
|5/3perminor seventh
|-
|(c)217edo
|4/5submajor third
| rowspan="3" |subminor seventh
| rowspan="3" |hyperfourth
|9/5perminor sixth
|3/5perminor second
|1/5perminor third
|3/5pertritone
|6/5perminor seventh
|-
|(c)270edo
|5/6submajor third
|11/6perminor sixth
|2/3perminor second
|1/6perminor third
|1/2pertritone
|4/3perminor seventh
|-
|(c)311edo
|6/7submajor third
|13/7perminor sixth
|
|1/7perminor third
|4/7pertritone
|9/7perminor seventh
|}

WIP