User:Eufalesio/Mappings of edos: Difference between revisions

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Different ways edos I deem important map intervals, made mostly for myself for notekeeping but may be useful to you.
Different ways edos I deem important map intervals, made mostly for myself for notekeeping but may be useful to you. See [[User:Eufalesio/Holopyth and Hemipyth|Holopyth and Hemipyth]] for mapping nomenclature.


== Meantonoid edos ==
== Meantonoid edos ==
Edos that temper out the syntonic comma, in the golden series.
Edos with flat fifths that temper the syntonic comma in the golden series.
{| class="wikitable"
{| class="wikitable"
|+
|+
!Prime
!Edo
!m2:d2
!5
!5
!7
!7
Line 15: Line 16:
!29
!29
|-
|-
|12edo
|19
| rowspan="4" |major third
|1:1
|minor seventh
| rowspan="3" |major third
| rowspan="2" |tritone
| rowspan="3" |subminor seventh
| rowspan="2" |minor sixth
| rowspan="3" |minor second
| rowspan="3" |minor third
|tritone
|tritone
| rowspan="2" |minor seventh
|minor sixth
|-
| rowspan="2" |minor second
|19edo
| rowspan="2" |minor third
| rowspan="3" |subminor seventh
| rowspan="3" |supertritone
| rowspan="3" |supertritone
|minor seventh
|-
|-
|31edo
|'''31'''
|2:1
| rowspan="2" |superfourth
| rowspan="2" |superfourth
|superminor sixth
|superminor sixth
|superminor seventh
|superminor seventh
|-
|-
|50edo
|50
|3:2
|1/2perminor sixth
|1/2perminor sixth
|1/2subminor second
|1/2subminor second
Line 40: Line 40:
|1/2perminor seventh
|1/2perminor seventh
|}
|}
Treating super/sub as meantone dieses (d2) not pythagorean commas
Treating super/sub as meantone dieses (d2) not pythagorean commas.


== Schismoid edos ==
== Compton edos ==
Edos that temper the schisma(s) or garischisma(c), or both(g).
{| class="wikitable"
{| class="wikitable"
!Prime
!Edo
!n:12edo
!5
!5
!7
!7
Line 55: Line 55:
!29
!29
|-
|-
|(g)41edo
|12
| rowspan="6" |submajor third
|1
| rowspan="2" |major third
|minor seventh
|tritone
|minor sixth
| rowspan="4" |minor second
| rowspan="4" |minor third
|tritone
|minor seventh
|-
|24
|2
|1/2dimminor seventh
| rowspan="2" |1/2augfourth
| rowspan="2" |1/2augminor sixth
|1/2augtritone
|1/2augminor seventh
|-
|'''72'''
|6
|1/6dimmajor third
|1/3dimminor seventh
|1/3augtritone
|1/3augminor seventh
|-
|84
|7
|1/7dimmajor third
|2/7dimminor seventh
|3/7augfourth
|3/7augminor sixth
|2/7augtritone
|2/7augminor seventh
|}
Using aug/dim fractions because the chain of fifth is heavily enfactored.
 
== Panschismoid edos ==
Edos that have very accurate fifths and temper schisma-sized commas.
 
=== Cassandroids ===
{| class="wikitable"
!Edo
!m2:pc
!5
!7
!11
!13
!17
!19
!23
!29
|-
|41
|3:1
| rowspan="3" |submajor third
| rowspan="3" |subminor seventh
| rowspan="3" |subminor seventh
| rowspan="3" |hyperfourth
| rowspan="3" |hyperfourth
| rowspan="3" |hyperminor sixth
| rowspan="3" |hyperminor sixth
| rowspan="2" |superminor second
| rowspan="2" |superminor second
| rowspan="6" |minor third
| rowspan="3" |minor third
|tritone
|tritone
| rowspan="2" |superminor seventh
| rowspan="2" |superminor seventh
|-
|-
|(g)53edo
|53
|4:1
|supertritone
|supertritone
|-
|-
|(g)94edo
|'''94'''
| rowspan="2" |1/2perminor second
|7:2
|1/2perminor second
|1/2pertritone
|1/2pertritone
|1/2perminor seventh
|1/2perminor seventh
|}
=== Euschismoids ===
{| class="wikitable"
!Edo
!m2:pc
!5
!7
!11
!13
!17
!19
!23
!29
|-
|-
|(s)130edo
|130
|10:2
| rowspan="4" |submajor third
|3/2subminor seventh
|3/2subminor seventh
|3perfourth
|3perfourth
|5/2perminor sixth
|5/2perminor sixth
|1/2perminor second
| rowspan="3" |minor third
|supertritone
|supertritone
|hyperminor seventh
|hyperminor seventh
|-
|-
|(s)159edo
|159
|12:3
| rowspan="2" |4/3subminor seventh
| rowspan="2" |4/3subminor seventh
| rowspan="2" |7/3perfourth
| rowspan="2" |7/3perfourth
Line 88: Line 163:
|4/3perminor seventh
|4/3perminor seventh
|-
|-
|(s)171edo
|171
|13:3
|7/3perminor sixth
|7/3perminor sixth
|supertritone
|supertritone
|5/3perminor seventh
|5/3perminor seventh
|-
|-
|(c)217edo
|224
|17:4
|5/4subminor seventh
|5/2perfourth
|9/4perminor sixth
|3/4perminor second
|1/4perminor third
|3/4pertritone
|3/2perminor seventh
|}
 
=== Garischismoids ===
{| class="wikitable"
!Edo
!5
!7
!11
!13
!17
!19
!23
!29
|-
|217
|4/5submajor third
|4/5submajor third
| rowspan="3" |subminor seventh
| rowspan="3" |subminor seventh
Line 103: Line 202:
|6/5perminor seventh
|6/5perminor seventh
|-
|-
|(c)270edo
|'''270'''
|5/6submajor third
|5/6submajor third
|11/6perminor sixth
|11/6perminor sixth
Line 111: Line 210:
|4/3perminor seventh
|4/3perminor seventh
|-
|-
|(c)311edo
|'''311'''
|6/7submajor third
|6/7submajor third
|13/7perminor sixth
|13/7perminor sixth
|
|4/7perminor second
|1/7perminor third
|1/7perminor third
|4/7pertritone
|4/7pertritone
|9/7perminor seventh
|9/7perminor seventh
|}
|}
WIP

Revision as of 21:32, 19 February 2026

Different ways edos I deem important map intervals, made mostly for myself for notekeeping but may be useful to you. See Holopyth and Hemipyth for mapping nomenclature.

Meantonoid edos

Edos with flat fifths that temper the syntonic comma in the golden series.

Edo m2:d2 5 7 11 13 17 19 23 29
19 1:1 major third subminor seventh tritone minor sixth minor second minor third supertritone minor seventh
31 2:1 superfourth superminor sixth superminor seventh
50 3:2 1/2perminor sixth 1/2subminor second 1/2subminor third 1/2perminor seventh

Treating super/sub as meantone dieses (d2) not pythagorean commas.

Compton edos

Edo n:12edo 5 7 11 13 17 19 23 29
12 1 major third minor seventh tritone minor sixth minor second minor third tritone minor seventh
24 2 1/2dimminor seventh 1/2augfourth 1/2augminor sixth 1/2augtritone 1/2augminor seventh
72 6 1/6dimmajor third 1/3dimminor seventh 1/3augtritone 1/3augminor seventh
84 7 1/7dimmajor third 2/7dimminor seventh 3/7augfourth 3/7augminor sixth 2/7augtritone 2/7augminor seventh

Using aug/dim fractions because the chain of fifth is heavily enfactored.

Panschismoid edos

Edos that have very accurate fifths and temper schisma-sized commas.

Cassandroids

Edo m2:pc 5 7 11 13 17 19 23 29
41 3:1 submajor third subminor seventh hyperfourth hyperminor sixth superminor second minor third tritone superminor seventh
53 4:1 supertritone
94 7:2 1/2perminor second 1/2pertritone 1/2perminor seventh

Euschismoids

Edo m2:pc 5 7 11 13 17 19 23 29
130 10:2 submajor third 3/2subminor seventh 3perfourth 5/2perminor sixth 1/2perminor second minor third supertritone hyperminor seventh
159 12:3 4/3subminor seventh 7/3perfourth hyperminor sixth 2/3perminor second 2/3pertritone 4/3perminor seventh
171 13:3 7/3perminor sixth supertritone 5/3perminor seventh
224 17:4 5/4subminor seventh 5/2perfourth 9/4perminor sixth 3/4perminor second 1/4perminor third 3/4pertritone 3/2perminor seventh

Garischismoids

Edo 5 7 11 13 17 19 23 29
217 4/5submajor third subminor seventh hyperfourth 9/5perminor sixth 3/5perminor second 1/5perminor third 3/5pertritone 6/5perminor seventh
270 5/6submajor third 11/6perminor sixth 2/3perminor second 1/6perminor third 1/2pertritone 4/3perminor seventh
311 6/7submajor third 13/7perminor sixth 4/7perminor second 1/7perminor third 4/7pertritone 9/7perminor seventh
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