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. 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. | ||
== | 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. | ||
== | == Comptons == | ||
Edos that temper the | 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. | ||
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|} | |} | ||
== | == 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 | ||
|} | |} | ||
== | == Panschismoids == | ||
Edos that have very accurate fifths and temper | 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, | 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. 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 (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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|17:4 | |17:4 | ||
|duphyperfourth | |duphyperfourth | ||
| | |upperminor third | ||
|downpertritone | |downpertritone | ||
|} | |} | ||
=== | === Non-cassandroid Ultimates === | ||
Have fifths a smidge sharper than just, along the optimal range for cassaschismic. Up/down can be used for | 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}} | |||
* 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 | * 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. | ||