71edo: Difference between revisions
Dave Keenan (talk | contribs) →Sagittal notation: Moved the explanation of ≈ to the end of the section. |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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== Notation == | == Notation == | ||
=== Sagittal notation === | |||
===Sagittal notation=== | ==== Best fifth notation ==== | ||
====Best fifth notation==== | ===== Evo flavor ===== | ||
=====Evo flavor===== | |||
<imagemap> | <imagemap> | ||
File:71-EDO_Evo_Sagittal.svg | File:71-EDO_Evo_Sagittal.svg | ||
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</imagemap> | </imagemap> | ||
=====Revo flavor===== | ===== Revo flavor ===== | ||
<imagemap> | <imagemap> | ||
File:71-EDO_Revo_Sagittal.svg | File:71-EDO_Revo_Sagittal.svg | ||
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</imagemap> | </imagemap> | ||
=====Evo-SZ flavor===== | ===== Evo-SZ flavor ===== | ||
<imagemap> | <imagemap> | ||
File:71-EDO_Evo-SZ_Sagittal.svg | File:71-EDO_Evo-SZ_Sagittal.svg | ||
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In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO. | In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO. | ||
====Second-best fifth notation==== | ==== Second-best fifth notation ==== | ||
This notation uses the same sagittal sequence as EDOs [[50edo#Sagittal notation|50]], [[57edo#Sagittal notation|57]], and [[64edo#Sagittal notation|64]]. | This notation uses the same sagittal sequence as EDOs [[50edo#Sagittal notation|50]], [[57edo#Sagittal notation|57]], and [[64edo#Sagittal notation|64]]. | ||
===== Evo flavor ===== | |||
<imagemap> | <imagemap> | ||
File:71b_Evo_Sagittal.svg | File:71b_Evo_Sagittal.svg | ||
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</imagemap> | </imagemap> | ||
=====Revo flavor===== | ===== Revo flavor ===== | ||
<imagemap> | <imagemap> | ||
File:71b_Revo_Sagittal.svg | File:71b_Revo_Sagittal.svg | ||
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In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO. | In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO. | ||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | |||
|- | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br>8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.3 | |||
| {{monzo| 113 -71 }} | |||
| {{mapping| 71 113 }} | |||
| −2.49 | |||
| 2.49 | |||
| 14.72 | |||
|- | |||
| 2.3.5 | |||
| 20480/19683, 393216/390625 | |||
| {{mapping| 71 113 165 }} | |||
| −2.01 | |||
| 2.14 | |||
| 12.69 | |||
|- | |||
| 2.3.5.7 | |||
| 64/63, 245/243, 2200/2187 | |||
| {{mapping| 71 113 165 200 }} (71d) | |||
| −2.53 | |||
| 2.06 | |||
| 12.19 | |||
|} | |||
== Instruments == | |||
A [[Lumatone mapping for 71edo]] is available. | |||
== Music == | == Music == | ||
; [[Bryan Deister]] | |||
* [https://www.youtube.com/shorts/nMMSQdIV30I ''71edo improv''] (2025) | |||
; [[Francium]] | ; [[Francium]] | ||
* [https://www.youtube.com/watch?v=_FPTUlO6jNI ''Dancing in the Mosh Pit''] (2023) | * [https://www.youtube.com/watch?v=_FPTUlO6jNI ''Dancing in the Mosh Pit''] (2023) | ||
; [[No Clue Music]] | |||
* [https://www.youtube.com/watch?v=5_4T9jWYn00 ''Spiraling - Randomness''] (2025) | |||
[[Category:Listen]] | [[Category:Listen]] | ||