65edo: Difference between revisions
m →Theory: removing the brackets changed the meaning to suggest that 65edo has the primes that 53edo has |
→Notation: added interval mappings for 65 and 65d Tags: Mobile edit Mobile web edit Advanced mobile edit |
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<references group="note" /> | |||
== Notation == | == Notation == | ||
=== | === Stein–Zimmermann–Gould notation === | ||
[[Stein–Zimmermann–Gould notation]] uses sharps and flats combined with quartertone accidentals and arrows: | |||
{{Sharpness- | {{Sharpness-sharp6-szg}} | ||
If double arrows are not desirable, arrows can be attached to quartertone accidentals: | |||
{{Sharpness-sharp6-qt-szg}} | |||
=== Kite's ups and downs notation === | |||
65edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, trup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, trud, dupflat etc. | |||
{{Sharpness-sharp6a}} | |||
Half-sharps and half-flats can be used to avoid triple arrows: | |||
{{Sharpness- | {{Sharpness-sharp6b}} | ||
=== Ivan Wyschnegradsky's notation === | === Ivan Wyschnegradsky's notation === | ||
Since a sharp raises by six steps, Wyschnegradsky accidentals borrowed from [[72edo]] can also be used: | Since a sharp raises by six steps, Wyschnegradsky accidentals borrowed from [[72edo]] can also be used: | ||
{{Sharpness-sharp6-iw}} | |||
{{ | |||
=== Sagittal notation === | === Sagittal notation === | ||
This notation uses the same sagittal sequence as | This notation uses the same sagittal sequence as edos [[72edo #Sagittal notation|72]] and [[79edo #Sagittal notation|79]]. | ||
==== Evo flavor ==== | ==== Evo flavor ==== | ||
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default [[File:65-EDO_Evo-SZ_Sagittal.svg]] | default [[File:65-EDO_Evo-SZ_Sagittal.svg]] | ||
</imagemap> | </imagemap> | ||
== Approximation to JI == | == Approximation to JI == | ||
=== | === 15-odd-limit interval mappings === | ||
{ | {{Q-odd-limit intervals|65}} | ||
{{Q-odd-limit intervals|65.1|apx=val|header=none|tag=none|title=15-odd-limit intervals by 65d val mapping}} | |||
| 65. | |||
| | |||
| | |||
| | |||
|} | |||
== Regular temperament properties == | == Regular temperament properties == | ||
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| 498.46 | | 498.46 | ||
| 4/3 | | 4/3 | ||
| [[Helmholtz]] / [[nestoria]] / [[photia]] | | [[Helmholtz (temperament)|Helmholtz]] / [[nestoria]] / [[photia]] | ||
|- | |- | ||
| 1 | | 1 | ||
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| [[Countdown]] | | [[Countdown]] | ||
|} | |} | ||
<nowiki/>* [[Normal | <nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | ||
== Octave stretch or compression == | |||
65edo tunes [[primes]] 2, 3, 5 and 11 very well, but its 7 and 13 have two about equally-bad mappings. [[Stretched and compressed tuning|Stretching or shrinking the octave]] of 65edo for improvements in its approximations of [[JI]] therefore depends on which mapping is used: the sharp tending 65d val wants octave shrinking, whereas the flat tending 65f val wants octave stretching; both can be achieved at the cost of relatively little damage to other primes. | |||
Compressed tunings of 65edo that well approximate JI include [[zpi|334zpi]], [[ed5|151ed5]] and [[equal tuning|225ed11]]. | |||
Stretched tunings of 65edo that well approximate JI include [[WE|13-lim WE-tuned 65f]] (18.473cET) and [[TE|13-lim TE-tuned 65f]] (18.474cET). | |||
== Scales == | == Scales == | ||
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[[Lumatone mapping for 65edo]] | [[Lumatone mapping for 65edo]] | ||
== | == Music == | ||
; [[Bryan Deister]] | |||
* [https://www.youtube.com/shorts/W5PXWFduPco ''microtonal improvisation in 65edo''] (2025) | |||
* [https://www.youtube.com/shorts/UJZw9NQuGnY ''Zanarkand - Nobuo Uematsu (microtonal cover in 65edo)''] (2026) | |||
* [https://www.youtube.com/shorts/zxgVvwXnIGQ ''Waltz in 65edo''] (2026) | |||
* [https://www.youtube.com/shorts/OtbEDFhjNkc ''65edo prelude''] (2026) | |||
* [https://www.youtube.com/shorts/c0eWd7UvNQU ''Black Hole Sun - Soundgarden (microtonal cover in 65edo)''] (2026) | |||
[[Category:Listen]] | [[Category:Listen]] | ||