77edo: Difference between revisions
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=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|77|columns= | {{Harmonics in equal|77|columns=11}} | ||
{{Harmonics in equal|77|columns= | {{Harmonics in equal|77|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 77edo (continued)}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 77 factors into primes as {{nowrap|7 × 11}}, 77edo contains [[7edo]] and [[11edo]] as subset edos. | Since 77 factors into primes as {{nowrap| 7 × 11 }}, 77edo contains [[7edo]] and [[11edo]] as subset edos. | ||
== Intervals == | == Intervals == | ||
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== Notation == | == Notation == | ||
=== Ups and downs notation === | === Ups and downs notation === | ||
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== Approximation to JI == | == Approximation to JI == | ||
=== | === Selected just intervals === | ||
{{ | {{Q-odd-limit intervals}} | ||
}} | |||
== Regular temperament properties == | == Regular temperament properties == | ||
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|- | |- | ||
| 2.3 | | 2.3 | ||
| {{ | | {{Monzo| -122 77 }} | ||
| {{ | | {{Mapping| 77 122 }} | ||
| +0.207 | | +0.207 | ||
| 0.207 | | 0.207 | ||
| Line 298: | Line 286: | ||
| 2.3.5 | | 2.3.5 | ||
| 32805/32768, 1594323/1562500 | | 32805/32768, 1594323/1562500 | ||
| {{ | | {{Mapping| 77 122 179 }} | ||
| −0.336 | | −0.336 | ||
| 0.785 | | 0.785 | ||
| Line 305: | Line 293: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 126/125, 1029/1024, 10976/10935 | | 126/125, 1029/1024, 10976/10935 | ||
| {{ | | {{Mapping| 77 122 179 216 }} | ||
| −0.021 | | −0.021 | ||
| 0.872 | | 0.872 | ||
| Line 312: | Line 300: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 121/120, 126/125, 176/175, 10976/10935 | | 121/120, 126/125, 176/175, 10976/10935 | ||
| {{ | | {{Mapping| 77 122 179 216 266 }} | ||
| +0.322 | | +0.322 | ||
| 1.039 | | 1.039 | ||
| Line 319: | Line 307: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 121/120, 126/125, 176/175, 196/195, 676/675 | | 121/120, 126/125, 176/175, 196/195, 676/675 | ||
| {{ | | {{Mapping| 77 122 179 216 266 285 }} | ||
| +0.222 | | +0.222 | ||
| 0.974 | | 0.974 | ||
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| 498.7<br>(46.8) | | 498.7<br>(46.8) | ||
| 4/3<br>(36/35) | | 4/3<br>(36/35) | ||
| [[Hendecatonic]] | | [[Hendecatonic (temperament)|Hendecatonic]] | ||
|} | |} | ||
<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 | ||
== Instruments == | |||
=== Skip fretting === | |||
'''Skip fretting system 77 9 11''' is a [[skip fretting]] system that tunes strings 11\77 apart, with frets placed at intervals of 9\77, or 8.555...-edo. All examples on this page are for 7-string [[guitar]]. | |||
; Intervals | |||
0\77=1/1: string 2 open | |||
77\77=2/1: string 7 fret 11 | |||
45\77=3/2: string 2 fret 5 | |||
25\77=5/4: string 1 fret 4 | |||
62\77=7/4: string 6 fret 2 | |||
35\77=11/8: string 4 fret 10 | |||
54\77=13/8: string 2 fret 6 | |||
7\77=17/16: string 1 fret 2 | |||
19\77=19/16: string 5 fret 7 | |||
40\77=23/16: string 4 fret 2 | |||
; Chords | |||
x00030x: Neutral 9th (saj6, v5) | |||
=== Keyboards === | |||
[[Lumatone mapping for 77edo|Lumatone mappings for 77edo]] are available. | |||
== Music == | == Music == | ||
; [[Bryan Deister]] | |||
* [https://www.youtube.com/shorts/wSZez2KgP2U ''microtonal improvisation in 77edo''] (2025) | |||
; [[Jake Freivald]] | ; [[Jake Freivald]] | ||
* [ | * [https://soundcloud.com/jdfreivald/a-seed-planted-starling-pure ''A Seed Planted''], in an [https://web.archive.org/web/20160729174100/http://soonlabel.com/xenharmonic/archives/1391 organ version] of [[Claudi Meneghin]]. | ||
; [[Joel Grant Taylor]] | ; [[Joel Grant Taylor]] | ||
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; [[Chris Vaisvil]] | ; [[Chris Vaisvil]] | ||
* [http://micro.soonlabel.com/star/20120830-77et-star.mp3 ''77et Star''] | * [https://web.archive.org/web/20201127015309/http://micro.soonlabel.com/star/20120830-77et-star.mp3 ''77et Star''] | ||
[[Category:Listen]] | [[Category:Listen]] | ||
[[Category:Star]] | [[Category:Star]] | ||
[[Category:Starling]] | [[Category:Starling]] | ||
[[Category:Valentine]] | [[Category:Valentine]] | ||