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=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|77|columns=9}}
{{Harmonics in equal|77|columns=11}}
{{Harmonics in equal|77|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 77edo (continued)}}
{{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 ===
Using [[Helmholtz–Ellis]] accidentals, 77edo can be notated using [[ups and downs notation]]:


77edo can be notated using [[ups and downs notation|ups and downs]]. Trup is equivalent to quudsharp, trudsharp is equivalent to quup, etc.
{{Sharpness-sharp7a}}
Alternatively, sharps and flats with arrows borrowed from [[Helmholtz–Ellis notation]] can be used:
{{Sharpness-sharp7}}
{{Sharpness-sharp7}}


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== Approximation to JI ==
== Approximation to JI ==
=== Zeta peak index ===
=== Selected just intervals ===
{| class="wikitable center-all"
{{Q-odd-limit intervals}}
|-
! colspan="3" | Tuning
! colspan="3" | Strength
! colspan="2" | Closest edo
! colspan="2" | Integer limit
|-
! ZPI
! Steps per octave
! Step size (cents)
! Height
! Integral
! Gap
! Edo
! Octave (cents)
! Consistent
! Distinct
|-
| [[414zpi]]
| 76.9918536925042
| 15.5860645308353
| 8.194847
| 1.311364
| 17.029289
| 77edo
| 1200.12696887432
| 10
| 10
|}


== Regular temperament properties ==
== Regular temperament properties ==
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|-
|-
| 2.3
| 2.3
| {{monzo| -122 77 }}
| {{Monzo| -122 77 }}
| {{mapping| 77 122 }}
| {{Mapping| 77 122 }}
| +0.207
| +0.207
| 0.207
| 0.207
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| 2.3.5
| 2.3.5
| 32805/32768, 1594323/1562500
| 32805/32768, 1594323/1562500
| {{mapping| 77 122 179 }}
| {{Mapping| 77 122 179 }}
| −0.336
| −0.336
| 0.785
| 0.785
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| 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 }}
| {{Mapping| 77 122 179 216 }}
| −0.021
| −0.021
| 0.872
| 0.872
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| 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 }}
| {{Mapping| 77 122 179 216 266 }}
| +0.322
| +0.322
| 1.039
| 1.039
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| 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 }}
| {{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 lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
<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]]
* [http://soonlabel.com/xenharmonic/wp-content/uploads/2013/10/Freivald-J.-A-Seed-Planted-2nd-Version-77edo.mp3 ''A Seed Planted'']{{dead link}}, in an [https://web.archive.org/web/20190412162407/http://soonlabel.com/xenharmonic/archives/1391 organ version] of [[Claudi Meneghin]].
* [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'']


== Instruments ==
[[Skip fretting system 77 9 11]]
[[Category:Listen]]
[[Category:Listen]]
[[Category:Star]]
[[Category:Star]]
[[Category:Starling]]
[[Category:Starling]]
[[Category:Valentine]]
[[Category:Valentine]]
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