77edo: Difference between revisions

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@@ Line 13: / Line 13: @@
 === Prime harmonics ===
 {{Harmonics in equal|77|columns=9}}
-{{Harmonics in equal|77|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 77edo (continued)}}
+{{Harmonics in equal|77|columns=10|start=10|collapsed=true|title=Approximation of prime harmonics in 77edo (continued)}}
 === Subsets and supersets ===
@@ Line 228: / Line 228: @@
 == Notation ==
 === Ups and downs notation ===
-Using [[Helmholtz–Ellis]] accidentals, 77edo can be notated using [[ups and downs notation]]:
+edo 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}}
@@ Line 260: / Line 264: @@
 == Approximation to JI ==
 === Zeta peak index ===
-{| class="wikitable center-all"
+{{ZPI
-|-
+| zpi = 414
-! colspan="3" | Tuning
+| steps = 76.9918536925042
-! colspan="3" | Strength
+| step size = 15.5860645308353
-! colspan="2" | Closest edo
+| tempered height = 8.194847
-! colspan="2" | Integer limit
+| pure height = 8.145298
-|-
+| integral = 1.311364
-! ZPI
+| gap = 17.029289
-! Steps per octave
+| octave = 1200.12696887432
-! Step size (cents)
+| consistent = 10
-! Height
+| distinct = 10
-! 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 ==
@@ Line 427: / Line 414: @@
 |}
 <nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|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
+\77=1/1: string 2 open
+\77=2/1: string 7 fret 11
+\77=3/2: string 2 fret 5
+\77=5/4: string 1 fret 4
+\77=7/4: string 6 fret 2
+\77=11/8: string 4 fret 10
+\77=13/8: string 2 fret 6
+\77=17/16: string 1 fret 2
+\77=19/16: string 5 fret 7
+\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 ==
+; [[Bryan Deister]
+* [https://www.youtube.com/shorts/wSZez2KgP2U ''microtonal improvisation in 77edo''] (2025)
 ; [[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]].
@@ Line 438: / Line 461: @@
 * [http://micro.soonlabel.com/star/20120830-77et-star.mp3 ''77et Star'']
-== Instruments ==
-[[Skip fretting system 77 9 11]]
 [[Category:Listen]]
 [[Category:Star]]
 [[Category:Starling]]
 [[Category:Valentine]]