8edf: Difference between revisions

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'''8~~[[EDF]]~~ (~~8ED3~~/2)''' is the ~~equal division of~~ the fifth into 8 steps of 87.7444 [[cent]]s each, making it very nearly [[88cET]]. It is related to the [[~~Tetracot family~~|octacot temperament]]. ~~8EDF~~ corresponds to 13.~~6761 edo~~ (similar to every third step of [[41edo]]).

'''8 equal divisions of the fifth''' ('''8edf''', '''8ed3/2''') is the [[tuning system]] that divides the fifth into 8 steps of 87.7444 [[cent]]s each, making it very nearly [[88cET]]. It is related to the [[Octacot|octacot temperament]]. 8edf corresponds to about 13.6761edo (similar to every third step of [[41edo]]).

==Intervals==

== Intervals ==

8edf can be notated either using native uranian (sesquitave) notation, where the notation repeats every period (i.e. [[Just fifth|just diatonic fifth]]), or using double sesquitave (Annapolis) notation, where the notation repeats every two periods (i.e. [[9/4|major diatonic ninth]]). This interprets 8edf as [[16ed9/4]], resulting in a tuning for the Natural and Harmonic Minor modes of Annapolis[6L 4s]. It can also be notated using tetratonic [[4edf]]-based notation.

~~8EDF~~ can be notated either using native uranian (sesquitave) notation, where the notation repeats every period (i.e. [[Just fifth|just diatonic fifth]]), or using double sesquitave (Annapolis) notation, where the notation repeats every two periods (i.e. [[9/4|major diatonic ninth]]). This interprets 8edf as 16[[~~edIX~~]], resulting in a tuning for the Natural and Harmonic Minor modes of Annapolis[6L 4s]. It can also be notated using ~~equalized~~ [[~~1L 3s (fifth-equivalent)|neptunian~~]] ~~(1L 3s<3/2>)~~ notation ~~as a superset of [[4edf]]~~.

The naturals result from a [[semiwolf]] generator (~[[7/6]]). For sesquitave notation, letters A-E can be used. For double sesquitave notation, Greek numerals 1-10 can be used (Α,Β,Γ,Δ,Ε,Ϛ/Ϝ,Ζ,Η,Θ,Ι).

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!Uranian

!Annapolis

!~~Equalized [[1L 3s (fifth-equivalent)|Neptunian]] using 6\8edf~~

!Tetratonic notation

|-

|'''0'''

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| | (augmented-like)

|}

== Music ==

* [https://m.youtube.com/watch?v=rzcuLiE3HhE Funny Snakecharmer] - [[Sven Karma]] (Dec 2023) - uses the [[Kartvelian scales#8edf Kartvelian tetradecatonic scale|8edf Kartvelian tetradecatonic scale]], alternating blocks of [[8edf]] and [[6ed4/3]]

== Images ==

~~[[Category:Edf]]~~

[[Category:Nonoctave]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''8[[EDF]] (8ED3/2)''' is the equal division of the fifth into 8 steps of 87.7444 [[cent]]s each, making it very nearly [[88cET]]. It is related to the [[Tetracot family|octacot temperament]]. 8EDF corresponds to 13.6761 edo (similar to every third step of [[41edo]]).
+'''8 equal divisions of the fifth''' ('''8edf''', '''8ed3/2''') is the [[tuning system]] that divides the fifth into 8 steps of 87.7444 [[cent]]s each, making it very nearly [[88cET]]. It is related to the [[Octacot|octacot temperament]]. 8edf corresponds to about 13.6761edo (similar to every third step of [[41edo]]).
-==Intervals==
+== Intervals ==
+edf can be notated either using native uranian (sesquitave) notation, where the notation repeats every period (i.e. [[Just fifth|just diatonic fifth]]), or using double sesquitave (Annapolis) notation, where the notation repeats every two periods (i.e. [[9/4|major diatonic ninth]]). This interprets 8edf as [[16ed9/4]], resulting in a tuning for the Natural and Harmonic Minor modes of Annapolis[6L 4s]. It can also be notated using tetratonic [[4edf]]-based notation.
-EDF can be notated either using native uranian (sesquitave) notation, where the notation repeats every period (i.e. [[Just fifth|just diatonic fifth]]), or using double sesquitave (Annapolis) notation, where the notation repeats every two periods (i.e. [[9/4|major diatonic ninth]]). This interprets 8edf as 16[[edIX]], resulting in a tuning for the Natural and Harmonic Minor modes of Annapolis[6L 4s]. It can also be notated using equalized [[1L 3s (fifth-equivalent)|neptunian]] (1L 3s<3/2>) notation as a superset of [[4edf]].
 The naturals result from a [[semiwolf]] generator (~[[7/6]]). For sesquitave notation, letters A-E can be used. For double sesquitave notation, Greek numerals 1-10 can be used (Α,Β,Γ,Δ,Ε,Ϛ/Ϝ,Ζ,Η,Θ,Ι).
@@ Line 24: / Line 23: @@
 !Uranian
 !Annapolis
-!Equalized [[1L 3s (fifth-equivalent)|Neptunian]] using 6\8edf
+!Tetratonic notation
 |-
 |'''0'''
@@ Line 239: / Line 238: @@
 | | (augmented-like)
 |}
+== Music ==
+* [https://m.youtube.com/watch?v=rzcuLiE3HhE Funny Snakecharmer] - [[Sven Karma]] (Dec 2023) - uses the [[Kartvelian scales#8edf Kartvelian tetradecatonic scale|8edf Kartvelian tetradecatonic scale]], alternating blocks of [[8edf]] and [[6ed4/3]]
 == Images ==
 [[File:8EDF_cheat_sheet_circle.png|400px|thumb|left|8EDF cheat sheet (sesquitave notation) - [[Media:8EDF cheat sheet.pdf|table only]]]]
-[[Category:Edf]]
 [[Category:Nonoctave]]
+{{Todo| review }}