8edf: Difference between revisions

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-'''[[EDF|Division of the just perfect fifth]] into 8 equal parts''' (8EDF) is related to the [[Tetracot family|octacot temperament]]. The step size is about 87.7444 cents (very nearly [[88cET]]), corresponding to 13.6761 edo (similar to every third step of [[41edo]]).
+'''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]]).
 ==Intervals==
+EDF can be notated either using sesquitave notation (the notation repeats every period, i.e. [[Just fifth|just diatonic fifth]]), or using double sesquitave notation (the notation repeats every two periods, i.e. [[9/4|major diatonic ninth]], interpreting it as 16[[edIX]]).
+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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 |1169.0981
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+== Rank 2 temperaments ==
+MOS scales and temperament listed by generator size and period:
+{| class="wikitable"
+|-
+! | Periods
+per octave
+! | Generator
+! | Scale pattern
+! | Temperaments
+|-
+| | 1
+| | 1\8
+| | 1L5s, 1L6s
+| | (pathological)
+|-
+| | 1
+| | 3\8
+| | [[3L 2s (fifth-equivalent)|3L2s (uranian)]]
+| | [[Semiwolf]]
+|-
+| | 2
+| | 3\8
+| | 2L 2s
+| | (augmented-like)
+|}
+== 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:Theory]]