8edf: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
'''8 | '''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. | |||
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). | 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 | !Uranian | ||
!Annapolis | !Annapolis | ||
! | !Tetratonic notation | ||
|- | |- | ||
|'''0''' | |'''0''' | ||
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|C | |C | ||
|Γ | |Γ | ||
|D | |^D, vE | ||
|- | |- | ||
|4 | |4 | ||
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|C# | |C# | ||
|Γ# | |Γ# | ||
| | |E | ||
|- | |- | ||
|5 | |5 | ||
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|D | |D | ||
|Δ | |Δ | ||
|E | |^E, vF | ||
|- | |- | ||
|6 | |6 | ||
| Line 98: | Line 97: | ||
|D# | |D# | ||
|Δ# | |Δ# | ||
| | |F | ||
|- | |- | ||
|7 | |7 | ||
| Line 109: | Line 108: | ||
|E | |E | ||
|Ε | |Ε | ||
|F | |^F, vC | ||
|- | |- | ||
|'''8''' | |'''8''' | ||
| Line 164: | Line 163: | ||
|C# | |C# | ||
|Η# | |Η# | ||
| | |E | ||
|- | |- | ||
|13 | |13 | ||
| Line 175: | Line 174: | ||
|D | |D | ||
|Θ | |Θ | ||
|^ | |^E, vF | ||
|- | |- | ||
|14 | |14 | ||
| Line 186: | Line 185: | ||
|D# | |D# | ||
|Θ# | |Θ# | ||
| | |F | ||
|- | |- | ||
|15 | |15 | ||
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|E | |E | ||
|Ι | |Ι | ||
| | |^F, vC | ||
|- | |- | ||
|'''16''' | |'''16''' | ||
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|'''A''' | |'''A''' | ||
|'''Α''' | |'''Α''' | ||
| | |C | ||
|} | |} | ||
[https://sevish.com/scaleworkshop/?name=8EDF%20Uranian&data=87.74437510817343%0A175.48875021634686%0A263.2331253245203%0A350.9775004326937%0A438.72187554086713%0A526.4662506490406%0A614.210625757214%0A701.9550008653874&freq=220&midi=57&vert=5&horiz=1&colors=white%20black%20white%20white%20black%20white%20black%20white&waveform=square&env=organ Scale workshop link for a keyboard/MIDI playable 8EDF (with graphical uranian scale, A=220Hz)] | [https://sevish.com/scaleworkshop/?name=8EDF%20Uranian&data=87.74437510817343%0A175.48875021634686%0A263.2331253245203%0A350.9775004326937%0A438.72187554086713%0A526.4662506490406%0A614.210625757214%0A701.9550008653874&freq=220&midi=57&vert=5&horiz=1&colors=white%20black%20white%20white%20black%20white%20black%20white&waveform=square&env=organ Scale workshop link for a keyboard/MIDI playable 8EDF (with graphical uranian scale, A=220Hz)] | ||
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| | (augmented-like) | | | (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 == | == Images == | ||
[[File:8EDF_cheat_sheet_circle.png|400px|thumb|left|8EDF cheat sheet (sesquitave notation) - [[Media:8EDF cheat sheet.pdf|table only]]]] | [[File:8EDF_cheat_sheet_circle.png|400px|thumb|left|8EDF cheat sheet (sesquitave notation) - [[Media:8EDF cheat sheet.pdf|table only]]]] | ||
[[Category:Nonoctave]] | [[Category:Nonoctave]] | ||
{{Todo| review }} | |||