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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]]).
{{Infobox ET}}
'''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 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 16[[edIX]] as a tuning for the Natural and Harmonic Minor modes of Annapolis[6L 4s]).
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).
 
{| class="wikitable center-all left-1 left-2"
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 [J]).
!Scale
 
!Cents
{| class="wikitable"
|-
! rowspan="2" |Scale degree
! rowspan="2" |Cents value
! colspan="3" |Approximate intervals
! colspan="3" |Approximate intervals
! rowspan="2" |Uranian interval
!Uranian
! rowspan="2" |Diatonic
!Diatonic
equivalent
! colspan="3" |Notation
! colspan="2" |Notation
|-
|-
!degree
!value
!7-limit
!7-limit
!11-limit
!11-limit
!19-limit
!19-limit
!Semiwolf
!interval
!Annapolis[6L 4s]
!equivalent
!Uranian
!Annapolis
!Tetratonic notation
|-
|-
! colspan="2" |'''0'''
|'''0'''
! colspan="3" |'''1'''
|'''0'''
! colspan="2" |'''unison'''
| colspan="3" |'''1'''
! colspan="2" |'''A'''
| colspan="2" |'''unison'''
|'''A'''
|'''Α'''
|C
|-
|-
|1
|1
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|min mos2nd
|min mos2nd
|minor second
|minor second
! colspan="2" |A#
|A#
|Α#
|^C, vD
|-
|-
|2
|2
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|maj mos2nd
|maj mos2nd
|major second
|major second
! colspan="2" |B
|B
|Β
|D
|-
|-
|3
|3
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|C
|C
|Γ
|Γ
|^D, vE
|-
|-
|4
|4
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|C#
|C#
|Γ#
|Γ#
|E
|-
|-
|5
|5
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|D
|D
|Δ
|Δ
|^E, vF
|-
|-
|6
|6
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|D#
|D#
|Δ#
|Δ#
|F
|-
|-
|7
|7
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|E
|E
|Ε
|Ε
|^F, vC
|-
|-
|'''8'''
|'''8'''
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|'''A'''
|'''A'''
|'''Ϛ/Ϝ'''
|'''Ϛ/Ϝ'''
|C
|-
|-
|9
|9
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|A#
|A#
|Ϛ#/Ϝ#
|Ϛ#/Ϝ#
|^C, vD
|-
|-
|10
|10
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|B
|B
|Ζ
|Ζ
|D
|-
|-
|11
|11
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|C
|C
|Η
|Η
|^D, vE
|-
|-
|12
|12
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|C#
|C#
|Η#
|Η#
|E
|-
|-
|13
|13
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|D
|D
|Θ
|Θ
|^E, vF
|-
|-
|14
|14
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|D#
|D#
|Θ#
|Θ#
|F
|-
|-
|15
|15
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|minor ninth
|minor ninth
|E
|E
|I (J)
|Ι
|^F, vC
|-
|-
|'''16'''
|'''16'''
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|'''double sesquitave'''
|'''double sesquitave'''
|'''major ninth'''
|'''major ninth'''
! colspan="2" |'''A'''
|'''A'''
|'''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&ampenv=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&ampenv=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:Edf]]
[[Category:Theory]]
[[Category:Nonoctave]]
[[Category:Nonoctave]]
{{Todo| review }}
Retrieved from "https://en.xen.wiki/w/8edf"