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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]]).
{{Infobox ET}}
==Intervals==
'''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]]).
{| class="wikitable"
 
== 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).
{| class="wikitable center-all left-1 left-2"
!Scale
!Cents
! colspan="3" |Approximate intervals
!Uranian
!Diatonic
! colspan="3" |Notation
|-
|-
!degree
!degree
!cents value
!value
!octave-reduced cents value
!7-limit
!11-limit
!19-limit
!interval
!equivalent
!Uranian
!Annapolis
!Tetratonic notation
|-
|-
|0
|'''0'''
|0
|'''0'''
|
| colspan="3" |'''1'''
| colspan="2" |'''unison'''
|'''A'''
|'''Α'''
|C
|-
|-
|1
|1
|87.7444
|87.7444
|
|21/20
|22/21
|20/19, 19/18
|min mos2nd
|minor second
|A#
|Α#
|^C, vD
|-
|-
|2
|2
|175.48875
|175.48875
|10/9
|
|
|21/19
|maj mos2nd
|major second
|B
|Β
|D
|-
|-
|3
|3
|263.2331
|263.2331
|''7/6''
|
|
|
|''perf mos3rd''
|subminor third
|C
|Γ
|^D, vE
|-
|-
|4
|4
|350.9775
|350.9775
|60/49, 49/40
|11/9
|
|
|aug mos3rd
|neutral third
|C#
|Γ#
|E
|-
|-
|5
|5
|438.7219
|438.7219
|''9/7''
|
|
|
|''perf mos4th''
|supermajor third
|D
|Δ
|^E, vF
|-
|-
|6
|6
|526.46625
|526.46625
|27/20
|
|
|19/14
|min mos5th
|wolf fourth
|D#
|Δ#
|F
|-
|-
|7
|7
|614.2106
|614.2106
|10/7
|
|
|27/19
|maj mos5th
|augmented fourth
|E
|Ε
|^F, vC
|-
|-
|8
|'''8'''
|701.955
|'''701.955'''
|'''3/2'''
|
|
|
|'''sesquitave'''
|'''just fifth'''
|'''A'''
|'''Ϛ/Ϝ'''
|C
|-
|-
|9
|9
|789.6994
|789.6994
|
|63/40
|11/7
|30/19
|min mos7th
|minor sixth
|A#
|Ϛ#/Ϝ#
|^C, vD
|-
|-
|10
|10
|877.44375
|877.44375
|5/3
|
|
|63/38
|maj mos7th
|major sixth
|B
|Ζ
|D
|-
|-
|11
|11
|965.1881
|965.1881
|''7/4''
|
|
|
|''perf mos8th''
|subminor seventh
|C
|Η
|^D, vE
|-
|-
|12
|12
|1052.9325
|1052.9325
|90/49, 35/18
|11/6
|
|
|aug mos8th
|neutral seventh
|C#
|Η#
|E
|-
|-
|13
|13
|1140.6769
|1140.6769
|''27/14''
|
|
|
|-
|''perf mos9th''
! colspan="3" |second octave
|supermajor seventh
|D
|Θ
|^E, vF
|-
|-
|14
|14
|1228.42125
|1228.42125
|28.42125
|81/40
|
|57/28
|min mos10th
|acute octave
|D#
|Θ#
|F
|-
|-
|15
|15
|1316.1656
|1316.1656
|116.1656
|15/7
|
|81/38
|maj mos10th
|minor ninth
|E
|Ι
|^F, vC
|-
|-
|16
|'''16'''
|1403.910
|'''1403.91'''
|203.910
|'''9/4'''
|-
|
|17
|
|1491.6544
|'''double sesquitave'''
|291.6544
|'''major ninth'''
|-
|'''A'''
|18
|'''Α'''
|1579.39875
|C
|379.39875
|}
|-
[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)]
|19
 
|1667.1431
== Rank 2 temperaments ==
|467.1431
 
|-
MOS scales and temperament listed by generator size and period:
|20
 
|1754.8875
{| class="wikitable"
|554.8875
|-
|21
|1842.6319
|642.6139
|-
|22
|1930.37625
|730.37625
|-
|23
|2018.1206
|818.1206
|-
|-
|24
! | Periods
|2105.865
per octave
|905.865
! | Generator
! | Scale pattern
! | Temperaments
|-
|-
|25
| | 1
|2193.6094
| | 1\8
|993.6049
| | 1L5s, 1L6s
| | (pathological)
|-
|-
|26
| | 1
|2281.35375
| | 3\8
|1081.35375
| | [[3L 2s (fifth-equivalent)|3L2s (uranian)]]
| | [[3L 2s (fifth-equivalent)#Temperaments|Semiwolf]]
|-
|-
|27
| | 2
|2369.0981
| | 3\8
|1169.0981
| | 2L 2s
| | (augmented-like)
|}
|}
[[Category:Edf]]
 
== 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:Nonoctave]]
{{Todo| review }}
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