Xenharmonic Wiki

8edf: Difference between revisions

← Older edit
VisualWikitext
Ayceman (talk | contribs)
autopatrolled, emailconfirmed
173 edits
m Cats
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,768 edits
 
(22 intermediate revisions by 7 users not shown)
Line 1: Line 1:
'''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 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).
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"
{| class="wikitable"
|-
!Scale
!Scale
!Cents
!Cents
Line 14: Line 12:
!Uranian
!Uranian
!Diatonic
!Diatonic
! colspan="2" |Notation
! colspan="3" |Notation
|-
|-
!degree
!degree
Line 23: Line 21:
!interval
!interval
!equivalent
!equivalent
!Sesquitave
!Uranian
!D-Sesquitave
!Annapolis
!Tetratonic notation
|-
|-
|'''0'''
|'''0'''
|'''0'''
|'''0'''
|'''1'''
| colspan="3" |'''1'''
|
| colspan="2" |'''unison'''
|
|'''unison'''
|'''unison'''
|'''A'''
|'''A'''
|'''Α'''
|'''Α'''
|C
|-
|-
|1
|1
Line 42: Line 39:
|20/19, 19/18
|20/19, 19/18
|min mos2nd
|min mos2nd
|min 2nd
|minor second
|A#
|A#
|Α#
|Α#
|^C, vD
|-
|-
|2
|2
Line 52: Line 50:
|21/19
|21/19
|maj mos2nd
|maj mos2nd
|maj 2nd
|major second
|B
|B
|Β
|Β
|D
|-
|-
|3
|3
Line 62: Line 61:
|
|
|''perf mos3rd''
|''perf mos3rd''
|submin 3rd
|subminor third
|C
|C
|Γ
|Γ
|^D, vE
|-
|-
|4
|4
Line 72: Line 72:
|
|
|aug mos3rd
|aug mos3rd
|neutral 3rd
|neutral third
|C#
|C#
|Γ#
|Γ#
|E
|-
|-
|5
|5
Line 82: Line 83:
|
|
|''perf mos4th''
|''perf mos4th''
|supermaj 3rd
|supermajor third
|D
|D
|Δ
|Δ
|^E, vF
|-
|-
|6
|6
Line 95: Line 97:
|D#
|D#
|Δ#
|Δ#
|F
|-
|-
|7
|7
Line 102: Line 105:
|27/19
|27/19
|maj mos5th
|maj mos5th
|aug fourth
|augmented fourth
|E
|E
|Ε
|Ε
|^F, vC
|-
|-
|'''8'''
|'''8'''
Line 115: Line 119:
|'''A'''
|'''A'''
|'''Ϛ/Ϝ'''
|'''Ϛ/Ϝ'''
|C
|-
|-
|9
|9
Line 122: Line 127:
|30/19
|30/19
|min mos7th
|min mos7th
|min 6th
|minor sixth
|A#
|A#
|Ϛ#/Ϝ#
|Ϛ#/Ϝ#
|^C, vD
|-
|-
|10
|10
Line 132: Line 138:
|63/38
|63/38
|maj mos7th
|maj mos7th
|maj 6th
|major sixth
|B
|B
|Ζ
|Ζ
|D
|-
|-
|11
|11
Line 142: Line 149:
|
|
|''perf mos8th''
|''perf mos8th''
|submin 7th
|subminor seventh
|C
|C
|Η
|Η
|^D, vE
|-
|-
|12
|12
Line 152: Line 160:
|
|
|aug mos8th
|aug mos8th
|neutral 7th
|neutral seventh
|C#
|C#
|Η#
|Η#
|E
|-
|-
|13
|13
Line 162: Line 171:
|
|
|''perf mos9th''
|''perf mos9th''
|supermaj 7th
|supermajor seventh
|D
|D
|Θ
|Θ
|^E, vF
|-
|-
|14
|14
Line 175: Line 185:
|D#
|D#
|Θ#
|Θ#
|F
|-
|-
|15
|15
Line 182: Line 193:
|81/38
|81/38
|maj mos10th
|maj mos10th
|min ninth
|minor ninth
|E
|E
|Ι
|Ι
|^F, vC
|-
|-
|'''16'''
|'''16'''
Line 192: Line 204:
|
|
|'''double sesquitave'''
|'''double sesquitave'''
|'''maj ninth'''
|'''major ninth'''
|'''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&ampenv=organ Scale workshop link for a keyboard/MIDI playable 8EDF (with graphical uranian scale, A=220Hz)]


== Rank 2 temperaments ==
== Rank 2 temperaments ==
Line 217: Line 231:
| | 3\8
| | 3\8
| | [[3L 2s (fifth-equivalent)|3L2s (uranian)]]
| | [[3L 2s (fifth-equivalent)|3L2s (uranian)]]
| | [[Semiwolf]]
| | [[3L 2s (fifth-equivalent)#Temperaments|Semiwolf]]
|-
|-
| | 2
| | 2
Line 225: Line 239:
|}
|}


== 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"