8edf: Difference between revisions
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==Intervals== | ==Intervals== | ||
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 | 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). | 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]). | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
!Scale | ! rowspan="2" |Scale degree | ||
!Cents | ! rowspan="2" |Cents value | ||
! colspan="3" |Approximate intervals | ! colspan="3" |Approximate intervals | ||
!Uranian | ! rowspan="2" |Uranian interval | ||
!Diatonic | ! rowspan="2" |Diatonic | ||
equivalent | |||
! colspan="2" |Notation | ! colspan="2" |Notation | ||
|- | |- | ||
!7-limit | !7-limit | ||
!11-limit | !11-limit | ||
!19-limit | !19-limit | ||
! | !Semiwolf | ||
! | !Annapolis[6L 4s] | ||
|- | |- | ||
|'''0''' | ! colspan="2" |'''0''' | ||
! colspan="3" |'''1''' | |||
|'''1''' | ! colspan="2" |'''unison''' | ||
! colspan="2" |'''A''' | |||
|'''unison''' | |||
|'''A | |||
|- | |- | ||
|1 | |1 | ||
| Line 43: | Line 35: | ||
|min mos2nd | |min mos2nd | ||
|minor second | |minor second | ||
|A | ! colspan="2" |A# | ||
|- | |- | ||
|2 | |2 | ||
| Line 53: | Line 44: | ||
|maj mos2nd | |maj mos2nd | ||
|major second | |major second | ||
|B | ! colspan="2" |B | ||
|- | |- | ||
|3 | |3 | ||
| Line 184: | Line 174: | ||
|minor ninth | |minor ninth | ||
|E | |E | ||
| | |I (J) | ||
|- | |- | ||
|'''16''' | |'''16''' | ||
| Line 193: | Line 183: | ||
|'''double sesquitave''' | |'''double sesquitave''' | ||
|'''major ninth''' | |'''major ninth''' | ||
|'''A | ! colspan="2" |'''A''' | ||
|} | |} | ||
[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)] | ||
Revision as of 05:06, 29 May 2021
8EDF (8ED3/2) is the equal division of the fifth into 8 steps of 87.7444 cents each, making it very nearly 88cET. It is related to the octacot temperament. 8EDF corresponds to 13.6761 edo (similar to every third step of 41edo).
Intervals
8EDF can be notated either using sesquitave notation (the notation repeats every period, i.e. just diatonic fifth), or using double sesquitave notation (the notation repeats every two periods, i.e. major diatonic ninth, interpreting 16edIX 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 [J]).
| Scale degree | Cents value | Approximate intervals | Uranian interval | Diatonic
equivalent |
Notation | |||
|---|---|---|---|---|---|---|---|---|
| 7-limit | 11-limit | 19-limit | Semiwolf | Annapolis[6L 4s] | ||||
| 0 | 1 | unison | A | |||||
| 1 | 87.7444 | 21/20 | 22/21 | 20/19, 19/18 | min mos2nd | minor second | A# | |
| 2 | 175.48875 | 10/9 | 21/19 | maj mos2nd | major second | B | ||
| 3 | 263.2331 | 7/6 | perf mos3rd | subminor third | C | Γ | ||
| 4 | 350.9775 | 60/49, 49/40 | 11/9 | aug mos3rd | neutral third | C# | Γ# | |
| 5 | 438.7219 | 9/7 | perf mos4th | supermajor third | D | Δ | ||
| 6 | 526.46625 | 27/20 | 19/14 | min mos5th | wolf fourth | D# | Δ# | |
| 7 | 614.2106 | 10/7 | 27/19 | maj mos5th | augmented fourth | E | Ε | |
| 8 | 701.955 | 3/2 | sesquitave | just fifth | A | Ϛ/Ϝ | ||
| 9 | 789.6994 | 63/40 | 11/7 | 30/19 | min mos7th | minor sixth | A# | Ϛ#/Ϝ# |
| 10 | 877.44375 | 5/3 | 63/38 | maj mos7th | major sixth | B | Ζ | |
| 11 | 965.1881 | 7/4 | perf mos8th | subminor seventh | C | Η | ||
| 12 | 1052.9325 | 90/49, 35/18 | 11/6 | aug mos8th | neutral seventh | C# | Η# | |
| 13 | 1140.6769 | 27/14 | perf mos9th | supermajor seventh | D | Θ | ||
| 14 | 1228.42125 | 81/40 | 57/28 | min mos10th | acute octave | D# | Θ# | |
| 15 | 1316.1656 | 15/7 | 81/38 | maj mos10th | minor ninth | E | I (J) | |
| 16 | 1403.91 | 9/4 | double sesquitave | major ninth | A | |||
Scale workshop link for a keyboard/MIDI playable 8EDF (with graphical uranian scale, A=220Hz)
Rank 2 temperaments
MOS scales and temperament listed by generator size and period:
| Periods
per octave |
Generator | Scale pattern | Temperaments |
|---|---|---|---|
| 1 | 1\8 | 1L5s, 1L6s | (pathological) |
| 1 | 3\8 | 3L2s (uranian) | Semiwolf |
| 2 | 3\8 | 2L 2s | (augmented-like) |
Images
