8edf: Difference between revisions
Scale workshop link |
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| Line 42: | Line 42: | ||
|20/19, 19/18 | |20/19, 19/18 | ||
|min mos2nd | |min mos2nd | ||
| | |minor second | ||
|A# | |A# | ||
|Α# | |Α# | ||
| Line 52: | Line 52: | ||
|21/19 | |21/19 | ||
|maj mos2nd | |maj mos2nd | ||
| | |major second | ||
|B | |B | ||
|Β | |Β | ||
| Line 62: | Line 62: | ||
| | | | ||
|''perf mos3rd'' | |''perf mos3rd'' | ||
| | |subminor third | ||
|C | |C | ||
|Γ | |Γ | ||
| Line 72: | Line 72: | ||
| | | | ||
|aug mos3rd | |aug mos3rd | ||
|neutral | |neutral third | ||
|C# | |C# | ||
|Γ# | |Γ# | ||
| Line 82: | Line 82: | ||
| | | | ||
|''perf mos4th'' | |''perf mos4th'' | ||
| | |supermajor third | ||
|D | |D | ||
|Δ | |Δ | ||
| Line 102: | Line 102: | ||
|27/19 | |27/19 | ||
|maj mos5th | |maj mos5th | ||
| | |augmented fourth | ||
|E | |E | ||
|Ε | |Ε | ||
| Line 122: | Line 122: | ||
|30/19 | |30/19 | ||
|min mos7th | |min mos7th | ||
| | |minor sixth | ||
|A# | |A# | ||
|Ϛ#/Ϝ# | |Ϛ#/Ϝ# | ||
| Line 132: | Line 132: | ||
|63/38 | |63/38 | ||
|maj mos7th | |maj mos7th | ||
| | |major sixth | ||
|B | |B | ||
|Ζ | |Ζ | ||
| Line 142: | Line 142: | ||
| | | | ||
|''perf mos8th'' | |''perf mos8th'' | ||
| | |subminor seventh | ||
|C | |C | ||
|Η | |Η | ||
| Line 152: | Line 152: | ||
| | | | ||
|aug mos8th | |aug mos8th | ||
|neutral | |neutral seventh | ||
|C# | |C# | ||
|Η# | |Η# | ||
| Line 162: | Line 162: | ||
| | | | ||
|''perf mos9th'' | |''perf mos9th'' | ||
| | |supermajor seventh | ||
|D | |D | ||
|Θ | |Θ | ||
| Line 182: | Line 182: | ||
|81/38 | |81/38 | ||
|maj mos10th | |maj mos10th | ||
| | |minor ninth | ||
|E | |E | ||
|Ι | |Ι | ||
| Line 192: | Line 192: | ||
| | | | ||
|'''double sesquitave''' | |'''double sesquitave''' | ||
|''' | |'''major ninth''' | ||
|'''A''' | |'''A''' | ||
|'''Α''' | |'''Α''' | ||
Revision as of 15:05, 11 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 it as 16edIX).
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).
| Scale | Cents | Approximate intervals | Uranian | Diatonic | Notation | |||
|---|---|---|---|---|---|---|---|---|
| degree | value | 7-limit | 11-limit | 19-limit | interval | equivalent | Sesquitave | D-Sesquitave |
| 0 | 0 | 1 | unison | unison | A | Α | ||
| 1 | 87.7444 | 21/20 | 22/21 | 20/19, 19/18 | min mos2nd | minor second | A# | Α# |
| 2 | 175.48875 | 10/9 | 21/19 | maj mos2nd | major second | B | Β | |
| 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 | Ι | |
| 16 | 1403.91 | 9/4 | double sesquitave | major ninth | A | Α | ||
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
