8edf
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 | min 2nd | A# | Α# |
| 2 | 175.48875 | 10/9 | 21/19 | maj mos2nd | maj 2nd | B | Β | |
| 3 | 263.2331 | 7/6 | perf mos3rd | submin 3rd | C | Γ | ||
| 4 | 350.9775 | 60/49, 49/40 | 11/9 | aug mos3rd | neutral 3rd | C# | Γ# | |
| 5 | 438.7219 | 9/7 | perf mos4th | supermaj 3rd | D | Δ | ||
| 6 | 526.46625 | 27/20 | 19/14 | min mos5th | wolf fourth | D# | Δ# | |
| 7 | 614.2106 | 10/7 | 27/19 | maj mos5th | aug 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 | min 6th | A# | Ϛ#/Ϝ# |
| 10 | 877.44375 | 5/3 | 63/38 | maj mos7th | maj 6th | B | Ζ | |
| 11 | 965.1881 | 7/4 | perf mos8th | submin 7th | C | Η | ||
| 12 | 1052.9325 | 90/49, 35/18 | 11/6 | aug mos8th | neutral 7th | C# | Η# | |
| 13 | 1140.6769 | 27/14 | perf mos9th | supermaj 7th | D | Θ | ||
| 14 | 1228.42125 | 81/40 | 57/28 | min mos10th | acute octave | D# | Θ# | |
| 15 | 1316.1656 | 15/7 | 81/38 | maj mos10th | min ninth | E | Ι | |
| 16 | 1403.91 | 9/4 | double sesquitave | maj 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
