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'''[[EDF | '''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]]). | ||
==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 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). | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| Line 122: | Line 128: | ||
|1169.0981 | |1169.0981 | ||
|} | |} | ||
== Rank 2 temperaments == | |||
MOS scales and temperament listed by generator size and period: | |||
{| class="wikitable" | |||
|- | |||
! | Periods | |||
per octave | |||
! | Generator | |||
! | Scale pattern | |||
! | Temperaments | |||
|- | |||
| | 1 | |||
| | 1\8 | |||
| | 1L5s, 1L6s | |||
| | (pathological) | |||
|- | |||
| | 1 | |||
| | 3\8 | |||
| | [[3L 2s (fifth-equivalent)|3L2s (uranian)]] | |||
| | [[Semiwolf]] | |||
|- | |||
| | 2 | |||
| | 3\8 | |||
| | 2L 2s | |||
| | (augmented-like) | |||
|} | |||
== Images == | |||
[[File:8EDF_cheat_sheet_circle.png|400px|thumb|left|8EDF cheat sheet (sesquitave notation) - [[Media:8EDF_cheat_sheet.pdf|table only]]]] | |||
[[Category:Edf]] | [[Category:Edf]] | ||
[[Category:Theory]] | |||
Revision as of 13:09, 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).
| degree | cents value | octave-reduced cents value |
|---|---|---|
| 0 | ||
| 1 | 87.7444 | |
| 2 | 175.48875 | |
| 3 | 263.2331 | |
| 4 | 350.9775 | |
| 5 | 438.7219 | |
| 6 | 526.46625 | |
| 7 | 614.2106 | |
| 8 | 701.955 | |
| 9 | 789.6994 | |
| 10 | 877.44375 | |
| 11 | 965.1881 | |
| 12 | 1052.9325 | |
| 13 | 1140.6769 | |
| second octave | ||
| 14 | 1228.42125 | 28.42125 |
| 15 | 1316.1656 | 116.1656 |
| 16 | 1403.910 | 203.910 |
| nonet | ||
| 17 | 1491.6544 | 291.6544 |
| 18 | 1579.39875 | 379.39875 |
| 19 | 1667.1431 | 467.1431 |
| 20 | 1754.8875 | 554.8875 |
| 21 | 1842.6319 | 642.6139 |
| 22 | 1930.37625 | 730.37625 |
| 23 | 2018.1206 | 818.1206 |
| 24 | 2105.865 | 905.865 |
| 25 | 2193.6094 | 993.6049 |
| 26 | 2281.35375 | 1081.35375 |
| 27 | 2369.0981 | 1169.0981 |
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
