94edo
The 94 equal temperament, often abbreviated 94-tET, 94-EDO, or 94-ET, is the scale derived by dividing the octave into 94 equally-sized steps, where each step represents a frequency ratio of 12.766 cents. It is a remarkable all-around utility temperament, good from low prime limit to very high prime limit situations. It is the first equal temperament to be consistent though the 23-limit, and no other equal temperament is so consistent until 282 and 311 make their appearance.
The list of 23-limit commas it tempers out is huge, but it's worth noting that it tempers out 32805/32768 and is thus a schismatic system, that it tempers out 225/224 and 385/384 and so is a marvel system, and that it also tempers out 3125/3087, 4000/3969, 5120/5103 and 540/539. It provides the optimal patent val for the rank five temperament tempering out 275/273, and for a number of other temperaments, such as isis.
Also, see the Table of 94edo intervals.
| prime 2 | prime 3 | prime 5 | prime 7 | prime 11 | prime 13 | prime 17 | prime 19 | prime 23 | prime 29 | prime 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| error | 0.0¢ | +0.17¢ | -3.33¢ | +1.39¢ | -2.38¢ | +2.03¢ | -2.83¢ | -3.90¢ | -2.74¢ | +4.47¢ | +3.90¢ |
Rank two temperaments
| Periods
per octave |
Generator | Cents | Associated
ratio |
Temperament |
|---|---|---|---|---|
| 1 | 3\94 | 38.298 | 49/48 | Slender |
| 1 | 5\94 | 63.830 | 25/24 | Sycamore/betic |
| 1 | 11\94 | 140.426 | 243/224
13/12 |
Tsaharuk |
| 1 | 19\94 | 242.553 | 147/128 | Septiquarter |
| 1 | 39\94 | 497.872 | 4/3 | Schismatic/garibaldi |
| 2 | 2\94 | 25.532 | 64/63 | Ketchup |
| 2 | 43\94 | 548.936 | 11/8 | Kleischismic |
| 2 | 11\94 | 140.426 | 27/25 | Fifive |
| 2 | 34\94 | 434.043 | 9/7 | Pogo, supers |
| 2 | 30\94 | 382.979 | 5/4 | Wizard/gizzard |
Below are some 23-limit temperaments supported by 94et. It might be noted that 94, a very good tuning for garibaldi temperament, shows us how to extend it to the 23-limit.
46&94 <<8 30 -18 -4 -28 8 -24 2 ... ||
68&94 <<20 28 2 -10 24 20 34 52 ... ||
53&94 <<1 -8 -14 23 20 -46 -3 -35 ... || (one garibaldi)
41&94 <<1 -8 -14 23 20 48 -3 -35 ... || (another garibaldi, only differing in the mappings of 17 and 23)
135&94 <<1 -8 -14 23 20 48 -3 59 ... || (another garibaldi)
130&94 <<6 -48 10 -50 26 6 -18 -22 ... || (a pogo extension)
58&94 <<6 46 10 44 26 6 -18 -22 ... || (a supers extension)
50&94 <<24 -4 40 -12 10 24 22 6 ... ||
72&94 <<12 -2 20 -6 52 12 -36 -44 ... || (a gizzard extension)
80&94 <<18 44 30 38 -16 18 40 28 ... ||
94 solo <<12 -2 20 -6 -42 12 -36 -44 ... || (a rank one temperament!)
Temperaments for which 94 is a MOS:
311&94 <<3 70 -42 69 -34 50 85 83...||
422&94 <<8 124 -18 90 -28 102 164 96 ... ||