94edo

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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.

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

Quanic

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 ... ||

Scales

garibaldi12

garibaldi17