editing disabled

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.

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