294edo

Revision as of 10:02, 25 January 2024 by BudjarnLambeth (talk | contribs) (Edo intro)
← 293edo 294edo 295edo →
Prime factorization 2 × 3 × 72
Step size 4.08163 ¢ 
Fifth 172\294 (702.041 ¢) (→ 86\147)
Semitones (A1:m2) 28:22 (114.3 ¢ : 89.8 ¢)
Consistency limit 5
Distinct consistency limit 5

Template:EDO intro

294edo has a very accurate fifth, only 0.086 cents sharp, but it has a 5/4 which is 1.441 cents sharp and a 7/4 which is 1.479 cents flat, so that 7/5 is 2.920 cents flat.

In the 5-limit it tempers out 393216/390625, the wuerschmidt comma, and |54 -37 2>, the monzisma. The patent val tempers out 10976/10935, the hemimage comma, and 50421/50000, the trimyna comma, and supplies the optimal patent val for trymyna temperament tempering out the trymyna, as well as its 11-limit extension, and also supplies the optimal patent val for the rank four temperament tempering out 3773/3750. The 294d val tempers out 16875/16807 and 19683/19600 instead, supporting mirkat temperament, whereas 294c tempers out 126/125 and 1029/1024, supporting valentine temperament.

294 = 2*3*49, and has divisors 2, 3, 6, 7, 14, 21, 42, 49, 98 and 147.


Approximation of prime harmonics in 294edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.09 +1.44 -1.48 -0.30 +0.29 +1.17 +0.45 +0.30 -1.01 +1.90
Relative (%) +0.0 +2.1 +35.3 -36.2 -7.3 +7.1 +28.6 +10.9 +7.3 -24.6 +46.6
Steps
(reduced)
294
(0)
466
(172)
683
(95)
825
(237)
1017
(135)
1088
(206)
1202
(26)
1249
(73)
1330
(154)
1428
(252)
1457
(281)