127edo

Revision as of 09:53, 25 January 2024 by BudjarnLambeth (talk | contribs) (EDO intro)

Template:EDO intro

← 126edo 127edo 128edo →
Prime factorization 127 (prime)
Step size 9.44882 ¢ 
Fifth 74\127 (699.213 ¢)
Semitones (A1:m2) 10:11 (94.49 ¢ : 103.9 ¢)
Consistency limit 5
Distinct consistency limit 5

127edo is interesting because of its approximations, defined by the commas it tempers out:

  • In the 5-limit, it tempers out the würschmidt comma, 393216/390625 and hence supports würschmidt temperament.
  • In the 7-limit, it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also.
  • In the 11-limit, it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the optimal patent val and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.

127edo is the 31st prime edo.

Harmonics

Approximation of odd harmonics in 127edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -2.74 +1.09 +4.40 +3.96 -3.29 +0.42 -1.65 -1.02 -4.60 +1.66 -4.65
Relative (%) -29.0 +11.5 +46.6 +42.0 -34.8 +4.4 -17.5 -10.8 -48.7 +17.6 -49.2
Steps
(reduced)
201
(74)
295
(41)
357
(103)
403
(22)
439
(58)
470
(89)
496
(115)
519
(11)
539
(31)
558
(50)
574
(66)

MOS Scales

MOS Scales of 127edo