126edo

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← 125edo 126edo 127edo →
Prime factorization 2 × 32 × 7
Step size 9.52381¢ 
Fifth 74\126 (704.762¢) (→37\63)
Semitones (A1:m2) 14:8 (133.3¢ : 76.19¢)
Consistency limit 7
Distinct consistency limit 7

126 equal divisions of the octave (abbreviated 126edo or 126ed2), also called 126-tone equal temperament (126tet) or 126 equal temperament (126et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 126 equal parts of about 9.52 ¢ each. Each step represents a frequency ratio of 21/126, or the 126th root of 2.

126edo has a distinctly sharp tendency, with the 3, 5, 7 and 11 all sharp. The equal temperament tempers out 2048/2025 in the 5-limit, 2401/2400 and 4375/4374 in the 7-limit, and 176/175, 896/891, and 1331/1323 in the 11-limit. It provides the optimal patent val for 7- and 11-limit srutal temperament. It also creates an excellent Porcupine[8] scale, mapping the large quills to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the thirds and fourths equally consonant within a few fractions of a cent.

Odd harmonics

Approximation of odd harmonics in 126edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +2.81 +4.16 +2.60 -3.91 +1.06 -2.43 -2.55 -0.19 -2.27 -4.11 +0.30
Relative (%) +29.5 +43.7 +27.3 -41.1 +11.2 -25.5 -26.8 -2.0 -23.9 -43.2 +3.1
Steps
(reduced)
200
(74)
293
(41)
354
(102)
399
(21)
436
(58)
466
(88)
492
(114)
515
(11)
535
(31)
553
(49)
570
(66)

Subsets and supersets

Since 126 factors into 2 × 32 × 7, 126edo has subset edos 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63.