142edo

← 141edo

142edo

143edo →

Prime factorization	2 × 71
Step size	8.4507 ¢
Fifth	83\142 (701.408 ¢)
Semitones (A1:m2)	13:11 (109.9 ¢ : 92.96 ¢)
Consistency limit	9
Distinct consistency limit	9

142 equal divisions of the octave (abbreviated 142edo or 142ed2), also called 142-tone equal temperament (142tet) or 142 equal temperament (142et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 142 equal parts of about 8.45 ¢ each. Each step represents a frequency ratio of 2^1/142, or the 142nd root of 2.

The equal temperament tempers out 32805/32768 (schisma) in the 5-limit; 1728/1715, 3136/3125, and 16875/16807 in the 7-limit; 176/175, 540/539 and 1375/1372 in the 11-limit. It is an excellent tuning for orwellismic, the rank-3 temperament tempering out 1728/1715, and a good one for guanyin, the 11-limit extension also tempering out 176/175. It is also excellent for semisept, the 31 & 111 temperament tempering out 1728/1715 and 3136/3125 and the 53 & 89 temperament tempering out both 1728/1715 and 32805/32768.

Prime harmonics

Approximation of prime harmonics in 142edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	-0.55	+2.42	+3.01	-2.02	-3.91	-3.55	-1.74	-2.92	+1.41	-4.19
	Relative (%)	+0.0	-6.5	+28.6	+35.6	-23.9	-46.2	-42.0	-20.6	-34.6	+16.7	-49.6
Steps (reduced)		142 (0)	225 (83)	330 (46)	399 (115)	491 (65)	525 (99)	580 (12)	603 (35)	642 (74)	690 (122)	703 (135)

Subsets and supersets

142edo has subset edos 2edo and 71edo.