154edo

← 153edo

154edo

155edo →

Prime factorization	2 × 7 × 11
Step size	7.79221 ¢
Fifth	90\154 (701.299 ¢) (→ 45\77)
Semitones (A1:m2)	14:12 (109.1 ¢ : 93.51 ¢)
Consistency limit	3
Distinct consistency limit	3

154 equal divisions of the octave (abbreviated 154edo or 154ed2), also called 154-tone equal temperament (154tet) or 154 equal temperament (154et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 154 equal parts of about 7.79 ¢ each. Each step represents a frequency ratio of 2^1/154, or the 154th root of 2.

154edo is a contorted 77et in the 7-limit; in the 11-limit, it tempers out 126/125, 1029/1024 and 243/242, which define the 11-limit 31 & 123 temperament, for which 154 provides a good tuning, though 185edo gives the optimal patent val. In the 13-limit, it tempers out 196/195, 364/363 and 676/675.

Prime harmonics

Approximation of prime harmonics in 154edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	-0.66	+3.30	-2.59	+1.93	+1.03	-3.66	-1.41	+2.89	-1.01	+0.42
	Relative (%)	+0.0	-8.4	+42.3	-33.3	+24.8	+13.2	-46.9	-18.1	+37.1	-12.9	+5.4
Steps (reduced)		154 (0)	244 (90)	358 (50)	432 (124)	533 (71)	570 (108)	629 (13)	654 (38)	697 (81)	748 (132)	763 (147)

Subsets and supersets

154 = 2 × 7 × 11, 154edo has subset edos 2, 7, 11, 14, 22, and 77.