153edo

153 equal divisions of the octave (abbreviated 153edo or 153ed2), also called 153-tone equal temperament (153tet) or 153 equal temperament (153et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 153 equal parts of about 7.84 ¢ each. Each step represents a frequency ratio of 2^1/153, or the 153rd root of 2.

← 152edo

153edo

154edo →

Prime factorization	32 × 17
Step size	7.84314 ¢
Fifth	89\153 (698.039 ¢)
Semitones (A1:m2)	11:14 (86.27 ¢ : 109.8 ¢)
Dual sharp fifth	90\153 (705.882 ¢) (→ 10\17)
Dual flat fifth	89\153 (698.039 ¢)
Dual major 2nd	26\153 (203.922 ¢) (convergent)
Consistency limit	5
Distinct consistency limit	5

153edo corresponds to every second step of 306edo, with 3rd harmonic falling almost exactly halfway between adjacent steps, resulting in multiple options for fifths, just like any dual-fifth systems.

Using 153edo for 2.9.21.11/5 subgroup, it tempers out 9801/9800, 40353607/40310784, and 645922816/645700815 with patent 9 and 21.

Odd harmonics

Approximation of odd harmonics in 153edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-3.92	-2.00	+3.72	+0.01	-2.30	-1.31	+1.93	-2.99	+0.53	-0.19	-0.82
	Relative (%)	-49.9	-25.5	+47.5	+0.1	-29.3	-16.7	+24.6	-38.2	+6.7	-2.5	-10.5
Steps (reduced)		242 (89)	355 (49)	430 (124)	485 (26)	529 (70)	566 (107)	598 (139)	625 (13)	650 (38)	672 (60)	692 (80)

Subsets and supersets

Since 153 factors into 3² × 17, 153edo has subset edos 3, 9, 17, and 51.