153edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 152edo153edo154edo →
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

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 21/153, or the 153rd root of 2.

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.