# 147edo

 ← 146edo 147edo 148edo →
Prime factorization 3 × 72
Step size 8.16327¢
Fifth 86\147 (702.041¢)
(semiconvergent)
Semitones (A1:m2) 14:11 (114.3¢ : 89.8¢)
Consistency limit 5
Distinct consistency limit 5

147 equal divisions of the octave (abbreviated 147edo or 147ed2), also called 147-tone equal temperament (147tet) or 147 equal temperament (147et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 147 equal parts of about 8.16 ¢ each. Each step represents a frequency ratio of 21/147, or the 147th root of 2.

## Theory

147edo has a very accurate fifth. Using the patent val, the equal temperament tempers out 32805/32768 in the 5-limit; 225/224 and 3125/3087 in the 7-limit; 243/242 in the 11-limit; 364/363 in the 13-limit; 442/441 and 595/594 in the 17-limit. It is the optimal patent val for 11-limit karadeniz, the 41 & 106 temperament.

### Prime harmonics

Approximation of prime harmonics in 147edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.09 -2.64 +2.60 +3.78 +0.29 +1.17 -3.64 +0.30 -1.01 -2.18
Relative (%) +0.0 +1.1 -32.3 +31.9 +46.4 +3.5 +14.3 -44.5 +3.6 -12.3 -26.7
Steps
(reduced)
147
(0)
233
(86)
341
(47)
413
(119)
509
(68)
544
(103)
601
(13)
624
(36)
665
(77)
714
(126)
728
(140)

### Subsets and supersets

Since 147 = 3 × 72, 147edo has subset edos 3, 7, 21 and 49.