# 148418edo

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 ← 148417edo 148418edo 148419edo →
Prime factorization 2 × 74209
Step size 0.00808527¢
Fifth 86819\148418 (701.955¢)
Semitones (A1:m2) 14061:11159 (113.7¢ : 90.22¢)
Consistency limit 39
Distinct consistency limit 39
Special properties

148418 equal divisions of the octave (abbreviated 148418edo or 148418ed2), also called 148418-tone equal temperament (148418tet) or 148418 equal temperament (148418et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 148418 equal parts of about 0.00809 ¢ each. Each step represents a frequency ratio of 21/148418, or the 148418th root of 2.

148418edo is a zeta peak edo, distinctly consistent through the 39-odd-limit. It marks the first equal temperament with lower relative errors after 16808 in the 23-, 29-, and 31-limit, the first after 83096 in the 37-limit, and the first after 95524 in the 41-limit. Some of the simpler commas it tempers out include 408761/408760, 453376/453375, 509796/509795, 601426/601425, 633556/633555, 709632/709631, 949026/949025, 1154440/1154439, 1163800/1163799, 1255501/1255500, 2023425/2023424, 2307361/2307360, 2697696/2697695, 3897166/3897165, 4096576/4096575, and 5909761/5909760.

### Prime harmonics

Approximation of prime harmonics in 148418edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00000 +0.00029 +0.00061 -0.00002 +0.00063 +0.00112 -0.00048 +0.00076 -0.00015 +0.00143 +0.00074
Relative (%) +0.0 +3.6 +7.6 -0.3 +7.8 +13.8 -6.0 +9.4 -1.8 +17.7 +9.2
Steps
(reduced)
148418
(0)
235237
(86819)
344616
(47780)
416662
(119826)
513442
(68188)
549212
(103958)
606653
(12981)
630469
(36797)
671378
(77706)
721012
(127340)
735292
(141620)

### Subsets and supersets

Since 148418 factors into 2 × 74209, 148418edo has subset edos 2 and 74209.