148418edo

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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

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 2^1/148418, or the 148418th root of 2.

148418edo is a very strong higher-limit tuning, distinctly consistent through the 39-odd-limit, and is a zeta peak edo. 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
Error	Absolute (¢)	+0.00000	+0.00029	+0.00061	-0.00002	+0.00063	+0.00112	-0.00048	+0.00076	-0.00015
	Relative (%)	+0.0	+3.6	+7.6	-0.3	+7.8	+13.8	-6.0	+9.4	-1.8
Steps (reduced)		148418 (0)	235237 (86819)	344616 (47780)	416662 (119826)	513442 (68188)	549212 (103958)	606653 (12981)	630469 (36797)	671378 (77706)

Approximation of prime harmonics in 148418edo (continued)

Harmonic		29	31	37	41	43	47	53	59	61
Error	Absolute (¢)	+0.00143	+0.00074	+0.00283	-0.00124	-0.00293	+0.00026	-0.00403	-0.00094	-0.00141
	Relative (%)	+17.7	+9.2	+35.0	-15.3	-36.2	+3.2	-49.8	-11.6	-17.4
Steps (reduced)		721012 (127340)	735292 (141620)	773177 (31087)	795157 (53067)	805355 (63265)	824401 (82311)	850126 (108036)	873090 (131000)	880228 (138138)

Subsets and supersets

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