238edo

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238edo

239edo →

Prime factorization	2 × 7 × 17
Step size	5.04202 ¢
Fifth	139\238 (700.84 ¢)
Semitones (A1:m2)	21:19 (105.9 ¢ : 95.8 ¢)
Consistency limit	3
Distinct consistency limit	3

238 equal divisions of the octave (abbreviated 238edo or 238ed2), also called 238-tone equal temperament (238tet) or 238 equal temperament (238et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 238 equal parts of about 5.04 ¢ each. Each step represents a frequency ratio of 2^1/238, or the 238th root of 2.

It is part of the optimal ET sequence for the apotropaia, enodia, fantastic, gizzard, gracecordial, hecate, marvel, marvell, vines, and wizard temperaments.

Theory

Prime harmonics

Approximation of prime harmonics in 238edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	-1.11	+1.92	-0.76	-1.74	+1.49	+0.93	-0.03	+1.98	-1.01	-0.50
	Relative (%)	+0.0	-22.1	+38.1	-15.0	-34.5	+29.5	+18.4	-0.7	+39.2	-19.9	-9.9
Steps (reduced)		238 (0)	377 (139)	553 (77)	668 (192)	823 (109)	881 (167)	973 (21)	1011 (59)	1077 (125)	1156 (204)	1179 (227)

Intervals

See Table of 238edo intervals.

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