239edo

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239edo

240edo →

Prime factorization	239 (prime)
Step size	5.02092 ¢
Fifth	140\239 (702.929 ¢)
Semitones (A1:m2)	24:17 (120.5 ¢ : 85.36 ¢)
Consistency limit	11
Distinct consistency limit	11

Theory

239et tempers out 2401/2400, 5120/5103, and 29360128/29296875 in the 7-limit, supporting the hemififths temperament, providing an excellent tuning. It also supports and provides a good tuning for quasiorwell and alphaquarter. In the 11-limit, it tempers out 3025/3024, 4000/3993, 5632/5625, and 12005/11979.

239edo is the 52nd prime edo.

Prime harmonics

Approximation of prime harmonics in 239edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.97	+0.30	+0.21	+0.98	-2.03	+0.48	-1.28	-0.66	-0.29	-0.27
	Relative (%)	+0.0	+19.4	+5.9	+4.2	+19.6	-40.5	+9.6	-25.5	-13.1	-5.7	-5.3
Steps (reduced)		239 (0)	379 (140)	555 (77)	671 (193)	827 (110)	884 (167)	977 (21)	1015 (59)	1081 (125)	1161 (205)	1184 (228)

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[379 -239⟩	[⟨239 379]]	-0.307	0.307	6.12
2.3.5	[3 -18 11⟩, [32 -7 -9⟩	[⟨239 379 555]]	-0.247	0.265	5.27
2.3.5.7	2401/2400, 5120/5103, 29360128/29296875	[⟨239 379 555 671]]	-0.204	0.241	4.80
2.3.5.7.11	2401/2400, 3025/3024, 4000/3993, 5120/5103	[⟨239 379 555 671 827]]	-0.220	0.218	4.34

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per octave	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	3\239	15.06	121/120	Yarman I (239)
1	11\239	35.15	1990656/1953125	Gammic (5-limit)
1	7\239	55.23	33/32	Escapade / alphaquarter
1	35\239	175.73	72/65	Quadrafifths (239f)
1	54\239	271.13	90/77	Quasiorwell (239)
1	70\239	351.46	49/40	Hemififths (7-limit)
1	79\239	396.65	44/35	Squarschmidt
1	83\239	416.74	14/11	Unthirds (239f)
1	116\239	582.43	7/5	Neptune (7-limit)