152edo

← 151edo

152edo

153edo →

Prime factorization	23 × 19
Step size	7.89474 ¢
Fifth	89\152 (702.632 ¢)
Semitones (A1:m2)	15:11 (118.4 ¢ : 86.84 ¢)
Consistency limit	11
Distinct consistency limit	11

Theory

152et is a strong 11-limit system, with the 3, 5, 7, and 11 slightly sharp. It tempers out 1600000/1594323 (amity comma) and [32 -7 -9⟩ (escapade comma) in the 5-limit; 4375/4374, 5120/5103, 6144/6125 and 16875/16807 in the 7-limit; 540/539, 1375/1372, 3025/3024, 4000/3993, 5632/5625 and 9801/9800 in the 11-limit.

It has two reasonable mappings for 13, with the 152f val scoring much better. The patent val tempers out 169/168, 325/324, 351/350, 364/363, 1001/1000, 1573/1568, and 4096/4095. The 152f val tempers out 352/351, 625/624, 640/637, 729/728, 847/845, 1188/1183, 1575/1573, 1716/1715 and 2080/2079.

It provides the optimal patent val for the 11-limit grendel and kwai linear temperaments, the 13-limit rank-2 temperament octopus, the 11-limit planar temperament laka, and the rank-5 temperament tempering out 169/168.

Paul Erlich has suggested that 152edo could be considered a sort of universal tuning.

Prime harmonics

Approximation of prime harmonics in 152edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.68	+0.53	+2.23	+1.31	-3.69	-2.32	+2.49	+3.30	-3.26	-0.30
	Relative (%)	+0.0	+8.6	+6.7	+28.2	+16.6	-46.7	-29.4	+31.5	+41.9	-41.3	-3.8
Steps (reduced)		152 (0)	241 (89)	353 (49)	427 (123)	526 (70)	562 (106)	621 (13)	646 (38)	688 (80)	738 (130)	753 (145)

Subsets and supersets

Since 152 factors into 2³ × 19, 152edo has subset edos 2, 4, 8, 19, 38, 76.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[241 -152⟩	[⟨152 241]]	-0.213	0.213	2.70
2.3.5	1600000/1594323, [32 -7 -9⟩	[⟨152 241 353]]	-0.218	0.174	2.21
2.3.5.7	4375/4374, 5120/5103, 16875/16807	[⟨152 241 353 427]]	-0.362	0.291	3.69
2.3.5.7.11	540/539, 1375/1372, 4000/3993, 5120/5103	[⟨152 241 353 427 526]]	-0.365	0.260	3.30
2.3.5.7.11.13	352/351, 540/539, 625/624, 729/728, 1575/1573	[⟨152 241 353 427 526 563]] (152f)	-0.494	0.373	4.73

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	7\152	55.26	33/32	Escapade / alphaquarter
1	31\152	244.74	15/13	Subsemifourth
1	39\152	307.89	3200/2673	Familia
1	43\152	339.47	243/200	Amity
1	49\152	386.84	5/4	Grendel
1	63\152	497.37	4/3	Kwai
1	71\152	560.53	242/175	Whoosh / whoops
2	7\152	55.26	33/32	Biscapade
2	9\152	71.05	25/24	Vishnu / acyuta (152f) / ananta (152)
2	43\152 (33\152)	339.47 (260.53)	243/200 (64/55)	Hemiamity
2	55\152 (21\152)	434.21 (165.79)	9/7 (11/10)	Supers
4	63\152 (13\152)	497.37 (102.63)	4/3 (35/33)	Undim / unlit
8	63\152 (6\152)	497.37 (47.37)	4/3 (36/35)	Twilight
8	74\152 (2\152)	584.21 (15.79)	7/5 (126/125)	Octoid (152f) / octopus (152)
19	63\152 (1\152)	497.37 (7.89)	4/3 (225/224)	Enneadecal
38	63\152 (1\152)	497.37 (7.89)	4/3 (225/224)	Hemienneadecal

Music

birdshite stalactite

• "athlete's feet" from razorblade tiddlywinks (2023) – Spotify | Bandcamp | YouTube