472edo

← 471edo

472edo

473edo →

Prime factorization	23 × 59
Step size	2.54237 ¢
Fifth	276\472 (701.695 ¢) (→ 69\118)
Semitones (A1:m2)	44:36 (111.9 ¢ : 91.53 ¢)
Consistency limit	11
Distinct consistency limit	11

Theory

472edo is enfactored in the 5-limit, with the same tuning as 118edo, defined by tempering out the schisma and the parakleisma, but the approximation to higher harmonics are much improved. It is a zeta peak integer edo, consistent to the 11-odd-limit or the no-13 29-odd-limit.

In the 7-limit, the equal temperament tempers out 2401/2400, 2460375/2458624, and 30623756184/30517578125; in the 11-limit, 9801/9800, 46656/46585, 117649/117612, and 234375/234256, supporting the maviloid temperament, the bisesqui temperament, and the octant temperament. Using the patent val, it tempers out 729/728, 1575/1573, 2200/2197, 4096/4095, and 21168/21125 in the 13-limit, so it also supports the 13-limit octant.

Prime harmonics

Approximation of prime harmonics in 472edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	-0.26	+0.13	-0.18	+0.38	+1.00	-0.72	-0.06	-0.31	+0.08	-0.97
	Relative (%)	+0.0	-10.2	+5.0	-7.2	+14.8	+39.2	-28.2	-2.2	-12.1	+3.3	-38.1
Steps (reduced)		472 (0)	748 (276)	1096 (152)	1325 (381)	1633 (217)	1747 (331)	1929 (41)	2005 (117)	2135 (247)	2293 (405)	2338 (450)

Subsets and supersets

Since 472 factors into 2³ × 59, 472edo has subset edos 2, 4, 8, 59, 118, and 236.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3.5.7	2401/2400, 32805/32768, [8 14 -13⟩	[⟨472 748 1096 1325]]	+0.0435	0.0814	3.20
2.3.5.7.11	2401/2400, 9801/9800, 32805/32768, 46656/46585	[⟨472 748 1096 1325 1633]]	+0.0130	0.0950	3.74
2.3.5.7.11.13	729/728, 1575/1573, 2200/2197, 2401/2400, 4096/4095	[⟨472 748 1096 1325 1633 1747]]	−0.0341	0.1365	5.37

Rank-2 temperaments

Note: 5-limit temperaments supported by 118et are not included.

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated ratio*	Temperaments
1	69\472	175.42	448/405	Sesquiquartififths
1	137\472	348.31	57344/46875	Subneutral
1	205\472	521.19	875/648	Maviloid
2	69\472	175.42	448/405	Bisesqui
8	196\472 (19\472)	498.31 (48.31)	4/3 (36/35)	Octant

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct