476edo

← 475edo

476edo

477edo →

Prime factorization	22 × 7 × 17
Step size	2.52101 ¢
Fifth	278\476 (700.84 ¢) (→ 139\238)
Semitones (A1:m2)	42:38 (105.9 ¢ : 95.8 ¢)
Dual sharp fifth	279\476 (703.361 ¢)
Dual flat fifth	278\476 (700.84 ¢) (→ 139\238)
Dual major 2nd	81\476 (204.202 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

476edo is consistent to the 7-odd-limit and the harmonic 3 is about halfway its steps. Using the patent val, it tempers out 2401/2400 in the 7-limit; 4000/3993, 12005/11979, 117649/117612, 1296000/1294139, 540/539, 441/440, 352947/352000, 24057/24010, 8019/8000, 9801/9800 and 160083/160000 in the 11-limit.

Odd harmonics

Approximation of odd harmonics in 476edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-1.11	-0.60	-0.76	+0.29	+0.78	-1.03	+0.81	+0.93	-0.03	+0.65	-0.54
	Relative (%)	-44.2	-23.8	-30.1	+11.6	+31.1	-40.9	+32.0	+36.8	-1.3	+25.7	-21.5
Steps (reduced)		754 (278)	1105 (153)	1336 (384)	1509 (81)	1647 (219)	1761 (333)	1860 (432)	1946 (42)	2022 (118)	2091 (187)	2153 (249)

Subsets and supersets

476 factors into 2² × 7 × 17, with subset edos 2, 4, 7, 14, 17, 28, 34, 68, 119, and 238. 952edo, which doubles it, gives a good correction to the harmonic 3, but unfortunately it is unconsistent in the 5-odd-limit.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.9	[1509 -476⟩	[⟨476 1509]]	-0.0460	0.0460	1.82
2.9.5	[33 -17 9⟩, [-65 0 28⟩	[⟨476 1509 1105]]	+0.0554	0.1482	5.88
2.9.5.7	703125/702464, 4802000/4782969, 4202539929/4194304000	[⟨476 1509 1105 1336]]	+0.1091	0.1586	6.29

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)*	Cents (reduced)*	Associated Ratio*	Temperaments
1	205\476	516.81	27/20	Gravity
2	205\476 (33\476)	516.81 (83.19)	27/20 (21/20)	Harry
28	197\476 (6\476)	496.64 (15.13)	4/3 (105/104)	Oquatonic

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