382edo

← 381edo

382edo

383edo →

Prime factorization	2 × 191
Step size	3.14136 ¢
Fifth	223\382 (700.524 ¢)
Semitones (A1:m2)	33:31 (103.7 ¢ : 97.38 ¢)
Dual sharp fifth	224\382 (703.665 ¢) (→ 112\191)
Dual flat fifth	223\382 (700.524 ¢)
Dual major 2nd	65\382 (204.188 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

382et is consistent to the 7-odd-limit and the harmonic 3 is about halfway between its steps. Using the patent val, it tempers out 65625/65536 in the 7-limit; 117440512/117406179, 25165824/25109315, 2097152/2096325, 4000/3993, 2734375/2725888, 2359296/2358125, 540/539, 1265625/1261568, 24057/24010 and 9801/9800 in the 11-limit. It supports bastille.

Odd harmonics

Approximation of odd harmonics in 382edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-1.43	+0.07	-1.29	+0.28	+1.56	+1.36	-1.36	-1.29	+0.92	+0.42	-0.00
	Relative (%)	-45.6	+2.3	-41.0	+8.9	+49.7	+43.2	-43.2	-41.1	+29.2	+13.5	-0.1
Steps (reduced)		605 (223)	887 (123)	1072 (308)	1211 (65)	1322 (176)	1414 (268)	1492 (346)	1561 (33)	1623 (95)	1678 (150)	1728 (200)

Subsets and supersets

382 factors into 2 × 191 with 2edo and 191edo as its subset edos. 764edo, which doubles it, gives a good correction to the harmonic 3.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.9	[1211 -382⟩	[⟨382 1211]]	-0.0439	0.0439	1.40
2.9.5	[38 -1 -15⟩, [25 -24 22⟩	[⟨382 1211 887]]	-0.0399	0.0363	1.16
2.9.5.7	4802000/4782969, 823543/819200, 102760448/102515625	[⟨382 1211 887 1072]]	+0.0846	0.2180	6.94