392edo

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392edo

393edo →

Prime factorization	23 × 72
Step size	3.06122 ¢
Fifth	229\392 (701.02 ¢)
Semitones (A1:m2)	35:31 (107.1 ¢ : 94.9 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

392et is consistent to the 7-odd-limit with a flat tendency in the prime harmonics. The equal temperament tempers out the parakleisma in the 5-limit; 321489/320000 (varunisma), 420175/419904 (wizma), 703125/702464 (meter), and 823543/819200 (quince comma) in the 7-limit; and 441/440, 8019/8000, 9801/9800, and 41503/41472 in the 11-limit. It supports qak and octowerck.

Odd harmonics

Approximation of odd harmonics in 392edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.93	-0.60	-1.48	+1.19	-0.30	+1.31	+1.53	-0.87	-0.57	+0.65	-0.72
	Relative (%)	-30.5	-19.6	-48.3	+38.9	-9.7	+42.8	+49.9	-28.5	-18.8	+21.2	-23.6
Steps (reduced)		621 (229)	910 (126)	1100 (316)	1243 (67)	1356 (180)	1451 (275)	1532 (356)	1602 (34)	1665 (97)	1722 (154)	1773 (205)

Subsets and supersets

392 factors into 2³ × 7², with subset edos 2, 4, 7, 8, 14, 28, 49, 56, 98, and 196.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[-621 392⟩	[⟨392 621]]	+0.2948	0.2949	9.63
2.3.5	[8 14 -13⟩, [-49 28 2⟩	[⟨392 621 910]]	+0.2826	0.2414	7.89
2.3.5.7	321489/320000, 420175/419904, 703125/702464	[⟨392 621 910 1100]]	+0.3437	0.2343	7.65
2.3.5.7.11	441/440, 8019/8000, 41503/41472, 703125/702464	[⟨392 621 910 1100 1356]]	+0.2922	0.2335	7.63

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated Ratio*	Temperaments
1	37\392	113.27	16/15	Misneb (5-limit)
1	103\392	315.31	6/5	Parakleismic (5-limit)
1	149\392	456.12	125/96	Qak
8	185\392 (11\392)	566.33 (33.67)	104/75 (55/54)	Octowerck (392f)
28	163\392 (5\392)	498.98 (15.31)	4/3 (105/104)	Oquatonic (5-limit)

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