6349edo

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6349edo

6350edo →

Prime factorization	7 × 907
Step size	0.189006 ¢
Fifth	3714\6349 (701.969 ¢)
Semitones (A1:m2)	602:477 (113.8 ¢ : 90.16 ¢)
Consistency limit	25
Distinct consistency limit	25

6349 equal divisions of the octave (abbreviated 6349edo or 6349ed2), also called 6349-tone equal temperament (6349tet) or 6349 equal temperament (6349et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 6349 equal parts of about 0.189 ¢ each. Each step represents a frequency ratio of 2^1/6349, or the 6349th root of 2.

6349edo is a strong 23-limit system, consistent to the 25-odd-limit, though 6079edo which among other things has a lower 23-limit relative error rather puts it in the shade. However, 6349edo can be used as a 41-limit system, consistent to the no-27 no-37, no-27 no-29, or no-17 no-29 41-odd-limit, as 27/17, 29/27, 37/29 and their octave complements exhaust the inconsistently mapped intervals in the full 41-odd-limit.

We may note it is a euzenius and akjaysmic system. Some simpler commas it tempers out in the higher limits include 123201/123200 in the 13-limit; 12376/12375, 28561/28560, 37180/37179 in the 17-limit; 23409/23408, 28900/28899, 43681/43680, and 89376/89375 in the 19-limit; 11271/11270, 21505/21054, 21736/21735, 23276/23275, and 25921/25920 in the 23-limit.

Prime harmonics

Approximation of prime harmonics in 6349edo

Harmonic		2	3	5	7	11	13	17	19	23
Error	Absolute (¢)	+0.0000	+0.0138	+0.0148	+0.0196	+0.0130	-0.0173	-0.0570	-0.0173	-0.0179
	Relative (%)	+0.0	+7.3	+7.9	+10.4	+6.9	-9.2	-30.2	-9.2	-9.5
Steps (reduced)		6349 (0)	10063 (3714)	14742 (2044)	17824 (5126)	21964 (2917)	23494 (4447)	25951 (555)	26970 (1574)	28720 (3324)

Approximation of prime harmonics in 6349edo (continued)

Harmonic		29	31	37	41	43	47	53	59	61
Error	Absolute (¢)	-0.0607	-0.0364	+0.0341	-0.0185	-0.0671	-0.0160	+0.0818	+0.0188	-0.0475
	Relative (%)	-32.1	-19.2	+18.1	-9.8	-35.5	-8.5	+43.3	+9.9	-25.1
Steps (reduced)		30843 (5447)	31454 (6058)	33075 (1330)	34015 (2270)	34451 (2706)	35266 (3521)	36367 (4622)	37349 (5604)	37654 (5909)

Subsets and supersets

Since 6349 factors into primes as 7 × 907, 6349edo contains 7edo and 907edo as subsets.