494edo

← 493edo

494edo

495edo →

Prime factorization	2 × 13 × 19
Step size	2.42915 ¢
Fifth	289\494 (702.024 ¢)
Semitones (A1:m2)	47:37 (114.2 ¢ : 89.88 ¢)
Consistency limit	17
Distinct consistency limit	17

The 494 equal divisions of the octave (494edo), or the 494(-tone) equal temperament (494tet, 494et) when viewed from a regular temperament perspective, divides the octave into 494 equal parts of about 2.43 cents each. It is a very strong 13- and 17-limit equal temperament. The step size is close to 729/728, the squbema, and a step is a squb.

Theory

494edo is a zeta peak and zeta peak integer edo and uniquely consistent through the 17-odd-limit. It tempers out the enneadeca, [-14 -19 19⟩, the tricot comma, [39 -29 3⟩, and the kwazy comma, [-53 10 16⟩ in the 5-limit. In the 7-limit, it tempers out 4375/4374 and 703125/702464; in the 11-limit 3025/3024 and 9801/9800; in the 13-limit 1716/1715, 2080/2079, 4096/4095, 4225/4224 and 6656/6655; and in the 17-limit, 1156/1155, 1275/1274, 2431/2430, and 2500/2499. Not until 1506 do we reach a division with a lower 13- or 17-limit relative error, and it is the first past 72 with a lower 17-limit relative error. 494 is divisible by 2, 13, 19, 26, 38 and 247.

Prime harmonics

Approximation of prime harmonics in 494edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.069	-0.079	+0.405	+0.099	-0.042	-0.502	-1.157	+0.875	+0.382	-0.906
	Relative (%)	+0.0	+2.9	-3.2	+16.7	+4.1	-1.7	-20.7	-47.6	+36.0	+15.7	-37.3
Steps (reduced)		494 (0)	783 (289)	1147 (159)	1387 (399)	1709 (227)	1828 (346)	2019 (43)	2098 (122)	2235 (259)	2400 (424)	2447 (471)

Intervals

Main article: Table of 494edo intervals

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[783 -494⟩	[⟨494 783]]	-0.0219	0.0219	0.90
2.3.5	[-14 -19 19⟩, [39 -23 3⟩	[⟨494 783 1147]]	-0.0032	0.0318	1.31
2.3.5.7	4375/4374, 703125/702464, [21 3 1 -10⟩	[⟨494 783 1147 1387]]	-0.0385	0.0670	2.76
2.3.5.7.11	3025/3024, 4375/4374, 131072/130977, 234375/234256	[⟨494 783 1147 1387 1709]]	-0.0365	0.0600	2.47
2.3.5.7.11.13	1716/1715, 2080/2079, 3025/3024, 4096/4095, 31250/31213	[⟨494 783 1147 1387 1709 1828]]	-0.0286	0.0576	2.37
2.3.5.7.11.13.17	1156/1155, 1275/1274, 1716/1715, 2080/2079, 2431/2430, 4096/4095	[⟨494 783 1147 1387 1709 1828 2019]]	-0.0069	0.0752	3.09

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per octave	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	27\494	65.59	27/26	Luminal
1	233\494	565.99	104/75	Tricot / trillium
2	67\494	162.75	1125/1024	Kwazy
2	86\494	208.91	44/39	Abigail
19	205\494 (3\494)	497.98 (7.29)	4/3 (225/224)	Enneadecal
38	205\494 (3\494)	497.98 (7.29)	4/3 (225/224)	Hemienneadecal