499edo

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499edo

500edo →

Prime factorization	499 (prime)
Step size	2.40481¢
Fifth	292\499 (702.204¢)
Semitones (A1:m2)	48:37 (115.4¢ : 88.98¢)
Consistency limit	9
Distinct consistency limit	9

499 equal divisions of the octave (abbreviated 499edo or 499ed2), also called 499-tone equal temperament (499tet) or 499 equal temperament (499et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 499 equal parts of about 2.4 ¢ each. Each step represents a frequency ratio of 2^1/499, or the 499th root of 2.

Theory

499et tempers out 33554432/33480783, 359661568/358722675 and 2401/2400 in the 7-limit; 100663296/100656875, 2097152/2096325, 536870912/535869675, 151263/151250, 104857600/104825259, 131072/130977, 200704/200475, 17537553/17500000, 19712/19683, 1479016/1476225, 3025/3024, 41503/41472, 532400/531441 and 67110351/67108864 in the 11-limit.

Prime harmonics

Approximation of prime harmonics in 499edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.25	+0.86	+0.31	-0.62	+1.16	+0.86	+0.68	-0.62	-0.32	-0.35
	Relative (%)	+0.0	+10.4	+35.8	+13.0	-25.6	+48.1	+35.6	+28.4	-25.7	-13.3	-14.4
Steps (reduced)		499 (0)	791 (292)	1159 (161)	1401 (403)	1726 (229)	1847 (350)	2040 (44)	2120 (124)	2257 (261)	2424 (428)	2472 (476)

Subsets and supersets

499edo is the 95th prime edo.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[791 -499⟩	⟨499 791]	-0.0787	0.0787	3.27
2.3.5	[32 -7 -9⟩, [1 36 -25⟩	⟨499 791 1159]	-0.1760	0.1519	6.32
2.3.5.7	2401/2400, 1959552/1953125, 26873856/26796875	⟨499 791 1159 1401]	-0.1598	0.1345	5.59

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated Ratio*	Temperaments
1	23\499	55.311	16875/16384	Escapade
1	126\499	303.006	25/21	Quinmite
1	146\499	351.102	49/40	Newt
1	178\499	428.056	2800/2187	Osiris

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

Music

Francium

• "still not desperate enough" from hope in dark times (2024) – Spotify | Bandcamp | YouTube