299edo

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299edo

300edo →

Prime factorization	13 × 23
Step size	4.01338 ¢
Fifth	175\299 (702.341 ¢)
Semitones (A1:m2)	29:22 (116.4 ¢ : 88.29 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

In the 5-limit, 299et tempers out the kleisma, 15625/15552, in the 7-limit 10976/10935, in the 11-limit 385/384; and in the 13-limit 325/324, 625/624 and 676/675. It provides the optimal patent val for the 13-limit rank-3 enlil temperament, and the rank-4 temperament tempering out 325/324 and 385/384.

Prime harmonics

Approximation of prime harmonics in 299edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.39	-1.03	-1.60	-1.49	-1.73	-0.61	-0.52	+1.83	+1.86	-1.22
	Relative (%)	+0.0	+9.6	-25.7	-39.9	-37.0	-43.1	-15.1	-13.0	+45.5	+46.4	-30.5
Steps (reduced)		299 (0)	474 (175)	694 (96)	839 (241)	1034 (137)	1106 (209)	1222 (26)	1270 (74)	1353 (157)	1453 (257)	1481 (285)

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[474 -299⟩	[⟨299 474]]	-0.1218	0.1218	3.04
2.3.5	15625/15552, [80 -49 -1⟩	[⟨299 474 694]]	+0.0665	0.2844	7.09
2.3.5.7	10976/10935, 15625/15552, 823543/819200	[⟨299 474 694 839]]	+0.1925	0.3291	8.20
2.3.5.7.11	385/384, 6250/6237, 10976/10935, 12005/11979	[⟨299 474 694 839 1034]]	+0.2399	0.3092	7.70
2.3.5.7.11.13	325/324, 385/384, 625/624, 10648/10647, 10976/10935	[⟨299 474 694 839 1034 1106]]	+0.2779	0.2948	7.34
2.3.5.7.11.13.17	325/324, 385/384, 595/594, 625/624, 2058/2057, 8624/8619	[⟨299 474 694 839 1034 1106 1222]]	+0.2595	0.2767	6.89
2.3.5.7.11.13.17.19	325/324, 343/342, 385/384, 595/594, 625/624, 1216/1215, 1445/1444	[⟨299 474 694 839 1034 1106 1222 1270]]	+0.2424	0.2627	6.54

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per octave	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	79\299	317.06	6/5	Hanson
1	124\299	505.69	75/56	Marfifths