429edo

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429edo

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Prime factorization	3 × 11 × 13
Step size	2.7972 ¢
Fifth	251\429 (702.098 ¢)
Semitones (A1:m2)	41:32 (114.7 ¢ : 89.51 ¢)
Consistency limit	11
Distinct consistency limit	11

Theory

429et is consistent to the 11-odd-limit. It tempers out 48828125/48771072, 65625/65536, 250047/250000, 359661568/358722675 and 5250987/5242880 in the 7-limit; 117440512/117406179, 806736/805255, 234375/234256, 26214400/26198073, 12005/11979, 1953125/1951488, 496125/495616, 1953125/1948617, 200704/200475, 42875/42768, 4302592/4296875, 352947/352000, 1879453125/1879048192, 184549376/184528125, 19712/19683, 1684375/1679616, 422576/421875, 184877/184320, 47265625/47258883, 3025/3024, 9453125/9437184, 160083/160000, 16808715/16777216, 532400/531441, 456533/455625, 102487/102400, 1771561/1769472 and 781258401/781250000 in the 11-limit. It supports vavoom, turkey, counterhanson and aluminium.

Prime harmonics

Approximation of prime harmonics in 429edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.14	-0.30	-0.99	-0.27	-1.37	+1.34	-1.01	+1.10	-0.21	-0.98
	Relative (%)	+0.0	+5.1	-10.7	-35.5	-9.6	-48.9	+47.8	-36.1	+39.2	-7.4	-35.0
Steps (reduced)		429 (0)	680 (251)	996 (138)	1204 (346)	1484 (197)	1587 (300)	1754 (38)	1822 (106)	1941 (225)	2084 (368)	2125 (409)

Subsets and supersets

429 factors into 3 × 11 × 13, with subset edos 3, 11, 13, 33, 39, and 143.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[680 -429⟩	[⟨429 680]]	-0.0451	0.0451	1.61
2.3.5	[24 -21 4⟩, [-20 -24 25⟩	[⟨429 680 996]]	+0.0130	0.0900	3.22
2.3.5.7	250047/250000, 823543/820125, 65625/65536	[⟨429 680 996 1204]]	+0.0982	0.1670	5.97
2.3.5.7.11	3025/3024, 42875/42768, 160083/160000, 456533/455625	[⟨429 680 996 1204 1484]]	+0.0941	0.1496	5.35
2.3.5.7.11.13	1001/1000, 676/675, 3025/3024, 47432/47385, 12005/11979	[⟨429 680 996 1204 1484 1587]]	+0.1400	0.1708	6.11

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated Ratio*	Temperaments
1	40\429	111.89	16/15	Vavoom
1	113\429	316.08	6/5	Counterhanson
1	170\429	475.52	320/243	Vulture
3	138\429 (5\429)	386.01 (13.99)	5/4 (393216/390625)	Mutt

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