1429edo

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1429edo

1430edo →

Prime factorization	1429 (prime)
Step size	0.839748 ¢
Fifth	836\1429 (702.029 ¢)
Semitones (A1:m2)	136:107 (114.2 ¢ : 89.85 ¢)
Consistency limit	9
Distinct consistency limit	9

Theory

1429et tempers out 4375/4374 in the 7-limit; 2657205/2656192, 759375/758912, 1953125/1951488, 2359296/2358125, 131072/130977, 369140625/369098752, 184549376/184528125, 645922816/645700815 and 3294225/3294172 in the 11-limit. It supports the gross temperament and the trillium temperament. 1429edo is the 226th prime edo.

Approximation of prime harmonics in 1429edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.074	-0.030	+0.243	+0.397	+0.060	+0.013	-0.242	-0.143	-0.046	+0.381
	Relative (%)	+0.0	+8.9	-3.5	+29.0	+47.2	+7.2	+1.6	-28.8	-17.0	-5.5	+45.3
Steps (reduced)		1429 (0)	2265 (836)	3318 (460)	4012 (1154)	4944 (657)	5288 (1001)	5841 (125)	6070 (354)	6464 (748)	6942 (1226)	7080 (1364)

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[2265 -1429⟩	⟨1429 2265]	-0.0235	0.0234	2.80
2.3.5	[39 -29 3⟩, [-66 -36 53⟩	⟨1429 2265 3318]	-0.0114	0.0257	3.06
2.3.5.7	4375/4374, [41 -15 -5 -2⟩, [-16 12 12 -11⟩	⟨1429 2265 3318 4012]	-0.0302	0.0395	4.70
2.3.5.7.11	4375/4374, 131072/130977, 759375/758912, 3294225/3294172	⟨1429 2265 3318 4012 4944]	-0.0471	0.0488	5.81
2.3.5.7.11.13	2080/2079, 4225/4224, 59319/59290, 67392/67375, 91125/91091, 27227340/27217619	⟨1429 2265 3318 4012 4944 5288]	-0.0420	0.0460	5.48
2.3.5.7.11.13.17	2080/2079, 2500/2499, 4225/4224, 12376/12375, 14875/14872, 108086/108045, 149175/149072, 1783600/1783419	⟨1429 2265 3318 4012 4944 5288 5841]	-0.0364	0.0447	5.32

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	109\1429	91.5325	[144 -22 -47⟩	Gross

Scales

• Gross13

Music

• Gross Pattern by Francium