1547edo

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1547edo

1548edo →

Prime factorization	7 × 13 × 17
Step size	0.775695 ¢
Fifth	905\1547 (702.004 ¢)
Semitones (A1:m2)	147:116 (114 ¢ : 89.98 ¢)
Consistency limit	15
Distinct consistency limit	15

Theory

Approximation of prime harmonics in 1547edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.049	-0.018	+0.017	+0.201	+0.326	-0.237	+0.354	+0.039	-0.230	-0.110
	Relative (%)	+0.0	+6.3	-2.3	+2.2	+25.9	+42.0	-30.5	+45.6	+5.0	-29.7	-14.2
Steps (reduced)		1547 (0)	2452 (905)	3592 (498)	4343 (1249)	5352 (711)	5725 (1084)	6323 (135)	6572 (384)	6998 (810)	7515 (1327)	7664 (1476)

1547edo is excellent in the 7-limit. It tempers out 4375/4374 and it is a member of the optimal GPV sequence for the rank-3 temperament associated with this comma.

In the 5-limit, it supports gross, which is a very high-accuracy temperament. The 118-tone maximal evenness scale produced by gross is concoctic, since it uses 118\1547 as the generator. In addition, 1547edo tempers out the septendecima and thus supports the chlorine temperament in 5-limit and also in the 7-limit. 1547edo tempers out the 5-limit comma [236 -61 -60⟩, thus associating a stack of 60 15/8s with 8/5, and 61 of them make a 5/4.

In the 7-limit, it supports semidimi. Another edo which is quite strong in the 7-limit is like 1547edo is 441edo, and 1547edo thus supports the brahmagupta temperament produced by merging 441 & 1547.

In the 11-limit, it is a tuning for the rank-3 temperament heimdall.

In higher limits, it supports 91th-octave temperament protactinium.

1547's divisors are 1, 7, 13, 17, 91, 119, 221.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[2452 -1547⟩	[⟨1547 2542]]	-0.015	0.015	1.99
2.3.5	[-52 -17 34⟩, [40 -56 21⟩	[⟨1547 2542 3592]]	-0.008	0.017	2.14
2.3.5.7	4375/4374, [-1 4 11 -11⟩, [46 -14 -3  -6⟩	[⟨1547 2542 3592 4343]]	-0.007	0.014	1.86
2.3.5.7.11	4375/4374, 151263/151250, 820125/819896, 2097152/2096325	[⟨1547 2542 3592 4343 5352]]	-0.017	0.024	3.10
2.3.5.7.11.13	4375/4374, 4096/4095, 10648/10647, 91125/91091, 105644/105625	[⟨1547 2542 3592 4343 5352 5725]]	-0.029	0.034	4.42

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	118\1547	91.532	[9 -32 18⟩	Gross
1	579\1547	449.127	35/27	Semidimi
7	670\1547 (7\1547)	519.715 (5.429)	27/20 (325/324)	Brahmagupta
17	321\1547 (48\1547)	248.998 (37.233)	[-23 5 9 -2⟩ (100352/98415)	Chlorine
91	642\1547 (13\1547)	497.996 (10.084)	4/3 (176/175)	Protactinium