1547edo

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← 1546edo

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

1547edo is consistent to the 15-odd-limit and is excellent in the 7-limit. It tempers out 4375/4374 and it is a member of the optimal ET 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 sixty 15/8's with 4/3, and sixty-one of them make 5/4.

In the 7-limit, it provides the optimal patent val for 7-limit brahmagupta, the 441 & 1106 temperament, and supports an alternative 11-limit extension to it. It also supports semidimi, the 171 & 1376 temperament.

In the 11-limit, 1547edo provides the optimal patent val for the aluminium temperament, which maps 135/128 to 1/13th of the occtave. It also tempers out 117649/117612, and is a tuning for the rank-3 temperament heimdall. In higher limits, it supports 91th-octave temperament protactinium.

Prime harmonics

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)

Divisors

1547 has subset edos 7, 13, 17, 91, 119, and 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, 117649/117612, 234375/234256, 2097152/2096325	[⟨1547 2542 3592 4343 5352]]	-0.017	0.024	3.10
2.3.5.7.11.13	4096/4095, 4375/4374, 6656/6655, 78125/78078, 85750/85683	[⟨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 (7-limit)
7	11\1547	8.533	1029/1024	Nitrogen
13	642\1547 (47\1547)	497.996 (36.458)	4/3 (?)	Aluminium
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

Music

Eliora

• Prelude and Fugue in Two Elements (Op. 2, No. 6)