1051edo

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1051edo

1052edo →

Prime factorization	1051 (prime)
Step size	1.14177 ¢
Fifth	615\1051 (702.188 ¢)
Semitones (A1:m2)	101:78 (115.3 ¢ : 89.06 ¢)
Consistency limit	3
Distinct consistency limit	3

Theory

1051et tempers out 2460375/2458624 in the 7-limit; 820125/819896, 2097152/2096325, 514714375/514434888, 180224/180075, 184549376/184528125, 43923/43904 and 20614528/20588575 in the 11-limit. From a regular temperament perspective, 1051edo only has a consistency limit of 3 and does poorly with approximating the harmonics 5 and 7. However, 1051edo has a good representation of the 2.3.11.13.15.17.19.35 subgroup.

Odd harmonics

Approximation of odd harmonics in 1051edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.233	-0.396	+0.537	+0.467	+0.157	-0.185	-0.162	+0.087	+0.489	-0.372	-0.301
	Relative (%)	+20.4	-34.6	+47.0	+40.9	+13.7	-16.2	-14.2	+7.7	+42.8	-32.6	-26.4
Steps (reduced)		1666 (615)	2440 (338)	2951 (849)	3332 (179)	3636 (483)	3889 (736)	4106 (953)	4296 (92)	4465 (261)	4616 (412)	4754 (550)

Subsets and supersets

1051edo is the 177th prime edo. 2102edo, which doubles it, gives a good correction to the harmonic 5. 4212edo, which quadruples it, gives a good correction to the harmonic 7.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[1666 -1051⟩	⟨1051 1666]	-0.0736	0.0736	6.45
2.3.15	[-68 1 17⟩, [42 -61 14⟩	⟨1051 1666 4106]	-0.0353	0.0810	7.09
2.3.15.35	2460375/2458624, 4096000/4084101, 299072265625/297538935552	⟨1051 1666 4106 5391]	-0.0333	0.0702	6.15
2.3.15.35.11	6250/6237, 180224/180075, 2460375/2458624, 43923/43904	⟨1051 1666 4106 5391 3636]	-0.0357	0.0630	5.52
2.3.15.35.11.13	1716/1715, 4096/4095, 6250/6237, 91125/91091, 6656/6655	⟨1051 1666 4106 5391 3636 3889]	-0.0214	0.0658	5.76
2.3.15.35.11.13.17	1275/1274, 1716/1715, 2431/2430, 4096/4095, 6250/6237, 6656/6655	⟨1051 1666 4106 5391 3636 3889 4296]	-0.0214	0.0609	5.33
2.3.15.35.11.13.17.19	1540/1539, 1275/1274, 1716/1715, 2431/2430, 4096/4095, 6250/6237, 41800/41769	⟨1051 1666 4106 5391 3636 3889 4296 4465]	-0.0331	0.0648	5.68

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	435\1051	496.67	5457/4096	Edson

Music

• you have to run! by Francium