1051edo

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← 1050edo

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

1051edo only has a consistency limit of 3 and does poorly with approximating the harmonic 5. However, it has a reasonable representation of the 2.3.7.11.17.19 subgroup.

Assume the patent val, 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.

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 and 7. 4212edo, which quadruples it, gives a good correction to the harmonic 3.

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
2.3.5	[-68 18 17⟩, [-26 -29 31⟩	⟨1051 1666 2440] (1051)	+0.0077	0.1298	11.4
2.3.5	[40 7 -22⟩, [63 -50 7⟩	⟨1051 1666 2441] (1051c)	-0.1562	0.1313	11.5

Music

• you have to run! by Francium