1051edo

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← 1050edo1051edo1052edo →
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

1051 equal divisions of the octave (abbreviated 1051edo or 1051ed2), also called 1051-tone equal temperament (1051tet) or 1051 equal temperament (1051et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1051 equal parts of about 1.14 ¢ each. Each step represents a frequency ratio of 21/1051, or the 1051st root of 2.

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 -35 +47 +41 +14 -16 -14 +8 +43 -33 -26
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

Francium