1106edo

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Prime factorization 2 × 7 × 79
Step size 1.08499¢ 
Fifth 647\1106 (701.989¢)
Semitones (A1:m2) 105:83 (113.9¢ : 90.05¢)
Consistency limit 17
Distinct consistency limit 17
Special properties

1106 equal divisions of the octave (abbreviated 1106edo or 1106ed2), also called 1106-tone equal temperament (1106tet) or 1106 equal temperament (1106et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1106 equal parts of about 1.08 ¢ each. Each step represents a frequency ratio of 21/1106, or the 1106th root of 2.

Theory

1106edo is a zeta peak edo. It is strong as a 7-limit system; the only edos lower than it with a lower 7-limit relative error being 171, 270, 342, 441 and 612. It is even stronger in the 11-limit; the only ones beating it out now being 270, 342 and 612. It is less strong in the 13- and 17-limit, but even so is distinctly consistent through the 17-odd-limit.

The equal temperament tempers out [-53 10 16 (kwazy comma) and [-13 -46 37 (supermajor comma) in the 5-limit; 4375/4374 and 52734375/52706752 in the 7-limit; 3025/3024 and 9801/9800 in the 11-limit; 4096/4095, 78125/78078, and 105644/105625 in the 13-limit; 2500/2499, 4914/4913, and 8624/8619 in the 17-limit. It notably supports supermajor, brahmagupta, and orga in the 7-limit, and semisupermajor in the 11-limit. In the higher limits, it supports the 79th-octave temperament gold.

Prime harmonics

Approximation of prime harmonics in 1106edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37
Error Absolute (¢) +0.000 +0.034 -0.057 +0.071 -0.143 +0.340 +0.289 -0.225 -0.065 +0.079 -0.370 +0.374
Relative (%) +0.0 +3.1 -5.2 +6.5 -13.1 +31.4 +26.6 -20.8 -6.0 +7.3 -34.1 +34.5
Steps
(reduced)
1106
(0)
1753
(647)
2568
(356)
3105
(893)
3826
(508)
4093
(775)
4521
(97)
4698
(274)
5003
(579)
5373
(949)
5479
(1055)
5762
(232)

Subsets and supersets

Since 1106 factors into 2 × 7 × 79, it has subset edos 2, 7, 14, 79, 158, and 553.

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢)
Tuning error
Absolute (¢) Relative (%)
2.3 [1753 -1106 [1106 1753]] −0.010 0.010 0.99
2.3.5 [-53 10 16, [-13 -46 37 [1106 1753 2568]] +0.001 0.019 1.73
2.3.5.7 4375/4374, 52734375/52706752, [46 -14 -3 -6 [1106 1753 2568 3105]] −0.006 0.020 1.83
2.3.5.7.11 3025/3024, 4375/4374, 5767168/5764801, 35156250/35153041 [1106 1753 2568 3105 3826]] +0.004 0.026 2.38
2.3.5.7.11.13 3025/3024, 4096/4095, 4375/4374, 78125/78078, 105644/105625 [1106 1753 2568 3105 3826 4093]] −0.012 0.043 3.94
2.3.5.7.11.13.17 2500/2499, 3025/3024, 4096/4095, 4375/4374, 4914/4913, 8624/8619 [1106 1753 2568 3105 3826 4093 4521]] −0.021 0.045 4.11

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
ratio*
Temperaments
1 213\1106 231.103 8/7 Orga (11-limit)
1 401\1106 435.081 9/7 Supermajor
2 150\1106 162.749 1125/1024 Kwazy
2 401\1106
(152\1106)
435.081
(164.919)
9/7
(11/10)
Semisupermajor
7 479\1106
(5\1106)
519.711
(5.424)
27/20
(5120/5103)
Brahmagupta (7-limit)
79 459\1106
(11\1106)
498.011
(11.935)
4/3
(?)
Gold

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct