1106edo: Difference between revisions

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fill in the temperament table
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completed the regular temperament table
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== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal
8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.3
|[1753, -1106⟩
|1106 1753
| -0.010
|0.010
|0.99
|-
|2.3.5
|<nowiki>-53  10 16,  40 -56 21</nowiki>
|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
|<nowiki>-0.006</nowiki>
|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, 456533/456300, 928125/927472
|1106 1753 2568 3105 3826 4093
|<nowiki>-0.012</nowiki>
|0.043
|3.94
|-
|2.3.5.7.11.13.17
|2500/2499, 3025/3024, 4096/4095, 8624/8619, 9801/9800, 14875/14572
|1106 1753 2568 3105 3826 4093 4521
|<nowiki>-0.021</nowiki>
|0.045
|4.11
|}
=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"

Revision as of 00:48, 6 July 2023

← 1105edo 1106edo 1107edo →
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

Template:EDO intro

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 limits, but even so is distinctly consistent through the 17-odd-limit.

It notably supports supermajor, brahmagupta, and orga in the 7-limit, and notably semisupermajor in the 11-limit. In 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
Error Absolute (¢) +0.000 +0.034 -0.057 +0.071 -0.143 +0.340 +0.289 -0.225 -0.065 +0.079 -0.370
Relative (%) +0.0 +3.1 -5.2 +6.5 -13.1 +31.4 +26.6 -20.8 -6.0 +7.3 -34.1
Steps
(reduced) 		1106
(0) 		1753
(647) 		2568
(356) 		3105
(893) 		3826
(508) 		4093
(775) 		4521
(97) 		4698
(274) 		5003
(579) 		5373
(949) 		5479
(1055)

Divisors

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, 40 -56 21 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, 456533/456300, 928125/927472 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, 8624/8619, 9801/9800, 14875/14572 1106 1753 2568 3105 3826 4093 4521 -0.021 0.045 4.11

Rank-2 temperaments

Periods
per 8ve 		Generator
(Reduced) 		Cents
(Reduced) 		Associated
Ratio 		Temperaments
1 213\1106 231.103 8/7 Orga
1 401\1106 435.081 9/7 Supermajor
2 401\1106 435.081 9/7 Semisupermajor
7 479\1106
(5\1106) 		519.711
(5.424) 		27/20
(325/324) 		Brahmagupta
79 459\1106
(11\1106) 		498.011
(11.935) 		4/3
(?) 		Gold
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