1106edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|1106}} | {{EDO intro|1106}} | ||
== Theory == | == Theory == | ||
1106edo is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak edo]]. It is strong as a 7-limit system; the only edos lower than it with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] being {{EDOs| 171, 270, 342, 441 and 612 }}. It is even stronger in the 11-limit; the only ones beating it out now being {{EDOs| 270, 342 and 612 }}. It is less strong in the 13 and 17 | 1106edo is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak edo]]. It is strong as a 7-limit system; the only edos lower than it with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] being {{EDOs| 171, 270, 342, 441 and 612 }}. It is even stronger in the 11-limit; the only ones beating it out now being {{EDOs| 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]]. | ||
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]]. | It notably supports [[supermajor]], [[brahmagupta]], and [[orga]] in the 7-limit, and notably [[semisupermajor]] in the 11-limit. In the higher limits, it supports the 79th-octave temperament [[gold]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|1106}} | {{Harmonics in equal|1106}} | ||
=== | === Subsets and supersets === | ||
Since 1106 factors into 2 × 7 × 79, it has subset edos {{EDOs| 2, 7, 14, 79, 158, and 553 }}. | Since 1106 factors into 2 × 7 × 79, it has subset edos {{EDOs| 2, 7, 14, 79, 158, and 553 }}. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" |[[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Comma list|Comma List]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" |Optimal | ! rowspan="2" | Optimal<br>8ve Stretch (¢) | ||
8ve Stretch (¢) | ! colspan="2" | Tuning Error | ||
! colspan="2" |Tuning Error | |||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
|2.3 | | 2.3 | ||
|{{monzo|1753 -1106}} | | {{monzo| 1753 -1106 }} | ||
|{{val|1106 1753}} | | {{val| 1106 1753 }} | ||
| -0.010 | | -0.010 | ||
|0.010 | | 0.010 | ||
|0.99 | | 0.99 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|{{monzo|-53 10 16}}, {{monzo|40 -56 21}} | | {{monzo| -53 10 16 }}, {{monzo| 40 -56 21 }} | ||
|{{val|1106 1753 2568}} | | {{val| 1106 1753 2568 }} | ||
| +0.001 | | +0.001 | ||
|0.019 | | 0.019 | ||
|1.73 | | 1.73 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|4375/4374, 52734375/52706752, {{monzo|46 -14 -3 -6}} | | 4375/4374, 52734375/52706752, {{monzo| 46 -14 -3 -6 }} | ||
|{{val|1106 1753 2568 3105}} | | {{val| 1106 1753 2568 3105 }} | ||
| | | -0.006 | ||
|0.020 | | 0.020 | ||
|1.83 | | 1.83 | ||
|- | |- | ||
|2.3.5.7.11 | | 2.3.5.7.11 | ||
|3025/3024, 4375/4374, 5767168/5764801, 35156250/35153041 | | 3025/3024, 4375/4374, 5767168/5764801, 35156250/35153041 | ||
|{{val|1106 1753 2568 3105 3826}} | | {{val| 1106 1753 2568 3105 3826 }} | ||
| +0.004 | | +0.004 | ||
|0.026 | | 0.026 | ||
|2.38 | | 2.38 | ||
|- | |- | ||
|2.3.5.7.11.13 | |2.3.5.7.11.13 | ||
|3025/3024, 4096/4095, 4375/4374, 456533/456300, 928125/927472 | | 3025/3024, 4096/4095, 4375/4374, 456533/456300, 928125/927472 | ||
|{{val|1106 1753 2568 3105 3826 4093}} | | {{val| 1106 1753 2568 3105 3826 4093 }} | ||
| | | -0.012 | ||
|0.043 | | 0.043 | ||
|3.94 | | 3.94 | ||
|- | |- | ||
|2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
|2500/2499, 3025/3024, 4096/4095, 8624/8619, 9801/9800, 14875/14572 | | 2500/2499, 3025/3024, 4096/4095, 8624/8619, 9801/9800, 14875/14572 | ||
|{{val|1106 1753 2568 3105 3826 4093 4521}} | | {{val| 1106 1753 2568 3105 3826 4093 4521 }} | ||
| | | -0.021 | ||
|0.045 | | 0.045 | ||
|4.11 | | 4.11 | ||
|} | |} | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||