1106edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == 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 [[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 [[consistency|distinctly consistent]] through the [[17-odd-limit]]. | 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 [[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 [[consistency|distinctly consistent]] through the [[17-odd-limit]]. | ||
It notably supports [[supermajor]], [[brahmagupta]], and [[orga]] in the 7-limit, and | The equal temperament [[tempering out|tempers out]] {{monzo| -53 10 16 }} (kwazy comma) and {{monzo| -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 === | === Prime harmonics === | ||
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== 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 | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
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|- | |- | ||
| 2.3 | | 2.3 | ||
| {{ | | {{Monzo| 1753 -1106 }} | ||
| {{ | | {{Mapping| 1106 1753 }} | ||
| | | −0.010 | ||
| 0.010 | | 0.010 | ||
| 0.99 | | 0.99 | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{ | | {{Monzo| -53 10 16 }}, {{monzo| -13 -46 37 }} | ||
| {{ | | {{Mapping| 1106 1753 2568 }} | ||
| +0.001 | | +0.001 | ||
| 0.019 | | 0.019 | ||
Line 40: | Line 41: | ||
| 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 }} | ||
| {{ | | {{Mapping| 1106 1753 2568 3105 }} | ||
| | | −0.006 | ||
| 0.020 | | 0.020 | ||
| 1.83 | | 1.83 | ||
Line 47: | Line 48: | ||
| 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 | ||
| {{ | | {{Mapping| 1106 1753 2568 3105 3826 }} | ||
| +0.004 | | +0.004 | ||
| 0.026 | | 0.026 | ||
Line 54: | Line 55: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 3025/3024, 4096/4095, 4375/4374, 78125/78078, 105644/105625 | | 3025/3024, 4096/4095, 4375/4374, 78125/78078, 105644/105625 | ||
| {{ | | {{Mapping| 1106 1753 2568 3105 3826 4093 }} | ||
| | | −0.012 | ||
| 0.043 | | 0.043 | ||
| 3.94 | | 3.94 | ||
Line 61: | Line 62: | ||
| 2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
| 2500/2499, 3025/3024, 4096/4095, 4375/4374, 4914/4913, 8624/8619 | | 2500/2499, 3025/3024, 4096/4095, 4375/4374, 4914/4913, 8624/8619 | ||
| {{ | | {{Mapping| 1106 1753 2568 3105 3826 4093 4521 }} | ||
| | | −0.021 | ||
| 0.045 | | 0.045 | ||
| 4.11 | | 4.11 | ||
Line 69: | Line 70: | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br> | ! Associated<br>ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
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| 9/7 | | 9/7 | ||
| [[Supermajor]] | | [[Supermajor]] | ||
|- | |||
| 2 | |||
| 150\1106 | |||
| 162.749 | |||
| 1125/1024 | |||
| [[Crazy]] | |||
|- | |- | ||
| 2 | | 2 | ||
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| [[Gold]] | | [[Gold]] | ||
|} | |} | ||
<nowiki>* | <nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[normal lists|minimal form]] in parentheses if distinct |