1106edo: Difference between revisions

Expand on theory
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== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{{comma basis begin}}
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" | Tuning Error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3
| 2.3
| {{monzo| 1753 -1106 }}
| {{monzo| 1753 -1106 }}
| {{mapping| 1106 1753 }}
| {{mapping| 1106 1753 }}
| -0.010
| &minus;0.010
| 0.010
| 0.010
| 0.99
| 0.99
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| 4375/4374, 52734375/52706752, {{monzo| 46 -14 -3 -6 }}
| 4375/4374, 52734375/52706752, {{monzo| 46 -14 -3 -6 }}
| {{mapping| 1106 1753 2568 3105 }}
| {{mapping| 1106 1753 2568 3105 }}
| -0.006
| &minus;0.006
| 0.020
| 0.020
| 1.83
| 1.83
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| 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 }}
| {{mapping| 1106 1753 2568 3105 3826 4093 }}
| -0.012
| &minus;0.012
| 0.043
| 0.043
| 3.94
| 3.94
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| 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 }}
| {{mapping| 1106 1753 2568 3105 3826 4093 4521 }}
| -0.021
| &minus;0.021
| 0.045
| 0.045
| 4.11
| 4.11
|}
{{comma basis end}}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
|-
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|-
| 1
| 1
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|-
|-
| 2
| 2
| 401\1106<br>(152\1106)
| 401\1106<br />(152\1106)
| 435.081<br>(164.919)
| 435.081<br />(164.919)
| 9/7<br>(11/10)
| 9/7<br />(11/10)
| [[Semisupermajor]]
| [[Semisupermajor]]
|-
|-
| 7
| 7
| 479\1106<br>(5\1106)
| 479\1106<br />(5\1106)
| 519.711<br>(5.424)
| 519.711<br />(5.424)
| 27/20<br>(5120/5103)
| 27/20<br />(5120/5103)
| [[Brahmagupta]] (7-limit)
| [[Brahmagupta]] (7-limit)
|-
|-
| 79
| 79
| 459\1106<br>(11\1106)
| 459\1106<br />(11\1106)
| 498.011<br>(11.935)
| 498.011<br />(11.935)
| 4/3<br>(?)
| 4/3<br />(?)
| [[Gold]]
| [[Gold]]
|}
{{rank-2 end}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
{{orf}}