Xenharmonic Wiki

80edo: Difference between revisions

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→Approximation to JI: this "mapping" has nothing to do with mapping matrices
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=== Consistent circles ===
=== Consistent circles ===
80edo is home to a staggering amount of [[consistent circle]]s, both ones closing after generating all 80 notes and ones closing after generating a subset edo like 2, 4, 5, 8, 10, 16 or 20.
80edo is home to a staggering amount of [[consistent circle]]s, both ones closing after generating all 80 notes and ones closing after generating a subset edo like 2, 4, 5, 8, 10, 16 or 20.
{| class="wikitable center-all"
{| class="wikitable center-1 center-2 center-3"
|+80-note circles by gen. with related temperaments organized by period
|+80-note circles by gen. with related temperaments organized by period
|-
|-
! [[Interval]]
! [[Interval]]
! [[Closing error|Closing Error]]
! [[Closing error|Closing<br>Error]]
! [[Circle#Definitions|Consistency]]
! [[Circle#Definitions|Consistency]]
! 1\1
! 1\1
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| [[17/16]]
| [[17/16]]
| 23.8%
| 23.8%
| strong
| Strong
| [[septendesemi]]
| [[Septendesemi]]
| [[srutal archagall]]
| [[Srutal archagall]]
| [[bidia]]
| [[Bidia]]
| [[pentorwell]]
| [[Pentorwell]]
| 80 & 104
| 80 & 104
| [[linus]]
| [[Linus]] retraction
| ?
| ?
| [[degrees]]
| [[Degrees]]
|-
|-
| [[11/10]]
| [[11/10]]
| 2.3%
| 2.3%
| strong
| Strong
| ?
| ?
| [[echidna]], [[semisupermajor]]
| [[Echidna]], [[semisupermajor]]
| ?
| ?
| [[trisey]], [[dodgy]]
| [[Trisey]], [[dodgy]]
| [[octopus]]
| [[Octopus]]
| [[decistearn]], [[deca]]
| [[Decistearn]], [[deca]]
| [[hexadecoid]]
| [[Hexadecoid]]
| [[degrees]]
| [[Degrees]]
|-  
|-  
| [[9/7]]
| [[9/7]]
| 44.9%
| 44.9%
| normal
| Normal
| [[supermajor]]
| [[Supermajor]]
| [[echidna]], [[semisupermajor]]
| [[Echidna]], [[semisupermajor]]
| ?
| ?
| ?
| ?
| [[octopus]]
| [[Octopus]]
| [[decistearn]], [[deca]]
| [[Decistearn]], [[deca]]
| [[hexadecoid]]
| [[Hexadecoid]]
| [[degrees]]
| [[Degrees]]
|}
|}


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|-
|-
! [[Interval]]
! [[Interval]]
! [[Closing error|Closing Error]]
! [[Closing error|Closing<br>Error]]
! [[Circle#Definitions|Consistency]]
! [[Circle#Definitions|Consistency]]
! Associated<br>Edostep
! Associated<br>Edostep
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| [[15/14]]
| [[15/14]]
| 37.1%
| 37.1%
| normal
| Normal
| 1\10
| 1\10
| [[deca]], [[decistearn]], [[linus]]
| [[Deca]], [[decistearn]], [[linus]]
|-
|-
| [[16/13]]
| [[16/13]]
| 35.2%
| 35.2%
| normal
| Normal
| 3\10
| 3\10
| [[deca]], [[decistearn]], [[linus]]
| [[Deca]], [[decistearn]], [[linus]]
|-
|-
| [[69/56]]
| [[69/56]]
| 93.6%
| 93.6%
| weak
| Weak
| 3\10
| 3\10
| [[decistearn]]
| [[Decistearn]]
|-
|-
| [[85/69]]
| [[85/69]]
| 69.3%
| 69.3%
| weak
| Weak
| 3\10
| 3\10
| [[decistearn]]
| [[Decistearn]]
|}
|}


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|-
|-
! [[Interval]]
! [[Interval]]
! [[Closing error|Closing Error]]
! [[Closing error|Closing<br>Error]]
! [[Circle#Definitions|Consistency]]
! [[Circle#Definitions|Consistency]]
! Associated<br>Edostep
! Associated<br>Edostep
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| [[12/11]]
| [[12/11]]
| 34.0%
| 34.0%
| normal
| Normal
| 1\8
| 1\8
| [[octopus]], 11-limit [[octoid]]
| [[Octopus]], 11-limit [[octoid]]
|-
|-
| [[85/78]]
| [[85/78]]
| 64.7%
| 64.7%
| weak
| Weak
| 1\8
| 1\8
| [[octopus]], [[octoid]]
| [[Octopus]], [[octoid]]
|-
|-
| [[13/10]]
| [[13/10]]
| 224.7%
| 224.7%
| sub-weak
| Sub-weak
| 3\8
| 3\8
| [[octopus]]
| [[Octopus]]
|-
|-
| [[35/27]]
| [[35/27]]
| 38.7%
| 38.7%
| normal
| Normal
| 3\8
| 3\8
| [[octopus]], 7-limit [[octoid]]
| [[Octopus]], 7-limit [[octoid]]
|-
|-
| [[22/17]]
| [[22/17]]
| 194.0%
| 194.0%
| sub-weak
| Sub-weak
| 3\8
| 3\8
| [[octopus]]
| [[Octopus]]
|-
|-
| [[48/37]]
| [[48/37]]
| 32.6%
| 32.6%
| normal
| Normal
| 3\8
| 3\8
| octoid/octopus extension
| Octoid/octopus extension
|-
|-
| [[83/64]]
| [[83/64]]
| 2.5%
| 2.5%
| super-strong
| Super-strong
| 3\8
| 3\8
| octoid/octopus extension
| Octoid/octopus extension
|}
|}


Line 337: Line 337:
|-
|-
! [[Interval]]
! [[Interval]]
! [[Closing error|Closing Error]]
! [[Closing error|Closing<br>Error]]
! [[Circle#Definitions|Consistency]]
! [[Circle#Definitions|Consistency]]
! Associated<br>Edostep
! Associated<br>Edostep
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| [[23/20]]
| [[23/20]]
| 65.4%
| 65.4%
| weak
| Weak
| 1\5
| 1\5
| [[trisey]] add-23, [[dodgy]] add-23
| [[Trisey]] add-23, [[dodgy]] add-23
|-
|-
| [[85/74]]
| [[85/74]]
| 2.5%
| 2.5%
| super-strong
| Super-strong
| 1\5
| 1\5
| [[Trisedodge family#Trisey|29-limit add-37 trisey extension]]
| [[Trisedodge family #Trisey|29-limit add-37 trisey extension]]
|-
|-
| [[33/25]]
| [[33/25]]
| 21.5%
| 21.5%
| strong
| Strong
| 2\5
| 2\5
| [[countdown]]
| [[Countdown]]
|-
|-
| [[37/28]]
| [[37/28]]
| 83.9%
| 83.9%
| weak
| Weak
| 2\5
| 2\5
| [[Trisedodge family#Trisey|29-limit add-37 trisey extension]]
| [[Trisedodge family#Trisey|29-limit add-37 trisey extension]]
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| [[95/72]]
| [[95/72]]
| 2.8%
| 2.8%
| super-strong
| Super-strong
| 2\5
| 2\5
| [[Trisedodge family#Trisey|29-limit add-37 trisey extension]]
| [[Trisedodge family#Trisey|29-limit add-37 trisey extension]]
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| [[19/16]]
| [[19/16]]
| 66.3%
| 66.3%
| weak
| Weak
| 1\4
| 1\4
| [[bidia]]
| [[Bidia]]
|-
|-
| [[25/21]]
| [[25/21]]
| 49.2%
| 49.2%
| normal
| Normal
| 1\4
| 1\4
| [[bidia]]
| [[Bidia]]
|-
|-
| [[44/37]]
| [[44/37]]
| 0.7%
| 0.7%
| super-strong
| Super-strong
| 1\4
| 1\4
| [[berylic]], [[bidia]] extension
| [[Berylic]], [[bidia]] extension
|}
|}


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