80edo: Difference between revisions
→Consistent circles: add 5-note circles |
m Make consistent circle a subsection of approximation to JI. Style |
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<nowiki>*</nowiki> based on treating 80edo as a no-31's [[37-limit]] temperament; other approaches are possible. Inconsistent interpretations in italic. | <nowiki>*</nowiki> based on treating 80edo as a no-31's [[37-limit]] temperament; other approaches are possible. Inconsistent interpretations in italic. | ||
== Consistent circles == | == Approximation to JI == | ||
=== 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- | {| class="wikitable center-all" | ||
|+80-note circles by gen. with related temperaments organized by period | |+80-note circles by gen. with related temperaments organized by period | ||
|- | |- | ||
! [[Interval]] | |||
! [[Closing error|Closing Error]] | |||
! [[Circle#Definitions|Consistency]] | |||
! 1\1 | |||
! 1\2 | |||
! 1\4 | |||
! 1\5 | |||
! 1\8 | |||
! 1\10 | |||
! 1\16 | |||
! 1\20 | |||
|- | |- | ||
| [[17/16]] | | [[17/16]] | ||
| Line 246: | Line 247: | ||
|} | |} | ||
{| class="wikitable center-all" | |||
{| class="wikitable center- | |||
|+10-note circles by gen. with related [[10th-octave temperaments]] | |+10-note circles by gen. with related [[10th-octave temperaments]] | ||
|- | |- | ||
! [[Interval]] | |||
! [[Closing error|Closing Error]] | |||
! [[Circle#Definitions|Consistency]] | |||
! [[Mapping]] | |||
! [[Regular temperament|Temperaments]] | |||
|- | |- | ||
| [[15/14]] | | [[15/14]] | ||
| Line 281: | Line 281: | ||
|} | |} | ||
{| class="wikitable center- | {| class="wikitable center-all" | ||
|+8-note circles by gen. with related [[8th-octave temperaments]] | |+8-note circles by gen. with related [[8th-octave temperaments]] | ||
|- | |- | ||
! [[Interval]] | |||
! [[Closing error|Closing Error]] | |||
! [[Circle#Definitions|Consistency]] | |||
! [[Mapping]] | |||
! [[Regular temperament|Temperaments]] | |||
|- | |- | ||
| [[12/11]] | | [[12/11]] | ||
| Line 333: | Line 333: | ||
|} | |} | ||
{| class="wikitable center- | {| class="wikitable center-all" | ||
|+5-note circles by gen. with related [[5th-octave temperaments]] | |+5-note circles by gen. with related [[5th-octave temperaments]] | ||
|- | |- | ||
! [[Interval]] | |||
! [[Closing error|Closing Error]] | |||
! [[Circle#Definitions|Consistency]] | |||
! [[Mapping]] | |||
! [[Regular temperament|Temperaments]] | |||
|- | |- | ||
| [[23/20]] | | [[23/20]] | ||
| Line 352: | Line 352: | ||
| super-strong | | super-strong | ||
| 1\5 | | 1\5 | ||
| [[Trisedodge family#Trisey|29-limit add-37 | | [[Trisedodge family#Trisey|29-limit add-37 trisey extension]] | ||
|- | |- | ||
| [[33/25]] | | [[33/25]] | ||
| Line 364: | Line 364: | ||
| weak | | weak | ||
| 2\5 | | 2\5 | ||
| [[Trisedodge family#Trisey|29-limit add-37 | | [[Trisedodge family#Trisey|29-limit add-37 trisey extension]] | ||
|- | |- | ||
| [[95/72]] | | [[95/72]] | ||
| Line 370: | Line 370: | ||
| super-strong | | super-strong | ||
| 2\5 | | 2\5 | ||
| [[Trisedodge family#Trisey|29-limit add-37 | | [[Trisedodge family#Trisey|29-limit add-37 trisey extension]] | ||
|} | |} | ||
{| class="wikitable center- | {| class="wikitable center-all" | ||
|+4-note circles with related [[4th-octave temperaments]] | |+4-note circles with related [[4th-octave temperaments]] | ||
|- | |- | ||
! [[Interval]] | |||
! [[Closing error|Closing Error]] | |||
! [[Circle#Definitions|Consistency]] | |||
! [[Regular temperament|Temperaments]] | |||
|- | |- | ||
| [[19/16]] | | [[19/16]] | ||