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User:BudjarnLambeth/Bird’s eye view of rank-2 temperaments: Difference between revisions

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{{Editable user page|If you see any temperaments in the wrong category, please move them to the correct category. <br><br>If you know of a temperament that is much-loved by a sizeable subset of the xen community but is not yet included here, please add it. <br><br>If you see a temperament on here that no one cares about, please remove it. But only remove it if '''nobody''' cares about it. Don't remove it just because you think it's useless. If a few other people do care about it, then don't remove it. <br><br>If you see any ways the wording of the page could be improved, please edit it to make those improvements. <br><br>If you see any typos or grammatical or factual errors, please make an edit to correct those.}}
<div style="border: 1px green solid; background-color: #efe; padding: 0.5em 1em; margin-bottom: 1em">
'''This page has been deprecated, but it is being kept in place for longevity as a reference material. Please see [[User:BudjarnLambeth/Survey of efficient temperaments by subgroup]] for the new version.'''
</div>




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Most would agree that a good temperament approximates some subset of [[just intonation]] relatively accurately with a relatively small number of notes.
Most would agree that a good temperament approximates some subset of [[just intonation]] relatively accurately with a relatively small number of notes.


What they disagree on is ''how'' accurate is "relatively accurate", ''how'' small is relatively small, and ''which'' JI subsets are interesting enough to be worth approximating.
What they disagree on is ''how'' accurate is "relatively accurate", ''how'' small is "relatively small", and ''which'' JI subsets are interesting enough to be worth approximating.




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* Exotemperament: > ~18 [[cents]] of [[error]] on more than one targeted interval
* Exotemperament: > ~18 [[cents]] of [[error]] on more than one targeted interval
* Low accuracy: < ~18c error on most targeted intervals
* Low accuracy: < ~18c error on most targeted intervals
* Medium accuracy: < 12c error on almost all targeted intervals
* Medium accuracy: < 12c error on most targeted intervals
* High accuracy: < 7c error on almost all targeted intervals
* High accuracy: < 7c error on almost all targeted intervals
* Very high accuracy: < 3.5c error on almost all targeted intervals
* Very high accuracy: < 3.5c error on almost all targeted intervals
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| schismic aka [[helmholtz]]
| schismic aka [[Helmholtz temperament|Helmholtz]]
| [[kwazy]]
| [[kwazy]]
|}
|}
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! Medium accuracy (7-12c)
! Medium accuracy (7-12c)
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|  
| [[magic]], [[meantone]], [[sensi]], [[superpyth]]
| [[magic]], [[meantone]], [[mothra]], [[sensi]], [[superpyth]]
| [[valentine]]
| [[valentine]]
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|  
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! High accuracy (3.5-7c)
! High accuracy (3.5-7c)
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| [[mothra]], [[orwell]]
| [[orwell]]
| [[diaschismic]], [[garibaldi]]
| [[diaschismic]], [[garibaldi]]
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| [[miracle]], [[wuerschmidt]]
| [[miracle]]
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| [[magic]], [[meanpop]], [[meantone]], [[valentine]]
| [[magic]], [[meanpop]], [[meantone]], [[mothra]], [[valentine]]
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| [[diaschismic]], [[mothra]], [[orwell]]
| [[diaschismic]], [[orwell]]
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| [[miracle]], [[wuerschmidt]]
| [[miracle]]
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| [[magic]], [[meantone]]
| [[magic]], [[meantone]], [[mothra]]
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| [[diaschismic]], [[mothra]], [[orwell]]
| [[diaschismic]], [[orwell]]
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| [[wuerschmidt]]
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|}
|}


== No-2s ==
== 3.5.7 and its extensions ==


{| class="wikitable"
{| class="wikitable"
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|}
|}


== No-3s ==
== Other no-2s subgroups ==
 
{| class="wikitable"
|+
!
! Approx. 10 notes
! Approx. 20 notes
! Approx. 30 notes
! Approx. 70 notes
! Over 100 notes
|-
! Exotemperament (18-∞c)
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|-
! Low accuracy (12-18c)
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! Medium accuracy (7-12c)
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|-
! High accuracy (3.5-7c)
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|-
! Very high accuracy (1-3.5c)
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|-
! Microtemperament (0-1c)
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|}
 
== No-3s subgroups ==


{| class="wikitable"
{| class="wikitable"
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|}
|}


== No-5s ==
== 2.3.7 and its extensions ==


{| class="wikitable"
{| class="wikitable"
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|}
|}


== No-7s ==
== 2.3.11 and its extensions ==
 
{| class="wikitable"
|+
!
! Approx. 10 notes
! Approx. 20 notes
! Approx. 30 notes
! Approx. 70 notes
! Over 100 notes
|-
! Exotemperament (18-∞c)
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|-
! Low accuracy (12-18c)
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|-
! Medium accuracy (7-12c)
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| [[neutral]] (no-5 no-7 [[rastmic]])
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|-
! High accuracy (3.5-7c)
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| no-5 no-7 [[pythrabian]]
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|-
! Very high accuracy (1-3.5c)
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| [[tribilo]] (no-5 no-7 [[nexus]])
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! Microtemperament (0-1c)
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| no-5 no-7 [[frameshift]]
|}
 
== 2.3.13, 2.3.17, etc ==
 
{| class="wikitable"
|+
!
! Approx. 10 notes
! Approx. 20 notes
! Approx. 30 notes
! Approx. 70 notes
! Over 100 notes
|-
! Exotemperament (18-∞c)
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|-
! Low accuracy (12-18c)
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|-
! Medium accuracy (7-12c)
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|-
! High accuracy (3.5-7c)
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|-
! Very high accuracy (1-3.5c)
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|-
! Microtemperament (0-1c)
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|}
 
== No-7s subgroups ==


{| class="wikitable"
{| class="wikitable"
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|}
|}


== No-11s ==
== No-11s subgroups ==


{| class="wikitable"
{| class="wikitable"
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|}
|}


== Higher subgroups ==
== Other subgroups ==


{| class="wikitable"
{| class="wikitable"
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