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Major restructure, if everyone hates it I’ll change back :p
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So that should provide a point of comparison to help measure these other temperaments against.
So that should provide a point of comparison to help measure these other temperaments against.


== Guide to tables ==
== How to read the table ==


'''Rows'''
'''Rows'''


The rows categorise temperaments by accuracy. That is, how closely they approximate [[just intonation]] intervals. The categories are:
The rows categorise temperaments by the [[just intonation subgroup]] they approximate.
* Exotemperament: > ~18 [[cents]] of [[error]] on more than one targeted interval
* Low accuracy: < ~18c error on most targeted intervals
* Medium accuracy: < 12c error on most targeted intervals
* High accuracy: < 7c error on almost all targeted intervals
* Very high accuracy: < 3.5c error on almost all targeted intervals
* Microtemperaments: < 1c on all targeted intervals
The definition of "targeted interval" is left deliberately vague, because some temperaments serve a specific purpose and must be assessed differently. In most cases on this page, it refers to the set of intervals that occur in a [[tonality diamond]] of the temperament's subgroup.


The 2.3.5 subgroup is what most theorists believe 12 tone equal temperament belongs to (but there is plenty of disagreement about that).


'''Columns'''
The 2.3.5.7 and 2.3.5.7.11 subgroups are the most commonly used, being not too complex and including lots of useful harmonies.
 
Subgroups with no 2s, e.g. 3.5.7.11, are the biggest and most jarring break away from familiar harmony, which you may consider a good or a bad thing.
 
Subgroups with 2s and 3s but no 5s, e.g. 2.3.7.11, preserve the most fundamental familiar intervals like the octave and the fifth, but do away with the 5-limit major and minor intervals of common practice harmony, forcing innovation while still keeping some familiarity.


The columns categorise temperaments by [[complexity]].  
Some theorists believe including 13, 17 or higher in a subgroup is pointless because the brain can't register such complex intervals. Others believe these intervals are registered by the brain, maybe subtly and subconsciously in some instances, but still they matter. It is up to you which theorists you believe on that.


Rank 2 temperaments can generate scales with any number of notes per [[equave]]. However, if they have too few notes, they won't be able approximate enough targeted intervals to be useful, and if they have too many notes, they will be filled with extra notes that don't serve much purpose and get in the way. Just how many notes is about right, varies from temperament to temperament. In layman’s terms: More notes needed = more complexity, less notes needed = less complexity. The real definition of complexity is more involved and rigorous than this, but this is good enough for the purposes of a broad overview page.


'''Columns'''


'''Subgroup categorisation'''
The columns categorise temperaments by the approximate number of notes needed to reach all the important intervals in a temperament.


If a temperament fits under multiple subgroup headings (e.g. both No-2s and No-5s) it should be placed only under the lowest numbered heading (in this example, No-2s).
All of the temperaments listed in this table have low badness (high relative accuracy), meaning they approximate their target JI subgroup much better than most temperaments with their same amount of needed notes.


== 5-limit ==
That means the temperaments in this table requiring more notes are also more accurate. The ones requiring less notes are less accurate but are good for their size.


{| class="wikitable"
{| class="wikitable"
|+
|+
!  
! JI subgroup
! Approx. 10 notes
! ~10 notes
! Approx. 20 notes
! ~20 notes
! Approx. 30 notes
! ~30 notes
! Approx. 70 notes
! ~70 notes
! Over 100 notes
! >100 notes
|-
|-
! Exotemperament (18-∞c)
! 2.3.5 (5 limit)
| [[antitonic]], [[bug]], [[dicot]], [[father]]
| [[augmented]], [[blackwood]], [[diaschismic]], [[dimipent]], [[meantone]], [[porcupine]], [[whitewood]]
|  
| [[hanson]], [[magic]], [[superpyth]]
|  
| [[valentine]], [[wuerschmidt]]
|  
| [[helmoltz]] (aka schismic)
|  
| [[kwazy]
|-
|-
! Low accuracy (12-18c)
! 2.3.7
| [[augmented]], [[blackwood]], [[dimipent]], [[porcupine]], [[whitewood]]
| [[semaphore]]
| [[superpyth]]
| [[bleu]], [[slendric]]
|  
|  
|  
|  
|  
|  
|-
|-
! Medium accuracy (7-12c)
! 2.3.11
| [[meantone]]
| [[hanson]], [[magic]]
| [[valentine]]
|  
|  
| [[neutral]] (no-5 no-7 [[rastmic]]), no-5 no-7 [[pythrabian]]
| [[tribilo]] (no-5 no-7 [[nexus]])
|  
|  
| no-5 no-7 [[frameshift]]
|-
|-
! High accuracy (3.5-7c)
! 2.5.n
| [[diaschismic]]
|
|
|
|  
|  
|-
! Very high accuracy (1-3.5c)
|  
|  
|  
|  
| [[wuerschmidt]]
|  
|  
|  
|  
|-
|-
! Microtemperament (0-1c)
! 3.5.n
|
|  
|  
|
| schismic aka [[helmholtz]]
| [[kwazy]]
|}
== 7-limit ==
{| class="wikitable"
|+
!
! Approx. 10 notes
! Approx. 20 notes
! Approx. 30 notes
! Approx. 70 notes
! Over 100 notes
|-
! Exotemperament (18-∞c)
| [[antitonic]], [[dicot]], [[father]]
|  
|  
|  
|  
Line 145: Line 118:
|  
|  
|-
|-
! Low accuracy (12-18c)
! 2.3.5.7 (7 limit)
| [[blacksmith]]
| [[blacksmith]]
| [[augene]], [[godzilla]], [[pajara]], [[porcupine]], [[whitewood]]
| [[augene]], [[godzilla]], [[magic]], [[meantone]], [[mothra]], [[orwell]], [[pajara]], [[porcupine]], [[shrutar]], [[whitewood]]
| [[diaschismic]], [[garibaldi]], [[hemiwuerschmidt]], [[miracle]], [[valentine]]
| [[ennealimmal]], [[harry]]
| [[enneadecal]], [[trinity]]
|-
! 2.3.5.11
|  
|  
| [[mohaha]], [[sensible]]
| [[larry]] (2.3.5.11 [[gravity]])
|  
|  
|  
|  
|-
|-
! Medium accuracy (7-12c)
! 2.3.5.n
|  
|  
| [[magic]], [[meantone]], [[mothra]], [[sensi]], [[superpyth]]
| [[cata]], [[nestoria]], [[sensipent]], [[srutal archagall]]
| [[valentine]]
|  
|  
|
|-
! High accuracy (3.5-7c)
|
| [[orwell]]
| [[diaschismic]], [[garibaldi]]
|  
|  
|  
|  
|-
|-
! Very high accuracy (1-3.5c)
! 2.3.7.11
|  
|  
| [[bleu]]
|  
|  
| [[miracle]]
|  
|  
|  
|  
|-
|-
! Microtemperament (0-1c)
! 2.3.7.n
|  
|  
|
|
| [[ennealimmal]]
| [[enneadecal]], [[trinity]]
|}
== 11-limit ==
{| class="wikitable"
|+
!
! Approx. 10 notes
! Approx. 20 notes
! Approx. 30 notes
! Approx. 70 notes
! Over 100 notes
|-
! Exotemperament (18-∞c)
| [[antitonic]], [[dicot]], [[father]]
|  
|  
|  
|  
Line 199: Line 153:
|  
|  
|-
|-
! Low accuracy (12-18c)
! 2.5.7.11
|
| [[augene]], [[blacksmith]], [[pajara]], [[porcupine]], [[whitewood]]
| [[godzilla]], [[superpyth]]
|  
|  
|  
|  
|-
! Medium accuracy (7-12c)
|  
|  
|
| [[magic]], [[meanpop]], [[meantone]], [[mothra]], [[valentine]]
|  
|  
|  
|  
|-
|-
! High accuracy (3.5-7c)
! 2.5.7.n
|  
|  
|  
|  
| [[diaschismic]], [[orwell]]
|  
|  
|  
|  
|-
! Very high accuracy (1-3.5c)
|  
|  
|
| [[miracle]]
|
|
|-
! Microtemperament (0-1c)
|
|
|
| [[ennealimmal]]
| [[enneadecal]], [[trinity]]
|}
== 13-limit ==
{| class="wikitable"
|+
!
! Approx. 10 notes
! Approx. 20 notes
! Approx. 30 notes
! Approx. 70 notes
! Over 100 notes
|-
|-
! Exotemperament (18-∞c)
! 2.5.11.n
|
|
|
|  
|  
|  
|  
|-
! Low accuracy (12-18c)
|  
|  
| [[augene]], [[blacksmith]], [[pajara]], [[porcupine]], [[whitewood]]
| [[superpyth]]
|  
|  
|  
|  
|-
|-
! Medium accuracy (7-12c)
! 3.5.7.n
|
|
| [[magic]], [[meantone]], [[mothra]]
|
|  
|  
|-
! High accuracy (3.5-7c)
|  
|  
|  
|  
| [[diaschismic]], [[orwell]]
|  
|  
|  
|  
|-
|-
! Very high accuracy (1-3.5c)
! 3.5.11.n
|  
|  
|  
|  
Line 281: Line 188:
|  
|  
|-
|-
! Microtemperament (0-1c)
! 2.3.5.7.11 (11 limit)
|  
|
|  
| [[augene]], [[blacksmith]], [[pajara]], [[porcupine]], [[whitewood]]
|  
| [[diaschismic]], godzilla]], [[hemiwuerschmidt]], [[magic]], [[meanpop]], [[meantone]], [[miracle]], [[mothra]], [[nautilus]], [[orwell]], [[shrutar]], [[superpyth]], [[valentine]]
| [[ennealimmal]]
| [[ennealimmal]], [[harry]]
| [[enneadecal]], [[trinity]]
| [[enneadecal]], [[trinity]]
|}
== 17-limit ==
{| class="wikitable"
|+
!
! Approx. 10 notes
! Approx. 20 notes
! Approx. 30 notes
! Approx. 70 notes
! Over 100 notes
|-
|-
! Exotemperament (18-∞c)
! 2.3.5.7.n
|
|  
|  
|  
|  
| [[unicorn]]
|  
|  
|  
|  
|-
|-
! Low accuracy (12-18c)
! 2.3.5.11.n
|  
|  
| [[sensible]]
|  
|  
| [[pajara]]
|  
|  
|  
|  
|-
|-
! Medium accuracy (7-12c)
! 2.3.7.11.n
|
|  
|  
| [[bleu]]
|  
|  
|  
|  
|  
|  
|-
|-
! High accuracy (3.5-7c)
! 2.5.7.11.n
|
|
| [[diaschismic]]
|
|
|-
! Very high accuracy (1-3.5c)
|  
|  
|  
|  
Line 335: Line 223:
|  
|  
|-
|-
! Microtemperament (0-1c)
! 3.5.7.11.n
|
|
|
| [[ennealimmal]]
| [[trinity]]
|}
 
== Higher limits ==
 
{| class="wikitable"
|+
!
! Approx. 10 notes
! Approx. 20 notes
! Approx. 30 notes
! Approx. 70 notes
! Over 100 notes
|-
! Exotemperament (18-∞c)
|  
|  
|  
|  
Line 361: Line 230:
|  
|  
|-
|-
! Low accuracy (12-18c)
! 13 limit
|
|
|
|
|  
|  
| [[augene]], [[blacksmith]], [[pajara]], [[porcupine]], [[whitewood]]
| [[diaschismic]], [[hemiwuerschmidt]], [[magic]], [[meantone]], [[mothra]], [[nautilus]], [[orwell]], [[shrutar]], [[superpyth]]
| [[ennealimmal]], [[harry]]
| [[enneadecal]], [[trinity]]
|-
|-
! Medium accuracy (7-12c)
! 17 limit
|  
|  
|  
|  
| [[diaschismic]], [[echidna]], [[pajara]], [[shrutar]]
| [[ennealimmal]], [[harry]]
| [[trinity]
! Higher limits
|  
|  
|  
|  
|  
| [[shrutar]]
|-
! High accuracy (3.5-7c)
|
|
|
|
|
|-
! Very high accuracy (1-3.5c)
|
|
|
|
|
|-
! Microtemperament (0-1c)
|
|
|
| [[ennealimmal]]
| [[ennealimmal]]
| [[trinity]]
| [[trinity]]
|}
== 3.5.7 and its extensions ==
{| class="wikitable"
|+
!
! Approx. 10 notes
! Approx. 20 notes
! Approx. 30 notes
! Approx. 70 notes
! Over 100 notes
|-
! Exotemperament (18-∞c)
|
|
|
|
|
|-
! Low accuracy (12-18c)
|
|
|
|
|
|-
! Medium accuracy (7-12c)
|
|
|
|
|
|-
! High accuracy (3.5-7c)
|
|
|
|
|
|-
! Very high accuracy (1-3.5c)
|
|
|
|
|
|-
! Microtemperament (0-1c)
|
|
|
|
|
|}
== Other no-2s subgroups ==
{| class="wikitable"
|+
!
! Approx. 10 notes
! Approx. 20 notes
! Approx. 30 notes
! Approx. 70 notes
! Over 100 notes
|-
! Exotemperament (18-∞c)
|
|
|
|
|
|-
! Low accuracy (12-18c)
|
|
|
|
|
|-
! Medium accuracy (7-12c)
|
|
|
|
|
|-
! High accuracy (3.5-7c)
|
|
|
|
|
|-
! Very high accuracy (1-3.5c)
|
|
|
|
|
|-
|-
! Microtemperament (0-1c)
! Other subgroups
|  
|  
|  
|  
Line 505: Line 258:
|}
|}


== No-3s subgroups ==
== Why you should use my favorite temperament ==


{| class="wikitable"
In this section, any editor may create their own subheading, under which they may describe a specific temperament they like and why they think people should use it.  
|+
!
! Approx. 10 notes
! Approx. 20 notes
! Approx. 30 notes
! Approx. 70 notes
! Over 100 notes
|-
! Exotemperament (18-∞c)
|
|
|
|
|
|-
! Low accuracy (12-18c)
|
|
|
|
|
|-
! Medium accuracy (7-12c)
|
| [[didacus]], [[orgone]]
|
|
|
|-
! High accuracy (3.5-7c)
|
|
|
|
|
|-
! Very high accuracy (1-3.5c)
|
|
|
|
|
|-
! Microtemperament (0-1c)
|
|
|
|
|
|}


== 2.3.7 and its extensions ==
One editor is allowed to add more than one temperament if they like, just keep it within reason.


{| class="wikitable"
Editors, please use simple, plain language as much as you can - imagine you're explaining this to a stranger at a bar who has no music theory knowledge at all, but is curious about it.
|+
!
! Approx. 10 notes
! Approx. 20 notes
! Approx. 30 notes
! Approx. 70 notes
! Over 100 notes
|-
! Exotemperament (18-∞c)
|
|
|
|
|
|-
! Low accuracy (12-18c)
| [[semaphore]]
|
|
|
|
|-
! Medium accuracy (7-12c)
|
| [[bleu]], [[slendric]]
|
|
|
|-
! High accuracy (3.5-7c)
|
|
|
|
|
|-
! Very high accuracy (1-3.5c)
|
|
|
|
|
|-
! Microtemperament (0-1c)
|
|
|
|
|
|}
 
== 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)
|
|
|
|
|
|-
! Low accuracy (12-18c)
|
|
|
|
|
|-
! Medium accuracy (7-12c)
|
| [[neutral]] (no-5 no-7 [[rastmic]])
|
|
|
|-
! High accuracy (3.5-7c)
|
| no-5 no-7 [[pythrabian]]
|
|
|
|-
! Very high accuracy (1-3.5c)
|
|
| [[tribilo]] (no-5 no-7 [[nexus]])
|
|
|-
! Microtemperament (0-1c)
|
|
|
|
| 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)
|
|
|
|
|
|-
! Low accuracy (12-18c)
|
|
|
|
|
|-
! Medium accuracy (7-12c)
|
|
|
|
|
|-
! High accuracy (3.5-7c)
|
|
|
|
|
|-
! Very high accuracy (1-3.5c)
|
|
|
|
|
|-
! Microtemperament (0-1c)
|
|
|
|
|
|}
 
== No-7s subgroups ==
 
{| class="wikitable"
|+
!
! Approx. 10 notes
! Approx. 20 notes
! Approx. 30 notes
! Approx. 70 notes
! Over 100 notes
|-
! Exotemperament (18-∞c)
|
|
|
|
|
|-
! Low accuracy (12-18c)
|
|
|
|
|
|-
! Medium accuracy (7-12c)
|
| [[mohaha]]
|
|
|
|-
! High accuracy (3.5-7c)
|
| [[sensible]], [[srutal archagall]]
|
|
|
|-
! Very high accuracy (1-3.5c)
|
| [[cata]], [[nestoria]], [[sensipent]]
|
|
|
|-
! Microtemperament (0-1c)
|
|
|
|
|
|}
 
== No-11s subgroups ==
 
{| class="wikitable"
|+
!
! Approx. 10 notes
! Approx. 20 notes
! Approx. 30 notes
! Approx. 70 notes
! Over 100 notes
|-
! Exotemperament (18-∞c)
|
|
|
|
|
|-
! Low accuracy (12-18c)
|
|
|
|
|
|-
! Medium accuracy (7-12c)
|
|
|
|
|
|-
! High accuracy (3.5-7c)
|
|
|
|
|
|-
! Very high accuracy (1-3.5c)
|
|
|
|
|
|-
! Microtemperament (0-1c)
|
|
|
|
|
|}
 
== Other subgroups ==
 
{| class="wikitable"
|+
!
! Approx. 10 notes
! Approx. 20 notes
! Approx. 30 notes
! Approx. 70 notes
! Over 100 notes
|-
! Exotemperament (18-∞c)
|
|
|
|
|
|-
! Low accuracy (12-18c)
|
|
|
|
|
|-
! Medium accuracy (7-12c)
|
|
|
|
|
|-
! High accuracy (3.5-7c)
|
|
|
|
|
|-
! Very high accuracy (1-3.5c)
|
|
|
|
|
|-
! Microtemperament (0-1c)
|
|
|
|
|
|}
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