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

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{{Editable user page|Please add temperaments you can think of that fit the categories. If any temperaments are in the incorrect category, please move them to the correct category.}}
Currently under reconstruction. Will be rewritten from the ground up maybe.
 
This is a page to easily navigate to temperaments that fit your interests.
 
'''Low complexity temperaments''' are likely to be of most interest to artists new to music tuning theory. That is because they tend to approximate all of the important intervals within less than 30 notes (occasionally even less than 12!), so they are the most practical to map onto a physical instrument.
 
'''Medium and higher''' complexity temperaments provide a bigger range of new intervals, and they approximate those intervals more accurately, but they may be unwieldy, requiring dozens or even hundreds of notes to approximate all the important intervals.
 
Feel free to add temperaments to the appropriate category if they are not already here. (If you're not sure which category to put them in, put them in honorable mentions).
 
== Low complexity temperaments ==
Temperaments which approximate most of their consonant intervals with less than 30 notes, and where those intervals are mostly less than 20 cents out of tune. (In a similar ballpark to 12edo.)
 
 
'''1.1''' 5-limit
 
[[augmented]], [[blackwood]], [[diminished]], [[mavila]], [[meantone]], [[porcupine]], [[srutal]]
 
 
'''1.2''' 7-limit
 
[[augene]], [[august]], [[blacksmith]],  [[diminished|septimal diminished]], [[dominant]], [[injera]], [[negri|septimal negri]], [[pajara]], [[semaphore]], [[septimal meantone]]
 
 
'''1.3''' No-2s subgroups of 7-limit
 
 
'''1.4''' Other subgroups of 7-limit
 
 
'''1.5''' 11-limit
 
[[augene|undecimal augene]], [[darjeeling]], [[dominant|undecimal dominant]], [[duodecim]], [[flattone|undecimal flattone]], [[godzilla]], [[hedgehog|undecimal hedgehog]], [[injera|undecimal injera]], [[keemun|undecimal keemun]], [[meanenneadecal]], [[nautilus|undecimal nautilus]], [[negric]], [[pajara|undecimal pajara]], [[porcupine|undecimal porcupine]], [[progress]], [[triforce]], [[undevigintone]]
 
 
'''1.6''' No-2s subgroups of 11-limit
 
 
'''1.7''' Other subgroups of 11-limit
 
 
'''1.8''' 13-limit
 
 
'''1.9''' No-2s of 13-limit
 
 
'''1.10''' No-2s subgroups of 13-limit
 
 
'''1.11''' Other subgroups of 13-limit
 
 
'''1.12''' Higher limits
 
 
'''1.13''' No-2s higher limit subgroups
 
 
'''1.14''' Other higher limit subgroups
 
== Medium complexity temperaments ==
 
Temperaments which approximate most of their consonant intervals with less than 70 notes, and where those intervals are mostly less than 5 cents out of tune.
 
 
'''2.1''' 5-limit
 
[[amity]], [[compton]], [[hanson]] (aka kleismic), [[helmholtz]] (aka schismic), [[magic]], [[negri]], [[orson]], [[passion]], [[ripple]], [[sensi]], [[superpyth]], [[tetracot]], [[wuerschmidt]]
 
 
'''2.2''' 7-limit
 
[[beatles]], [[catler]], [[cynder]], [[diaschismic]], [[doublewide]], [[flattone]], [[garibaldi]], [[hedgehog]], [[keemun]], [[lemba]], [[liese]], [[magic|septimal magic]], [[miracle]], [[myna]], [[nautilus]], [[orwell]], [[porcupine|septimal porcupine]], [[sensi|septimal sensi]], [[superpyth|septimal superpyth]]
 
 
'''2.3''' No-2s subgroups of 7-limit
 
 
'''2.4''' Other subgroups of 7-limit
* [[didacus]] (2.5.7)
 
 
'''2.5''' 11-limit
 
[[andromeda]], [[astrology]], [[catnip]], [[diaschismic|undecimal diaschismic]] [[fleetwood]], [[magic|undecimal magic]], [[meanpop]], [[migration]], [[miracle|undecimal miracle]], [[mohajira]], [[negroni]], [[nusecond]], [[orwell|undecimal orwell]], [[pajarous]], [[porky]], [[quasisupra]], [[sensis]], [[squares]], [[superpyth|undecimal superpyth]], [[suprapyth]], [[telepathy]], [[undecimal meantone]], [[valentine]], [[vigintiduo]]
 
 
'''2.6''' No-2s subgroups of 11-limit
 
 
'''2.7''' Other subgroups of 11-limit
* [[didacus|undecimal didacus]] (2.5.7.11)
* [[orgone]] (2.7.11)
 
 
'''2.8''' 13-limit
 
 
'''2.9''' No-2s of 13-limit
 
 
'''2.10''' No-2s subgroups of 13-limit
 
 
'''2.11''' Other subgroups of 13-limit
* [[cata]] (2.3.5.13)
 
 
'''2.12''' Higher limits
 
 
'''2.13''' No-2s higher limit subgroups
 
 
'''2.14''' Other higher limit subgroups
 
== High complexity temperaments ==
 
Temperaments where most of their consonant intervals are less than 1 cent out of tune. Usually require at least 100 notes per equave for the best approximation.
 
 
'''3.1''' 5-limit
 
[[amity]], [[counterschismic]], [[dodifo]], [[enneadecal]], [[ennealimmal]], [[gammic]], [[hanson]] (aka kleismic), [[helmholtz]] (aka schismic), [[kwazy]], [[lafa]], [[luna]], [[minortone]], [[monzismic]], [[parakleismic]], [[qintosec]], [[squarschmidt]], [[tricot]], [[vavoom]], [[vishnu]], [[vulture]], [[whoosh]]
 
 
'''3.2''' 7-limit
 
[[abigail]], [[brahmagupta]], [[decoid]],  [[enneadecal|septimal enneadecal]], [[ennealimmal|septimal ennealimmal]], [[newt]], [[orga]], [[pontiac]], [[quasiorwell]], [[sesquiquartififths]], [[subneutral]], [[supermajor]], [[tertiaseptal]], [[vishnu|septimal vishnu]], [[vulture]]
 
 
'''3.3''' No-2s subgroups of 7-limit
 
 
'''3.4''' Other subgroups of 7-limit
* [[slendric]] (2.3.7)
 
 
'''3.5''' 11-limit
 
[[abigail|undecimal abigail]], [[bisesqui]], [[decoid|undecimal decoid]], [[hemienneadecal]], [[hemiennealimmal]], [[hemitert]], [[newt|undecimal newt]], [[orga|undecimal orga]], [[quadraennealimmal]], [[quasiorwell|undecimal quasiorwell]], [[quasithird]], [[semisupermajor]], [[vishnu|undecimal vishnu]]
 
 
'''3.6''' No-2s subgroups of 11-limit
 
 
'''3.7''' Other subgroups of 11-limit
 
 
'''3.8''' 13-limit
 
 
'''3.9''' No-2s of 13-limit
 
 
'''3.10''' No-2s subgroups of 13-limit
 
 
'''3.11''' Other subgroups of 13-limit
 
 
'''3.12''' Higher limits
 
 
'''3.13''' No-2s higher limit subgroups
 
 
'''3.14''' Other higher limit subgroups
 
== Honorable mentions ==
 
Temperaments which are interesting in some way, but might not meet the criteria for the other lists.
 
 
'''4.1''' 5-limit
 
 
'''4.2''' 7-limit
 
 
'''4.3''' No-2s subgroups of 7-limit
 
 
'''4.4''' Other subgroups of 7-limit
 
 
'''4.5''' 11-limit
 
 
'''4.6''' No-2s subgroups of 11-limit
 
 
'''4.7''' Other subgroups of 11-limit
 
 
'''4.8''' 13-limit
 
 
'''4.9''' No-2s of 13-limit
 
 
'''4.10''' No-2s subgroups of 13-limit
 
 
'''4.11''' Other subgroups of 13-limit
 
 
'''4.12''' Higher limits
 
 
'''4.13''' No-2s higher limit subgroups
 
 
'''4.14''' Other higher limit subgroups
 
== Exotemperaments ==
 
Temperaments where most intervals are at least 20 cents out of tune.
 
 
'''5.1''' 5-limit
 
[[father]], [[bug]]
 
 
'''5.2''' 7-limit
 
 
'''5.3''' No-2s subgroups of 7-limit
 
 
'''5.4''' Other subgroups of 7-limit
 
 
'''5.5''' 11-limit
 
 
'''5.6''' No-2s subgroups of 11-limit
 
 
'''5.7''' Other subgroups of 11-limit
 
 
'''5.8''' 13-limit
 
 
'''5.9''' No-2s of 13-limit
 
 
'''5.10''' No-2s subgroups of 13-limit
 
 
'''5.11''' Other subgroups of 13-limit
 
 
'''5.12''' Higher limits
 
 
'''5.13''' No-2s higher limit subgroups
 
 
'''5.14''' Other higher limit subgroups
 
== Rank-3 low complexity temperaments ==
 
All the temperaments listed before this point are [[rank-2 temperament]]s, which are intuitive to understand because they have just one [[period]] and one [[generator]].
 
By contrast, a [[rank-3 temperament]] has ''three'' generators. Read the rank-3 temperament article to learn more. If you don’t get it, don’t worry, there are more than enough rank-2 temperaments to explore and most composers stick to those.
 
 
'''6.1''' 7-limit
 
[[starling]]
 
 
'''6.2''' 11-limit
 
[[starling|undecimal starling]]
 
 
'''6.3''' No-2s subgroups of 11-limit
 
 
'''6.4''' Other subgroups of 11-limit
 
 
'''6.5''' 13-limit
 
 
'''6.6''' No-2s of 13-limit
 
 
'''6.7''' No-2s subgroups of 13-limit
 
 
'''6.8''' Other subgroups of 13-limit
 
 
'''6.9''' Higher limits
 
 
'''6.10''' No-2s higher limit subgroups
 
 
'''6.11''' Other higher limit subgroups
 
== Rank-3 medium complexity temperaments ==
 
 
'''7.1''' 7-limit
 
[[gamelismic]], [[rank-3 kleismic]], [[marvel]], [[sensamagic]], [[starling]]
 
 
'''7.2''' 11-limit
 
[[portent]], [[sensamagic|undecimal sensamagic]], [[starling|undecimal starling]], [[unimarv]]
 
 
'''7.3''' No-2s subgroups of 11-limit
 
 
'''7.4''' Other subgroups of 11-limit
 
 
'''7.5''' 13-limit
 
[[sensamagic|tridecimal sensamagic]], [[unimarv|tridecimal unimarv]]
 
 
'''7.6''' No-2s of 13-limit
 
 
'''7.7''' No-2s subgroups of 13-limit
 
 
'''7.8''' Other subgroups of 13-limit
* [[rank-3 kleismic|tridecimal rank-3 kleismic]] (2.3.5.7.13)
 
 
'''7.9''' Higher limits
 
 
'''7.10''' No-2s higher limit subgroups
 
 
'''7.11''' Other higher limit subgroups
 
== Rank-3 high complexity temperaments ==
 
 
'''8.1''' 7-limit
 
 
'''8.2''' 11-limit
 
 
'''8.3''' No-2s subgroups of 11-limit
 
 
'''8.4''' Other subgroups of 11-limit
 
 
'''8.5''' 13-limit
 
 
'''8.6''' No-2s of 13-limit
 
 
'''8.7''' No-2s subgroups of 13-limit
 
 
'''8.8''' Other subgroups of 13-limit
 
 
'''8.9''' Higher limits
 
 
'''8.10''' No-2s higher limit subgroups
 
 
'''8.11''' Other higher limit subgroups
 
== Rank-3 honorable mentions ==
 
 
'''9.1''' 7-limit
 
 
'''9.2''' 11-limit
 
 
'''9.3''' No-2s subgroups of 11-limit
 
 
'''9.4''' Other subgroups of 11-limit
 
 
'''9.5''' 13-limit
 
 
'''9.6''' No-2s of 13-limit
 
 
'''9.7''' No-2s subgroups of 13-limit
 
 
'''9.8''' Other subgroups of 13-limit
 
 
'''9.9''' Higher limits
 
 
'''9.10''' No-2s higher limit subgroups
 
 
'''9.11''' Other higher limit subgroups
 
== Rank-3 exotemperaments ==
 
 
'''10.1''' 7-limit
 
 
'''10.2''' 11-limit
 
 
'''10.3''' No-2s subgroups of 11-limit
 
 
'''10.4''' Other subgroups of 11-limit
 
 
'''10.5''' 13-limit
 
 
'''10.6''' No-2s of 13-limit
 
 
'''10.7''' No-2s subgroups of 13-limit
 
 
'''10.8''' Other subgroups of 13-limit
 
 
'''10.9''' Higher limits
 
 
'''10.10''' No-2s higher limit subgroups
 
 
'''10.11''' Other higher limit subgroups
 
 
== Rank-4 and higher temperaments ==
Temperaments of [[Rank-4 temperament|rank 4]] and above.
 
 
'''11.1''' 7-limit
 
 
'''11.2''' 11-limit
 
 
'''11.3''' 13-limit
 
 
'''11.4''' No-2s of 13-limit
 
 
'''11.5''' No-2s subgroups of 13-limit
 
 
'''11.6''' Other subgroups of 13-limit
 
 
'''11.7''' Higher limits
 
 
'''11.8''' No-2s higher limit subgroups
 
 
'''11.9''' Other higher limit subgroups

Revision as of 05:30, 16 October 2024

Currently under reconstruction. Will be rewritten from the ground up maybe.

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