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

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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, septimal diminished, dominant, injera, 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

undecimal augene, darjeeling, undecimal dominant, duodecim, undecimal flattone, godzilla, undecimal hedgehog, undecimal injera, undecimal keemun, meanenneadecal, undecimal nautilus, negric, undecimal pajara, 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, 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, septimal magic, miracle, myna, nautilus, orwell, septimal porcupine, septimal sensi, septimal superpyth


2.3 No-2s subgroups of 7-limit


2.4 Other subgroups of 7-limit


2.5 11-limit

andromeda, astrology, catnip, undecimal diaschismic fleetwood, undecimal magic, meanpop, migration, undecimal miracle, mohajira, negroni, nusecond, undecimal orwell, pajarous, porky, quasisupra, sensis, squares, undecimal superpyth, suprapyth, telepathy, undecimal meantone, valentine, vigintiduo


2.6 No-2s subgroups of 11-limit


2.7 Other subgroups of 11-limit


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


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, helmholtz (aka schismic), kwazy, lafa, luna, minortone, monzismic, parakleismic, qintosec, squarschmidt, tricot, vavoom, vishnu, vulture, whoosh


3.2 7-limit

abigail, brahmagupta, decoid, septimal enneadecal, septimal ennealimmal, newt, orga, pontiac, quasiorwell, sesquiquartififths, subneutral, supermajor, tertiaseptal, septimal vishnu, vulture


3.3 No-2s subgroups of 7-limit


3.4 Other subgroups of 7-limit


3.5 11-limit

undecimal abigail, bisesqui, undecimal decoid, hemienneadecal, hemiennealimmal, hemitert, undecimal newt, undecimal orga, quadraennealimmal, undecimal quasiorwell, quasithird, semisupermajor, 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 temperaments, 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 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, marvel, sensamagic, starling


7.2 11-limit portent, undecimal sensamagic, undecimal starling, unimarv


7.3 No-2s subgroups of 11-limit


7.4 Other subgroups of 11-limit


7.5 13-limit tridecimal sensamagic, tridecimal unimarv


7.6 No-2s of 13-limit


7.7 No-2s subgroups of 13-limit


7.8 Other subgroups of 13-limit


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 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

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