Survey of efficient temperaments by subgroup: Difference between revisions

! ~10 notes per equave<ref group="note">Number of notes per equave was estimated by multiplying the temperament’s [[graham complexity]] by 2.</ref>

| [[hanson]], [[magic]], [[meantone]], [[negri]], [[augmented (temperament)|augmented]], [[porcupine]], [[diminished (temperament)|diminished]], [[whitewood]], [[blackwood]], [[mavila]]

| [[helmholtz (temperament)|helmholtz]], [[orson]], [[würschmidt]], [[sensipent]], [[compton]], [[valentine]], [[diaschismic]], [[tetracot]], [[passion]], [[superpyth]], [[ripple]]

| [[kwazy]], [[luna]], [[vishnu]], [[parakleismic]], [[escapade]], [[amity]], [[misty]], [[gravity]], [[rodan]]

| [[enneadecal]], [[gammic]], [[vulture]]

| [[porcupine]], [[pajara]], [[keemun]], [[negri]], [[doublewide]], [[injera]], [[dominant (temperament)|dominant]], [[august]], [[diminished (temperament)|diminished]], [[blackwood]]

| [[orwell]], [[valentine]], [[myna]], [[magic]], [[meantone]], [[mothra]], [[superpyth]], [[flattone]], [[liese]], [[beatles]], [[augene]], [[hedgehog]], [[nautilus]], [[catler]], [[godzilla]], [[lemba]]

| [[amity]], [[hemiwürschmidt]], [[harry]], [[miracle]], [[garibaldi]], [[diaschismic]], [[sensi]]

| [[misty]], [[unidec]], [[catakleismic]]

| [[triforce]], [[blackwood]], [[pajaric]], [[negric]]

| [[orwell]], [[valentine]], [[mohajira]], [[porcupine]], [[hedgehog]], [[astrology]], [[vigintiduo]], [[augene]], [[nautilus]], [[catnip]], [[undevigintone]], [[injera]], [[keemun]], [[progress]], [[dominant (temperament)|dominant]], [[meanenneadecal]], [[duodecim]]

| [[mothra]], [[nusecond]], [[meantone]], [[squares]], [[quasisupra]], [[pajara]], [[telepathy]], [[suprapyth]], [[negroni]], [[porky]], [[fleetwood]], [[pajarous]], [[sensis]], [[flattone]], [[godzilla]], [[darjeeling]]

| [[miracle]], [[shrutar]], [[magic]], [[meanpop]], [[migration]], [[andromeda]], [[superpyth]]

| [[negric]]

| [[augene]], [[porcupine]], [[hedgehog]], [[triforce]], [[godzilla]], [[negri]], [[armodue (temperament)|armodue]]

| [[nusecond]], [[modus]], [[lupercalia]], [[fokkertone]], [[winston]], [[pajara]], [[sensis]], [[ringo]], [[flattone]], [[darjeeling]], [[meanenneadecal]]

| [[miraculous]], [[leapday]], [[andromeda]], [[superkleismic]], [[mothra]], [[mohajira]], [[undevigintone]], [[ogene]], [[nautilus]], [[negroni]], [[injera]]

| [[lemba]]+, [[hedgehog]]+

| [[nusecond]]+, [[crepuscular]], [[winston]]+, [[pajara]], [[negroni]]+, [[sensis]]+, [[ringo]]+, [[pajarous]], [[augene]]+

| [[miraculous]], [[lupercalia]]+, [[mohajira]], [[superpyth]]+, [[meantoid]], [[injera]], [[meanenneadecal]]

| [[niner]]++

| [[wilsec]], [[winston]]++, [[augene]]++, [[sensis]]++

| [[roman]]++, [[mohajira]], [[lupercalia]]++, [[superpyth]]++, [[negroni]]++, [[meanenneadecal]], [[ringo]]++, [[injera]], [[meantoid]]

| [[lupercalia]]+++, [[nautilus]]+++, [[negroni]]+++, [[injera]]+

Subgroups ''without'' a "5" ''don't have'' multiple of 3 intervals (eg the 5/3 major sixth, the 5/4 major third, the 6/5 minor third).

! ~10 notes per equave

| [[negra]]

| no-11 [[godzilla]], no-11 [[pajara]], no-11 [[duodecim]]

| no-11 [[magic]], no-11 [[sensis]], no-11 [[meanpop]]

| no-11 [[catakleismic]]

| [[porcupine]], [[mavila]], [[dicot]], [[flattone]]

| [[orson]]+, [[tetracot]], [[mohaha]]

| [[larry]] (no-7 [[gravity]]), [[countdown]], no-7 [[catalan]]

| [[escapade]]

| [[srutal archagall]], [[stutzel]]

| [[sensipent]], [[nestoria]]

| [[würschmidt]]<ref group="note">Subgroup 2.3.5.23 version.</ref>, [[cata]]

| [[slendric]], [[archy]], [[bleu]], [[semaphore]]

| [[stearnsmic clan|stearnsmic]], [[skwares]]

| [[hemif]], [[leapfrog]]

| [[bleu]], [[supra]], [[semaphore]]+

| [[skwares]], [[stearnsmic clan|stearnsmic]]+, [[suhajira]]

| no-5 [[miracle]], [[radon]]^, [[hemif]]^<ref group="note">^Hemif beats radon in 2.3.7.11, radon beats hemif in 2.3.7.11.13 (in damage not badness).</ref>, [[leapfrog]]

| [[baladic]], [[oceanfront]], no-5 [[negra]]

| no-5 no-11 [[liese]], no-11 [[skwares]]

| [[neutral (temperament)|neutral]] (2.3.11 [[rastmic]]), [[namo]], [[paralimmal]], [[io]]

| [[tribilo]] (2.3.11 [[nexus]]), [[huxley]]

| [[barbados]], [[boethian]], [[semitonic]], [[superflat]], [[hydrothermal]]

| [[threedic]], [[pepperoni]]

| [[didacus]], [[frostburn]], no-3 [[oodako]], [[augment]]

| [[rainy]], [[mercy]], [[huntington]]

| [[llywelyn]], [[silver]], [[baldy]]

| [[roulette]]

| [[insect]], [[sulis]], [[wizz]], [[vengeance]], [[marveltri]], [[superquintal]], [[movila]]

| no-3 no-7 [[emka]], [[wizz]]+

| [[orgone]], [[shipwreck]], [[stacks]], [[ultrakleismic]], [[machine]]

| [[counterultrakleismic]], [[mechanism]], [[mabon]]

| [[machine|apparatus]]

| [[canopus]], [[BPS]], [[sirius]], [[arcturus]], [[dubhe]], [[Catalog of 3.5.7 subgroup rank two temperaments|vega]]  

| [[izar]], [[mintra]]

| [[alhena]], [[remus]]

| [[erigone]]

| [[aldebaran]], [[deneb]], [[polaris]]

| [[alnilam]], [[fomalhaut]]

| [[mintaka]] (no-13), [[keladic]]

| [[mebsuta]], [[minalzidar]]

| [[mintaka]] (with 13)

| [[meanquad]], [[tetrahanson]], [[tetrameantone]], [[quarchy]], [[tetrominant]]

| [[antipyth]], [[juggernaut]]

| [[greeley]], [[halftone]], [[semiwolf]], [[auk]]

! ~50 notes

! ~60 notes

! ~70 notes

! ~80 notes

! >90 notes

| [[ennealimmal]], [[quintosec]], [[counterhanson]], [[undim]]

| [[alphatricot]], [[quintile]]

| [[minortone]], [[vavoom]]

| [[ennealimmal]], [[tertiaseptal]], [[hemififths]], [[quadritikleismic]], [[grendel]], [[unidec]]

| [[hendecatonic]]

| [[sesquiquartififths]], [[quinmite]], [[parakleismic]]

| [[neptune]], [[gamera]], [[nessafof]], [[octoid]], [[septiquarter]]

| [[supermajor (temperament)|supermajor]], [[enneadecal]], [[term]]

| [[unidec]], [[tritikleismic]], [[hemithirds]], [[wizard]], [[diaschismic]]

| [[quadritikleismic]], [[harry]]

| [[quasiorwell]], [[octoid]], [[sqrtphi]], [[hemiwürschmidt]], [[ennealimnic]], [[catakleismic]]

| [[hemienneadecal]], [[hemiennealimmal]], [[abigail]], [[hemitert]], [[newt]], [[decoid]], [[vishnu]]

| [[hemififths]], [[orwell]], [[magic]]

| [[diaschismic]], [[myna]], [[sensus]], [[meanpop]]

| [[cassandra]], [[grosstone]]

| [[widefourth]], [[octopus]], [[mystery]], [[buzzard]], [[catakleismic]], [[rodan]], [[shrutar]]

| [[abigail]], [[satin]], [[trinity]], [[newt]], [[acyuta]], [[deca]], [[quasiorwell]], [[decoid]], [[vulture]], [[hemiennealimmal]], [[emkay]], [[countercata]]

| [[leapday]], [[superkleismic]]+, [[fokkertone]]+, [[fokkertone]]

| [[hendec]], [[marvolo]], [[diaschismic]], [[sensus]], [[andromeda]], [[modus]]

| [[comptone]]

| [[heinz]], [[octopus]], [[lizard]], [[rodan]], [[echidna]], [[shrutar]]

| [[satin]], [[trinity]], [[octoid]], [[quincy]], [[mirkat]], [[ekadash]]+, [[quadritikleismic]], [[neominor]]+, [[ennealimnic]], [[sqrtphi]]

| [[octacot]], [[andromeda]], [[fokkertone]]+, [[fokkertone]]

| [[hendec]]+, [[sensus]]+, [[crepuscular]]+, [[hitchcock]], [[modus]]

| [[marvolo]], [[miraculous]]+

| [[octopus]], [[ennealim]], [[bikleismic]], [[srutal]], [[valentino]]+

| [[newt|neonewt]]+, [[deca]]+, [[vulture]], [[satin]], [[stearnscape]]+, [[hemiennealimmal]], [[trinity]], [[quincy]], [[octoid]], [[sqrtphi]]

| [[srutaloo]], [[shrutar]]

| [[satin]], [[trinity]], [[sqrtphi]]+, [[gizzard]]+, [[ketchup]], [[semisept]], [[cassandric]]

| no-11 [[harry]], [[unicorn]]

| no-11 [[buzzard]], no-11 [[orwell]]

| no-11 [[cassandra]]

| no-11 [[hemischis]]

| no-11 [[ennealimmal]], no-11 [[decoid]], no-11 [[ennealimnic]], no-11 [[quadritikleismic]]

| no-7 [[quintosec]], [[quintile]]+, no-7 [[maquila]], [[sensible]], [[ampersand]]+

| [[twentcufo]], no-7 [[emka]], no-7 [[gwazy]], no-7 [[rodan]], no-7 [[cataclysmic]], no-7 [[sfourth]]

| [[majvam]]+

| no-7 [[hemienneadecal]], no-7 [[vulture]]

| [[majvam]]

| no-5 [[quanic]]

| [[hypnosis]]

| rank-2 [[pythrabian]]

| rank-2 [[frameshift]]

| [[Subgroup temperaments #Daemotertiaschis|daemotertiaschis]]

These are the top 105 rank-2 temperament pages with the most incoming links on the wiki as of 23 Oct 2025, about one year after this section was first written.

# '''[[Meantone]] (479)'''

# '''[[Porcupine]] (195)'''

# '''[[Superpyth]] (162)'''

# '''[[Magic]] (153)'''

# '''[[Mavila]] (127)'''

# '''[[Miracle]] (112)'''

# '''[[Orwell]] (111)'''

# '''[[Blackwood]] (95)'''

# '''[[Flattone]] (95)'''

# '''[[Sensi]] (92)'''

# '''[[Pajara]] (91)'''

# '''[[Slendric]] (89)'''

# '''[[Valentine]] (87)'''

# '''[[Negri]] (84)'''

# '''[[Tetracot]] (82)'''

# '''[[Mohajira]] (79)'''

# '''[[Compton]] (70)'''

# '''[[Amity]] (69)'''

# '''[[Diaschismic]] (69)'''

# [[Garibaldi]] (68)

# [[Dicot]] (64)

# [[Ennealimmal]] (60)

# [[Father]] (60)

# [[Diminished (temperament)|Diminished]] (59)

# [[Mothra]] (58)

# [[Myna]] (57)

# [[Rodan]] (57)

# [[Catakleismic]] (57)

# [[Godzilla]] (56)

# [[Hanson]] (56)

# [[Squares]] (55)

# [[Hemififths]] (54)

# [[Injera]] (53)

# [[Octacot]] (53)

# [[Semaphore]] (52)

# [[Archy]] (50)

# [[Augmented (temperament)|Augmented]] (50)

# [[Helmholtz (temperament)|Helmholtz]] (48)

# [[Superkleismic]] (46)

# [[Whitewood]] (43)

# [[Buzzard]] (43)

# [[Orgone]] (42)

# [[Dominant (temperament)|Dominant]] (42)

# [[Kleismic]] (42) (already listed as ''hanson'')

# [[Liese]] (42)

# [[Didacus]] (41)

# [[Hemiwürschmidt]] (41)

# [[Parakleismic]] (41)

# [[Vishnu]] (40)

# [[Enneadecal]] (40)

# [[Hemithirds]] (40)

# [[Lemba]] (40)

# [[Srutal]] (39)

# [[Hedgehog]] (39)

# [[Luna]] (38)

# [[Triforce]] (38)

# [[Echidna]] (37)

# [[Ripple]] (36)

# [[Tritonic]] (36)

# [[Escapade]] (36)

# [[Passion]] (35)

# [[Schismic]] (35) (already listed as ''helmholtz'')

# [[Nautilus]] (34)

# [[Bleu]] (34)

# [[Vulture]] (33)

# [[Wizard]] (33)

# [[Orson]] (32)

# [[Schismatic]] (32) (already listed as ''helmholtz'')

# [[Unidec]] (31)

# [[Muggles]] (30)

# [[Sensipent]] (30)

# [[Tritikleismic]] (30)

# [[Beatles]] (29)

# [[Bohpier]] (29)

# [[Machine]] (29)

# [[Misty]] (28)

# [[Mohaha]] (28)

# [[Pontiac]] (28)

# [[Sqrtphi]] (24)