Survey of efficient temperaments by subgroup: Difference between revisions

== How to read the tables ==

'''The rows categorise temperaments by the [[just intonation subgroup]] they approximate.'''

The 2.3.5 subgroup is what most theorists believe 12 tone equal temperament belongs to. If those theorists are correct, then 2.3.5 should encompass all the harmonies that are familiar to most Western listeners.

The same temperament may occur multiple times on a table if it is good at approximating multiple different subgroups. For example, magic is good at approximating both the 7-limit and the 11-limit, so it is listed under both.

'''The columns categorise temperaments by the approximate number of notes-per-[[equave]] needed to reach all the temperament’s important intervals'''.

All of the temperaments listed in these tables 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.

{| class="wikitable center-all"

|-

! ~40 notes

|-

| [[hanson]], [[misty]], [[magic]], [[meantone]], [[negri]], [[augmented]], [[porcupine]], [[dimipent]], [[whitewood]], [[blackwood]], [[mavila]]

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

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

|-

| [[porcupine]], [[pajara]], [[keemun]], [[negri]], [[doublewide]], [[injera]], [[dominant]], [[august]], [[diminished]], [[blacksmith]]

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

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

|-

| [[triforce]], [[blacksmith]], [[pajaric]], [[negric]]

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

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

|-

| [[negric]]

| [[augene]], [[porcupine]], [[hedgehog]], [[triforce]], [[godzilla]], [[negri]], [[armodue]]

| [[nusecond]], [[modus]], [[lupercalia]], [[Meantone_family#Tridecimal_meantone|meantone]], [[winston]], [[pajara]], [[sensis]], [[ringo]], [[flattone]], [[darjeeling]], [[meanenneadecal]]

|-

|  

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

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

|-

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| [[niner]]++

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

|-

| [[negra]]

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

| no-11 [[catakleismic]]

|-

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

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

| [[escapade]]

|-

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

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

|  

|-

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

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

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|-

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

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| [[slendric]]+

|-

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

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

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

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|-

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

| [[rainy]], [[mercy]], [[huntington]], [[llywelyn]], [[baldy]]

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|-

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

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| [[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]]

| [[erigone]]

|-

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

|  

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

|-

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

| [[mintaka]] (with 13)

|  

|-

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

|  

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|-

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

|  

! >90 notes

|-

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

|  

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|-

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

| [[hendecatonic]]

| [[supermajor]], [[enneadecal]], [[term]]

|-

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

|  

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

|-

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

|-

| [[leapday]], [[superkleismic]]+, [[meantonic]], [[huygens]]

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

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

|-

| [[octacot]], [[andromeda]], [[meantonic]], [[huygens]]

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

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

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

|-

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

|-

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

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

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

|-

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

|  

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

|-

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| no-5 [[quanic]]

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| [[hypnosis]]

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| rank-2 [[pythrabian]]

| rank-2 [[frameshift]]

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# '''[[Compton]] (51)'''

# [[Ennealimmal]] (50)

# [[Dicot]] (47)

# [[Garibaldi]] (47)