Survey of efficient temperaments by subgroup: Difference between revisions
→Most linked-to rank-2 temperaments: update for 2026 |
Review for 17- & 19-limit; might still be more to move around |
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! JI subgroup | ! JI subgroup | ||
! ~ | ! ~5 notes per equave<ref group="note">Number of notes per equave is estimated by the temperament's [[graham complexity]] of a reasonable odd limit.</ref> | ||
! ~10 notes | |||
! ~15 notes | |||
! ~20 notes | ! ~20 notes | ||
|- | |- | ||
! 5-limit <br>(2.3.5) | ! 5-limit <br>(2.3.5) | ||
| [[ | | [[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]] | ||
| [[ | | [[Luna]], [[vishnu]], [[parakleismic]], [[escapade]], [[amity]], [[misty]], [[gravity]], [[rodan]] | ||
| [[ | | [[Enneadecal]], [[gammic]], [[vulture]] | ||
|- | |- | ||
! 7-limit <br>(2.3.5.7) | ! 7-limit <br>(2.3.5.7) | ||
| [[ | | [[Dominant (temperament)|Dominant]], [[august]], [[blackwood]] | ||
| [[Magic]], [[meantone]], [[superpyth]], [[liese]], [[augene]], [[porcupine]], [[pajara]], [[negri]], [[keemun]], [[catler]], [[godzilla]], [[hedgehog]], [[injera]], [[nautilus]], [[diminished (temperament)|diminished]] | |||
| [[ | | [[Garibaldi]], [[orwell]], [[sensi]], [[mothra]], [[flattone]], [[beatles]], [[doublewide]], [[lemba]] | ||
| [[Catakleismic]], [[miracle]], [[valentine]], [[myna]], [[diaschismic]] | |||
|- | |- | ||
! 11-limit <br>(2.3.5.7.11) | ! 11-limit <br>(2.3.5.7.11) | ||
| [[ | | | ||
| [[Porcupine]], [[augene]], [[hedgehog]], [[catnip]], [[nautilus]], [[injera]], [[godzilla]], [[triforce]], [[progress]], [[meanenneadecal]], [[duodecim]], [[negric]], [[dominant (temperament)|dominant]], [[blackwood]], [[pajaric]] | |||
| [[Orwell]], [[nusecond]], [[squares]], [[quasisupra]], [[pajara]], [[porky]], [[sensis]], [[telepathy]], [[suprapyth]], [[pajarous]], [[flattone]], [[keemun]], [[darjeeling]] | |||
| [[Miracle]], [[valentine]], [[shrutar]], [[magic]], [[andromeda]], [[mothra]], [[migration]], [[meantone]], [[mohajira]], [[superpyth]], [[undevigintone]], [[astrology]], [[vigintiduo]], [[negroni]], [[fleetwood]] | |||
|- | |- | ||
! 13-limit <br>(2.3.5.7.11.13) | ! 13-limit <br>(2.3.5.7.11.13) | ||
| [[ | | | ||
| [[Porcupinefowl]], [[hedgehog]], [[triforce]], [[godzilla]], [[augene]], [[negric]], [[negri]], [[armodue (temperament)|armodue]] | |||
| [[ | | [[Winston]], [[sensis]], [[ringo]], [[flattone]], [[darjeeling]], [[meanenneadecal]], [[pajara]] | ||
| [[Miraculous]], [[leapday]], [[superkleismic]], [[mothra]], [[nusecond]], [[modus]], [[lupercalia]], [[mohajira]], [[fokkertone]], [[undevigintone]], [[ogene]], [[negroni]], [[nautilus]], [[injera]] | |||
|- | |- | ||
! 17-limit <br>(2.3.5.7.11.13.17) | ! 17-limit <br>(2.3.5.7.11.13.17) | ||
| | | | ||
| | | | ||
| [[ | | [[Pajara]], [[pajarous]] | ||
| [[ | | [[Miraculous]], [[mohajira]], [[crepuscular]], [[injera]], [[meanenneadecal]] | ||
|- | |- | ||
! 19-limit <br>(2.3.5.7.11.13.17.19) | ! 19-limit <br>(2.3.5.7.11.13.17.19) | ||
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| [[ | | [[Mohajira]], [[injera]], [[meanenneadecal]] | ||
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! Higher prime limits | ! Higher prime limits | ||
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|} | |} | ||
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|- | |- | ||
! JI subgroup | ! JI subgroup | ||
! ~ | ! ~5 notes per equave | ||
! ~10 notes | |||
! ~15 notes | |||
! ~20 notes | ! ~20 notes | ||
|- | |- | ||
! 2.3.5.7.other ''n'' | ! 2.3.5.7.other ''n'' | ||
| [[ | | [[Negra]] | ||
| | | No-11 [[godzilla]], no-11 [[pajara]], no-11 [[duodecim]] | ||
| | | No-11 [[magic]], no-11 [[sensis]], no-11 [[meanpop]] | ||
| | | No-11 [[catakleismic]] | ||
|- | |- | ||
! 2.3.5.11 <br>and its extensions | ! 2.3.5.11 <br>and its extensions | ||
| [[ | | [[Porcupine]], [[mavila]], [[dicot]], [[flattone]] | ||
| [[ | | [[Tetracot]], [[mohaha]] | ||
| [[ | | [[Larry]], [[countdown]], no-7 [[catalan]] | ||
| [[ | | [[Escapade]] | ||
|- | |- | ||
! 2.3.5.other ''n'' | ! 2.3.5.other ''n'' | ||
| [[ | | [[Srutal archagall]], [[stutzel]] | ||
| [[ | | [[Sensipent]], [[nestoria]] | ||
| [[ | | [[Würschmidt]]<ref group="note">Subgroup 2.3.5.23 version.</ref>, [[cata]] | ||
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|- | |- | ||
! 2.3.7 | ! 2.3.7 | ||
| [[ | | [[Slendric]], [[archy]], [[bleu]], [[semaphore]] | ||
| [[stearnsmic clan|stearnsmic]], [[skwares]] | | No-5 [[stearnsmic clan|stearnsmic]], [[skwares]] | ||
| [[ | | [[Hemif]], [[leapfrog]] | ||
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|- | |- | ||
! 2.3.7.11 <br>and its extensions | ! 2.3.7.11 <br>and its extensions | ||
| [[ | | [[Bleu]], [[supra]], [[semaphore]]+ | ||
| [[ | | [[Skwares]], [[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]] | ||
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! 2.3.7.other ''n'' | ! 2.3.7.other ''n'' | ||
| [[ | | [[Baladic]], [[oceanfront]], no-5 [[negra]] | ||
| | | No-5 no-11 [[liese]], no-11 [[skwares]] | ||
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! 2.3.11 <br>and its extensions | ! 2.3.11 <br>and its extensions | ||
| [[ | | [[Neutral (temperament)|neutral]], [[namo]], [[paralimmal]], [[io]] | ||
| [[ | | [[Tribilo]], [[huxley]] | ||
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! 2.3.other ''n'' | ! 2.3.other ''n'' | ||
| [[ | | [[Barbados]], [[boethian]], [[semitonic]], [[superflat]], [[hydrothermal]] | ||
| [[ | | [[Threedic]], [[pepperoni]] | ||
| [[Subgroup temperaments #Historical|historical]] | | [[Subgroup temperaments #Historical|historical]] | ||
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|- | |- | ||
! 2.5.7 <br>and its extensions | ! 2.5.7 <br>and its extensions | ||
| [[ | | [[Didacus]], [[frostburn]], no-3 [[oodako]], [[augment]] | ||
| [[ | | [[Rainy]], [[mercy]], [[huntington]] | ||
| [[ | | [[Llywelyn]], [[silver]], [[baldy]] | ||
| [[ | | [[Roulette]] | ||
|- | |- | ||
! 2.5.other ''n'' | ! 2.5.other ''n'' | ||
| [[ | | [[Insect]], [[sulis]], [[wizz]], [[vengeance]], [[marveltri]], [[superquintal]], [[movila]] | ||
| | | No-3 no-7 [[emka]] | ||
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|- | |- | ||
! 2.7 <br>and its extensions | ! 2.7 <br>and its extensions | ||
| [[ | | [[Orgone]], [[shipwreck]], [[stacks]], [[ultrakleismic]], [[machine]] | ||
| [[ | | [[Counterultrakleismic]], [[mechanism]], [[mabon]] | ||
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| [[ | | [[Apparatus]] | ||
|- | |- | ||
! 3.5.7 <br>and its extensions | ! 3.5.7 <br>and its extensions | ||
| [[ | | [[Canopus]], [[BPS]], [[sirius]], [[arcturus]], [[dubhe]], [[vega]] | ||
| [[ | | [[Izar]], [[mintra]] | ||
| [[ | | [[Alhena]], [[remus]] | ||
| [[ | | [[Erigone]] | ||
|- | |- | ||
! 3.5.other ''n'' | ! 3.5.other ''n'' | ||
| [[ | | [[Aldebaran]], [[deneb]], [[polaris]] | ||
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| [[ | | [[Alnilam]], [[fomalhaut]] | ||
|- | |- | ||
! 3.7 <br>and its extensions | ! 3.7 <br>and its extensions | ||
| [[ | | [[Mintaka]] (no-13), [[keladic]] | ||
| [[ | | [[Mebsuta]], [[minalzidar]] | ||
| [[ | | [[Mintaka]] (with 13) | ||
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|- | |- | ||
! 4.''n'' <br>and its extensions | ! 4.''n'' <br>and its extensions | ||
| [[ | | [[Meanquad]], [[tetrahanson]], [[tetrameantone]], [[quarchy]], [[tetrominant]] | ||
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! 5.''n'' <br>and its extensions | ! 5.''n'' <br>and its extensions | ||
| [[ | | [[Antipyth]], [[juggernaut]] | ||
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! Other subgroups | ! Other subgroups | ||
| [[ | | [[Greeley]], [[halftone]], [[semiwolf]], [[auk]] | ||
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|+ | |+ | ||
! JI subgroup | ! JI subgroup | ||
! ~ | ! ~25 notes | ||
! ~ | ! ~30 notes | ||
! ~ | ! ~35 notes | ||
! ~ | ! ~40 notes | ||
! > | ! >45 notes | ||
|- | |- | ||
! 5-limit <br>(2.3.5) | ! 5-limit <br>(2.3.5) | ||
| [[ennealimmal]], [[quintosec]], [[counterhanson]], [[undim]] | | [[Kwazy]], [[ennealimmal]], [[quintosec]], [[counterhanson]], [[undim]], [[quintile]] | ||
| [[Alphatricot]] | |||
| [[ | | [[Minortone]], [[vavoom]] | ||
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|- | |- | ||
! 7-limit <br>(2.3.5.7) | ! 7-limit <br>(2.3.5.7) | ||
| [[ | | [[Hemififths]] | ||
| [[Hemiwürschmidt]], [[unidec]] | |||
| [[ | | [[Ennealimmal]], [[sesquiquartififths]], [[parakleismic]], [[amity]], [[harry]], [[misty]], [[hendecatonic (temperament)|hendecatonic]] | ||
| [[Septiquarter]] | |||
| [[Supermajor (temperament)|Supermajor]], [[enneadecal]], [[term]], [[neptune (temperament)|neptune]], [[tertiaseptal]], [[gamera]], [[quinmite]], [[nessafof]], [[octoid]], [[quadritikleismic]], [[grendel]] | |||
|- | |- | ||
! 11-limit <br>(2.3.5.7.11) | ! 11-limit <br>(2.3.5.7.11) | ||
| [[ | | [[Meanpop]] | ||
| [[Unidec]], [[wizard]], [[diaschismic]] | |||
| [[ | | [[Harry]], [[hemithirds]] | ||
| [[ | | [[Tritikleismic]], [[hemiwürschmidt]] | ||
| [[Hemienneadecal]], [[hemiennealimmal]], [[abigail]], [[hemitert]], [[newt]], [[decoid]], [[vishnu]], [[quasiorwell]], [[octoid]], [[quadritikleismic]], [[sqrtphi]], [[ennealimnic]], [[catakleismic]] | |||
|- | |- | ||
! 13-limit <br>(2.3.5.7.11.13) | ! 13-limit <br>(2.3.5.7.11.13) | ||
| [[ | | [[Hemififths]], [[andromeda]], [[magic]] | ||
| [[ | | [[Mystery]], [[myna]], [[sensus]], [[meanpop]] | ||
| [[ | | [[Cassandra]], [[diaschismic]], [[orwell]], [[grosstone]] | ||
| [[Buzzard]], [[rodan]], [[shrutar]] | |||
| [[Abigail]], [[newt]], [[acyuta]], [[deca]], [[quasiorwell]], [[decoid]], [[vulture]], [[hemiennealimmal]], [[emkay]], [[satin]], [[trinity]], [[widefourth]], [[countercata]], [[octopus]], [[catakleismic]] | |||
|- | |- | ||
! 17-limit <br>(2.3.5.7.11.13.17) | ! 17-limit <br>(2.3.5.7.11.13.17) | ||
| [[ | | [[Leapday]], [[superkleismic]], [[fokkertone]] | ||
| [[ | | [[Hendec]], [[sensus]], [[andromeda]], [[modus]] | ||
| [[ | | [[Comptone]], [[diaschismic]] | ||
| [[Heinz]], [[octopus]], [[lizard]], [[marvolo]], [[rodan]], [[echidna]], [[shrutar]] | |||
| [[ | | [[Satin]], [[trinity]], [[octoid]], [[quincy]], [[mirkat]], [[quadritikleismic]], [[ennealimnic]], [[sqrtphi]] | ||
|- | |- | ||
! 19-limit <br>(2.3.5.7.11.13.17.19) | ! 19-limit <br>(2.3.5.7.11.13.17.19) | ||
| [[ | | [[Fokkertone]], [[wilsec]] | ||
| [[ | | [[Hitchcock]], [[andromeda]] | ||
| [[ | | [[Marvolo]] | ||
| [[ | | [[Octopus]], [[ennealim]], [[bikleismic]], [[srutal]] | ||
| [[ | | [[Satin]], [[trinity]], [[hemiennealimmal]], [[quincy]], [[octoid]], [[sqrtphi]] | ||
|- | |- | ||
! Higher prime limits | ! Higher prime limits | ||
| | | | ||
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| [[ | | | ||
| [[ | | [[Srutaloo]], [[shrutar]] | ||
| [[Satin]], [[trinity]], [[ketchup]], [[semisept]], [[cassandric]] | |||
|- | |- | ||
! 2.3.5.7.other ''n'' | ! 2.3.5.7.other ''n'' | ||
| | | 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]] | ||
|- | |- | ||
! 2.3.5.11 <br>and its extensions | ! 2.3.5.11 <br>and its extensions | ||
| | | [[Quintosec]], no-7 [[maquila]], [[sensible]] | ||
| [[ | | [[Twentcufo]], no-7 [[emka]], no-7 [[gwazy]], no-7 [[rodan]], no-7 [[cataclysmic]], no-7 [[sfourth]] | ||
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| | | No-7 [[hemienneadecal]], no-7 [[vulture]] | ||
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! 2.3.5.other ''n'' | ! 2.3.5.other ''n'' | ||
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| [[ | | [[Majvam]] | ||
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! 2.3.7.11 <br>and its extensions | ! 2.3.7.11 <br>and its extensions | ||
| | | No-5 [[quanic]] | ||
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! 2.3.7.other ''n'' | ! 2.3.7.other ''n'' | ||
| [[ | | [[Hypnosis]] | ||
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! 2.3.11 <br>and its extensions | ! 2.3.11 <br>and its extensions | ||
| | | Rank-2 [[pythrabian]] | ||
| | | Rank-2 [[frameshift]] | ||
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| [[ | | [[Daemotertiaschis]] | ||
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! 2.5.other ''n'' | ! 2.5.other ''n'' | ||