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Survey of efficient temperaments by subgroup: Difference between revisions

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''If you see a temperament on here that does not have good accuracy for its size in a particular subgroup, please delete that temperament from that subgroup’s row of the table.'')
''If you see a temperament on here that does not have good accuracy for its size in a particular subgroup, please delete that temperament from that subgroup’s row of the table.'')
'''Development notices (will be resolved and removed before the page returns to main space):
* (^) = list item has not yet been ordered by damage
* (^^^) = cell is currently ordered alphabetically, needs to be re-ordered by damage
* (£££) = cell is currently ordered by badness, needs to be re-ordered by damage
* (!!) = todo: check that none of the ones in this cell are extreme exotemperaments (>20 cents error on most intervals), remove them if they are'''




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|+
|+
! JI subgroup
! JI subgroup
! 5 to 15 notes
! ~10 notes per equave
! 15 to 25 notes
! ~20 notes
! 25 to 50 notes
! ~30 notes
! 50 to 100 notes
! ~40 notes
! >100 notes
! ~50 notes
! ~60 notes
! ~70 notes
! ~80 notes
! >90 notes
|-
|-
! 5-limit <br>(2 . 3 . 5)
! 5-limit <br>(2 . 3 . 5)
| [[diaschismic]], [[meantone]], [[augmented]], [[porcupine]], [[dimipent]], [[whitewood]], [[blackwood]], [[mavila]]
| [[hanson]], [[magic]], [[meantone]], [[negri]], [[augmented]], [[porcupine]], [[dimipent]], [[mavila]], [[blackwood]], [[misty]](^), [[whitewood]](^)
| [[helmholtz]] (aka schismic), [[hanson]], [[sensi]], [[tetracot]], [[magic]], [[negri]], [[superpyth]], [[ripple]]
| [[helmhpltz]], [[orson]], [[wuerschmidt]], [[sensipent]], [[compton]], [[diaschismic]], [[tetracot]], [[passion]], [[superpyth]], [[ripple]], [[valentine]](^)
| [[orson]], [[amity]], [[wuerschmidt]], [[compton]], [[valentine]], [[passion]]
| [[luna]], [[vishnu]], [[amity]], [[gravity]](^), [[kwazy]](^), [[parakleismic]](^)
| [[vishnu]], [[parakleismic]], [[pental]], [[gravity]], [[misty]], [[rodan]]
|
| [[kwazy]], [[ennealimmal]], [[minortone]], [[luna]]
| [[ennealimmal]]
|
| [[minortone]](^), [[vavoom]](^)
|
|
|-
|-
! 7-limit <br>(2 . 3 . 5 . 7)
! 7-limit <br>(2 . 3 . 5 . 7)
| [[triforce]], [[schism]], [[dominant]], [[august]], [[diminished]], [[superpelog]], [[blacksmith]], [[inflated]], [[opossum]]
| [[porcupine]], [[pajara]], [[keemun]], [[negri]], [[doublewide]], [[injera]], [[dominant]], [[august]], [[diminished]], [[blacksmith]]
| [[shrutar]], [[magic]], [[sensi]], [[meantone]], [[mothra]], [[superpyth]], [[flattone]], [[liese]], [[beatles]], [[augene]], [[porcupine]], [[pajara]], [[godzilla]], [[hedgehog]], [[negri]], [[keemun]], [[doublewide]], [[nautilus]], [[catler]], [[injera]], [[semaphore]], [[lemba]]
| [[orwell]], [[myna]], [[magic]], [[meantone]], [[mothra]], [[superpyth]], [[flattone]], [[liese], [[beatles]], [[augene]], [[hedgehog]], [[nautilus]], [[catler]], [[godzilla]], [[lemba]], [[schism]](^), [[valentine]](^)
| [[hemiwuerschmidt]], [[catakleismic]], [[miracle]], [[garibaldi]], [[orwell]], [[valentine]], [[myna]], [[diaschismic]]
| [[miracle]], [[garibaldi]], [[sensi]], [[amity]](^), [[diaschismic]](^), [[harry]](^), [[hemiwuerschmidt]](^)
| [[ennealimmal]], [[amity]], [[harry]], [[hemififths]], [[parakleismic]], [[misty]], [[unidec]]
| [[catakleismic]], [[misty]], [[unidec]] (^^^)
| [[Ragismic_microtemperaments#Supermajor|supermajor]], [[enneadecal]], [[sesquiquartififths]], [[pontiac]], [[tertiaseptal]], [[trinity]]
| [[ennealimmal]], [[hemififths]], [[tertiaseptal]] (^^^)
|
| [[parakleismic]], [[sesquiquartififths]] (^^^)
|
| [[enneadecal]], [[pontiac]],[[Ragismic_microtemperaments#Supermajor|supermajor]] (^^^)
|-
|-
! 11-limit <br>(2 . 3 . 5 . 7 . 11)
! 11-limit <br>(2 . 3 . 5 . 7 . 11)
| [[superpelog]], [[blacksmith]], [[opossum]], [[pajaric]], [[august]]
| [[august]], [[blacksmith]], [[pajaric]], [[triforce]] (^^^)
| [[mohajira]], [[superpyth]], [[quasisupra]], [[pajara]], [[telepathy]], [[suprapyth]], [[porcupine]], [[negroni]], [[porky]], [[hedgehog]], [[fleetwood]], [[pajarous]], [[astrology]], [[vigintiduo]], [[augene]], [[sensis]], [[nautilus]], [[catnip]], [[undevigintone]], [[injera]], [[flattone]], [[godzilla]], [[darjeeling]], [[keemun]], [[progress]], [[dominant]], [[triforce]], [[negric]], [[meanenneadecal]], [[duodecim]]
| [[orwell]], [[mohajira]], [[porcupine]], [[hedgehog]], [[astrology]], [[vigintiduo]], [[augene]], [[nautilus]], [[catnip]], [[undevigintone]], [[injera]], [[keemun]], [[progress]], [[dominant]], [[negric]], [[meanenneadecal]], [[duodecim]], [[opossum]], [[valentine]](^)
| [[hemiwuerschmidt]], [[miracle]], [[cassandra]], [[diaschismic]], [[valentine]], [[shrutar]], [[orwell]], [[magic]], [[meanpop]], [[migration]], [[nusecond]], [[andromeda]], [[mothra]], [[squares]], [[meantone]]
| [[nusecond]], [[squares]], [[meantone]], [[quasisupra]], [[pajara]], [[telepathy]], [[suprapyth]], [[negroni]], [[porky]], [[fleetwood]], [[pajarous]], [[sensis]], [[flattone]], [[godzilla]], [[darjeeling]], [[mothra]](^)
| [[unidec]], [[harry]], [[sqrtphi]], [[tritikleismic]], [[hemiwuerschmidt]], [[ennealimnic]], [[hemithirds]], [[catakleismic]], [[wizard]]
| [[miracle]], [[magic]], [[meanpop]], [[migration]], [[andromeda]], [[superpyth]], [[shrutar]](^)
| [[hemienneadecal]], [[hemiennealimmal]], [[ennealimmal]], [[vishnu]], [[quasiorwell]], [[trinity]]
| [[diaschismic]], [[hemithirds]], [[tritikleismic]], [[unidec]], [[wizard]] (^^^)
|
| [[harry]]
| [[cassandra]], [[catakleismic]], [[ennealimnic]], [[hemiwuerschmidt]], [[quasiorwell]], [[sqrtphi]] (^^^)
| [[hemienneadecal]], [[hemiennealimmal]], [[trinity]], [[vishnu]] (^^^)
|-
|-
! 13-limit <br>(2 . 3 . 5 . 7 . 11 . 13)
! 13-limit <br>(2 . 3 . 5 . 7 . 11 . 13)
|
| [[negric]]
| [[mohajira]], [[winston]], [[pajara]], [[undevigintone]], [[superpyth]], [[sensis]], [[negroni]], [[nautilus]], [[ogene]], [[ringo]], [[flattone]], [[injera]], [[augene]], [[darjeeling]], [[meanenneadecal]], [[porcupine]], [[hedgehog]], [[triforce]], [[godzilla]], [[negric]], [[negri]],[[Mavila_family#Armodue|armodue]], [[blacksmith]]
| [[negri]], [[Mavila_family#Armodue|armodue]], [[opossum]], [[triforce]], [[blacksmith]], [[augene]], [[lupercalia]], [[porcupine]], [[hedgehog]], [[godzilla]] (£££)
| [[cassandra]], [[diaschismic]], [[myna]], [[orwell]], [[shrutar]], [[miraculous]], [[sensus]], [[meanpop]], [[andromeda]], [[magic]], [[superkleismic]], [[mothra]], [[nusecond]], [[modus]], [[lupercalia]], [[meantone]]
| [[meantone]], [[winston]], sensis, [[meanenneadecal]], [[darjeeling]], [[flattone]], [[ringo]], [[nusecond]], [[modus]], [[pajara]] (£££)
| [[hemiwuerschmidt]], [[mirkat]], [[harry]], [[sqrtphi]], [[tritikleismic]], [[countercata]], [[hemiseven]], [[catakleismic]]
| [[mirkat]], [[miraculous]], [[andromeda]], [[superkleismic]], [[injera]], [[nautilus]] , [[undevigintone]], [[ogene]], [[mohajira]], [[mothra]], [[superpyth]], [[negroni]], [[diaschismic]] (£££)
| [[semihemiennealimmal]], [[abigail]], [[ennealimmia]], [[decoid]], [[hemiennealimmal]], [[trinity]], [[enneadecal]], [[octoid]]
| [[orwell]], [[magic]] (£££)
| [[myna]], [[sensus]], [[meanpop]] (£££)
| [[cassandra]]
| [[catakleismic]], [[shrutar]] (£££)
| [[abigail]], [[hemiennealimmal]], [[harry]], [[semihemiennealimmal]], [[decoid]], [[trinity]] (£££)
|-
|-
! 17-limit <br>(2 . 3 . 5 . 7 . 11 . 13 . 17)
! 17-limit <br>(2 . 3 . 5 . 7 . 11 . 13 . 17)
|  
|  
| [[mohajira]], [[injera]], [[meanenneadecal]], [[pajara]]
|
| [[diaschismic]], [[echidna]], [[shrutar]], [[sensus]], [[miraculous]], [[andromeda]], [[modus]]
| [[pajara]]
| [[mirkat]], [[harry]], [[sqrtphi]], [[tritikleismic]], [[countercata]], [[hemiseven]]
| [[mirkat]], [[miraculous]], [[mohajira]], [[injera]], [[meanenneadecal]] (£££)
| [[trinity]], [[hemiennealimmal]], [[ennealimmal]], [[octoid]]
|
| [[sensus]], [[diaschismic]], [[modus]], [[andromeda]] (£££)
|
| [[echidna]], [[shrutar]] (£££)
| [[harry]], [[sqrtphi]], [[tritikleismic]], [[octoid]], [[trinity]] (£££)
|-
|-
! 19-limit <br>(2 . 3 . 5 . 7 . 11 . 13 . 17 . 19)
! 19-limit <br>(2 . 3 . 5 . 7 . 11 . 13 . 17 . 19)
|  
|  
| [[mohajira]], [[injera]], [[meanenneadecal]], [[marvolo]]
|
| [[shrutar]], [[andromeda]], [[modus]], [[hitchcock]]
|
| [[sqrtphi]], [[ketchup]]
| [[injera]], [[mohajira]], [[meanenneadecal]], [[shrutar]] (£££)
| [[trinity]], [[hemiennealimmal]], [[ennealimmal]], [[octoid]]
| [[andromeda]]
| [[hitchcock]], [[modus]] (£££)
| [[marvolo]]
|  
| [[sqrtphi]], [[octoid]], [[ketchup]], [[trinity]] (£££)
|-
|-
! Higher prime limits
! Higher prime limits
|  
|  
| [[marvolo]]
|  
| [[srutal]], [[shrutar]], [[hitchcock]]
|  
| [[decistearn]], [[ketchup]]
|
| [[trinity]], [[satin]]
|
|
|
| [[shrutar]]
| [[satin]], [[ketchup]], [[trinity]] (£££)
|-
|-
! 2 . 3 . 5 . 7 . other n
! 2 . 3 . 5 . 7 . other n
| [[negra]
|
| no-11 [[sensis]], no-11 [[meanpop]], no-11 [[magic]] (£££)
| no-11 [[catakleismic]]
| [[unicorn]]
|  
|  
| no-11 [[magic]], no-11 [[sensis]], no-11 [[meanpop]], [[negra]]
| no-11 [[cassandra]]
| no-11 [[catakleismic]], no-11 [[cassandra]], [[unicorn]]
| no-11 [[hemischis]]
| no-11 [[decoid]], no-11 [[hemischis]], no-11 [[tritikleismic]]
| no-11 [[decoid]], no-11 [[ennealimmal]] (£££)
| no-11 [[ennealimmal]]
|-
|-
! 2 . 3 . 5 . 11 <br>and its extensions
! 2 . 3 . 5 . 11 . other n
| [[mavila]]
| [[mavila]], [[porkypine]] (^^^)
| [[sensible]], [[mohaha]], [[porkypine]]
| [[mohaha]], [[tetracot]] (^^^)
| [[tetracot]]
| [[larry]] (2.3.5.11 gravity)
| [[larry]] (2.3.5.11 [[gravity]])
|
| [[sensible]]
|
|
|
|  
|  
|-
|-
! 2 . 3 . 5 . other n
! 2 . 3 . 5 . other n
| [[stützel]]
| [[srutal archagall]], [[stutzel]] (^^^)
| [[nestoria]], [[cata]], [[sensipent]], [[srutal archagall]]
| [[nestoria]], [[sensipent]] (^^^)
| [[wuerschmidt]] (2.3.5.23)
| [[cata]], [[wuerschmidt]] (2.3.5.23) (^^^)
|
|
|
|
|  
|  
|  
|  
|-
|-
! 2 . 3 . 7
! 2 . 3 . 7
| [[archy]], [[semaphore]]
| [[archy]], [[bleu]], [[semaphore]], [[slendric]] (^^^)
| [[bleu]]
| [[skwares]]
| [[slendric]]
| no-5 [[hemififths]]
| no-5 [[hemififths]]
|
|
|
|
|
|  
|  
|-
|-
! 2 . 3 . 7 . 11 <br>and its extensions
! 2 . 3 . 7 . 11 <br>and its extensions
| [[semaphore]]
| [[bleu]], [[supra]] (^^^)
| [[skwares]], [[bleu]], [[suhajira]], [[supra]]
| [[skwares]], [[suhajira]] (^^^)
| no-5 [[miracle]], [[hemififths]], [[slendric]], [[radon]]
| no-5 [[miracle]], [[radon]], no-5 [[hemififths]] (^^^)
|
|
|
|
|  
|  
|  
|  
|-
|-
! 2 . 3 . 7 . other n
! 2 . 3 . 7 . other n
| no-5 [[negra]]
| [[baladic]], no-5 [[negra]], [[oceanfront]] (^^^)
| [[baladic]]
|
| [[oceanfront]]
|
|  
| [[hypnosis]]
| [[hypnosis]]
|
|
|
|  
|  
|-
|-
! 2 . 3 . 11 <br>and its extensions
! 2 . 3 . 11 <br>and its extensions
| [[paralimmal]], [[huxley]], [[io]]
| [[io]], [[namo], [[Rastmic_clan#Neutral|neutral] (2.3.11 [[rastmic]]), [[paralimmal]] (^^^) (!!)
| 2.3.11 [[pythrabian]], [[neutral]] (2.3.11 [[rastmic]]), [[namo]]
| [[huxley]], [[tribilo]] (2.3.11 [[nexus]]) (^^^)
| [[tribilo]] (2.3.11 [[nexus]])
|  
|  
|
| 2.3.11 [[pythrabian]]
| 2.3.11 [[frameshift]]
| 2.3.11 [[frameshift]]
|
|
|
|-
|-
!2 . 3 . other n
! 2 . 3 . other n
| [[barbados]], [[superflat]], [[hydrothermal]], [[dog]]
| [[barbados]], [[boethian]], [[dog]], [[hydrothermal]], [[semitonic]], [[superflat]] (^^^) (!!)
| [[threedic]], [[semitonic]]
| [[pepperoni]], [[threedic]] (^^^)
| [[boethian]], [[pepperoni]]
| [[Subgroup_temperaments#Historical|historical]]
| [[historical]]
|
|
|
|
|
|
|  
|-
|-
! 2 . 5 . 7 <br>and its extensions
! 2 . 5 . 7 <br>and its extensions
| no-3 [[oodako]], no-3 [[pajara]]
| [[didacus]], [[frostburn]], no-3 [[oodako]] (^^^) (!!)
| [[didacus]], [[llywelyn]]
| [[baldy]], [[llywelyn]], [[mercy]], [[rainy]] (^^^)
| [[rainy]], [[mercy]], [[frostburn]], [[baldy]]
|
|
|
|
|
|
| [[Subgroup temperaments#Daemotertiaschis|daemotertiaschis]]
| [[Subgroup temperaments#Daemotertiaschis|daemotertiaschis]]
| [[ostara]]
|-
|-
! 2 . 5 . other n
! 2 . 5 . other n
| [[movila]]
| [[insect]], [[marveltri]], [[movila]], [[sulis]], [[superquintal]], [[trader]], [[vengeance]], [[wizz]] (^^^) (!!)
| [[wizz]], [[vengeance]], [[marveltri]], [[superquintal]], [[trader]]
|
| [[insect]], [[sulis]]
|
|
|
|
|
|  
|  
|  
|  
|-
|-
! 2 . 7 <br>and its extensions
! 2 . 7 <br>and its extensions
| [[ultrakleismic]], [[shipwreck]], [[mabon]], [[demon]], [[machine]]
| [[demon]], [[machine]], [[orgone]], [[shipwreck]], [[stacks]], [[ultrakleismic]] (^^^) (!!)
| [[orgone]], [[counterultrakleismic]], [[machine|apparatus]]
| [[counterultrakleismic]], [[mabon]], [[machine|mechanism]] (^^^)
| [[stacks]], [[machine|mechanism]]
|
|
| [[machine|apparatus]]
|
|
|
|  
|  
|  
|-
|-
! 3 . 5 . 7 <br>and its extensions
! 3 . 5 . 7 <br>and its extensions
| [[canopus]], [[BPS]], [[sirius]], [[arcturus]], [[vega]]
| [[arcturus]], [[BPS]], [[canopus]], [[dubhe]] (3.5.7.17), [[sirius]], [[Catalog of 3.5.7 subgroup rank two temperaments|vega]] (^^^)
| [[mintra]] (3.5.7.11), [[dubhe]] (3.5.7.17)
| [[izar]], [[mintra]] (3.5.7.11) (^^^)
| [[miaplacidus]], [[mintra]] (3.5.7.11.13)
| [[No-twos_subgroup_temperaments#Alhena|alhena]]
| [[izar]], [[BPS|athena]]
|
|
|
|
|  
|  
|  
|-
|-
!3 . 5 . other n
! 3 . 5 . other n
| [[polaris]], [[aldebaran]]
| [[aldebaran]], [[deneb]], [[polaris]] (^^^)
| [[deneb]]
|
| [[No-twos subgroup temperaments#Fomalhaut|fomalhaut]]
|
| [[alnilam]]
| [[alnilam]], [[No-twos subgroup temperaments#Fomalhaut|fomalhaut]] (^^^)
|
|
|
|
|  
|  
|-
|-
! 3 . 7 <br>and its extensions
! 3 . 7 <br>and its extensions
| [[mintaka]] (3.7.11), [[keladic]]
| [[keladic]], [[mintaka]] (3.7.11) (^^^)
| [[mintaka]] (3.7.11.13), [[minalzidar]]
| [[mebsuta]], [[minalzidar]] (^^^)
| [[mebsuta]]
| [[mintaka]] (3.7.11.13)
|  
|
|
|
|
|  
|  
|
|-
|-
! 4 . n <br>and its extensions
! 4 . n <br>and its extensions
| [[tetrameantone]], [[quarchy]]
| [[meanquad]], [[tetrahanson]], [[tetrameantone]], [[tetrominant]], [[quarchy]] (^^^)
| [[tetrahanson]], [[meanquad]]
|
| [[Subgroup temperaments#Fourwar|fourwar]]
| [[Subgroup temperaments#Fourwar|fourwar]]
|
|
|
|
|  
|  
|  
|  
|-
|-
! 5 . n <br>and its extensions
! 5 . n <br>and its extensions
| [[juggernaut]]
| [[antipyth]], [[juggernaut]] (^^^)
| [[antipyth]]
|
|
|
|
|
|  
|  
|  
|  
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|-
|-
! Other subgroups
! Other subgroups
| [[halftone]], [[semiwolf]], [[auk]]
| [[auk]], [[greeley]], [[halftone]], [[semiwolf]] (^^^)
| [[greeley]]
|
|
|
|
|
|  
|  
|  
|  
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