Survey of efficient temperaments by subgroup: Difference between revisions
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== Which temperaments should I use to make music? == | == Which temperaments should I use to make music? == | ||
There are many different schools of thought within RTT (regular temperament theory). | There are many different schools of thought within RTT (regular temperament theory). | ||
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== How to read the tables == | == How to read the tables == | ||
'''Rows''' | '''Rows''' | ||
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Subgroups with no 2s, e.g. 3.5.7.11, are the most jarring break away from familiar harmony, which one may consider a good or a bad thing. | Subgroups with no 2s, e.g. 3.5.7.11, are the most jarring break away from familiar harmony, which one may consider a good or a bad thing. | ||
Subgroups with 2s and 3s but no 5s, e.g. 2.3.7.11, preserve the most fundamental familiar intervals like the octave and the fifth, but do away with the 5-limit major and minor intervals of common practice harmony<ref>According to the 2.3.5 reading of common practice harmony. Alternate readings are possible.</ref>, forcing innovation while still keeping some familiarity. | Subgroups with 2s and 3s but no 5s, e.g. 2.3.7.11, preserve the most fundamental familiar intervals like the octave and the fifth, but do away with the 5-limit major and minor intervals of common practice harmony<ref group="note">According to the 2.3.5 reading of common practice harmony. Alternate readings are possible.</ref>, forcing innovation while still keeping some familiarity. | ||
Some theorists believe including 13, 17 or higher in a subgroup is pointless because the brain can't register such complex intervals. Others believe these intervals are registered by the brain, perhaps subtly and subconsciously in some instances, but still there. | Some theorists believe including 13, 17 or higher in a subgroup is pointless because the brain can't register such complex intervals. Others believe these intervals are registered by the brain, perhaps subtly and subconsciously in some instances, but still there. | ||
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{| class="wikitable center-all" | {| class="wikitable center-all" | ||
| | |- | ||
! JI subgroup | ! JI subgroup | ||
! ~10 notes per equave<ref>Number of notes per equave was estimated by multiplying the temperament’s [[graham complexity]] by 2.</ref> | ! ~10 notes per equave<ref group="note">Number of notes per equave was estimated by multiplying the temperament’s [[graham complexity]] by 2.</ref> | ||
! ~20 notes | ! ~20 notes | ||
! ~30 notes | ! ~30 notes | ||
! ~40 notes | ! ~40 notes | ||
|- | |- | ||
! 5-limit <br>(2 . 3 . 5) | ! 5-limit <br />(2.3.5) | ||
| [[hanson]], [[misty]], [[magic]], [[meantone]], [[negri]], [[augmented]], [[porcupine]], [[dimipent]], [[whitewood]], [[blackwood]], [[mavila]] | | [[hanson]], [[misty]], [[magic]], [[meantone]], [[negri]], [[augmented]], [[porcupine]], [[dimipent]], [[whitewood]], [[blackwood]], [[mavila]] | ||
| [[helmholtz]], [[orson]], [[wuerschmidt]], [[sensipent]], [[compton]], [[valentine]], [[diaschismic]], [[tetracot]], [[passion]], [[superpyth]], [[ripple]] | | [[helmholtz]], [[orson]], [[wuerschmidt]], [[sensipent]], [[compton]], [[valentine]], [[diaschismic]], [[tetracot]], [[passion]], [[superpyth]], [[ripple]] | ||
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| [[enneadecal]], [[gammic]], [[vulture]] | | [[enneadecal]], [[gammic]], [[vulture]] | ||
|- | |- | ||
! 7-limit <br>(2 . 3 . 5 . 7) | ! 7-limit <br />(2.3.5.7) | ||
| [[porcupine]], [[pajara]], [[keemun]], [[negri]], [[doublewide]], [[injera]], [[dominant]], [[august]], [[diminished]], [[blacksmith]] | | [[porcupine]], [[pajara]], [[keemun]], [[negri]], [[doublewide]], [[injera]], [[dominant]], [[august]], [[diminished]], [[blacksmith]] | ||
| [[orwell]], [[valentine]], [[myna]], [[magic]], [[meantone]], [[mothra]], [[superpyth]], [[flattone]], [[liese]], [[beatles]], [[augene]], [[hedgehog]], [[nautilus]], [[catler]], [[godzilla]], [[lemba]], | | [[orwell]], [[valentine]], [[myna]], [[magic]], [[meantone]], [[mothra]], [[superpyth]], [[flattone]], [[liese]], [[beatles]], [[augene]], [[hedgehog]], [[nautilus]], [[catler]], [[godzilla]], [[lemba]], | ||
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| [[misty]], [[unidec]], [[catakleismic]] | | [[misty]], [[unidec]], [[catakleismic]] | ||
|- | |- | ||
! 11-limit <br>(2 . 3 . 5 . 7 . 11) | ! 11-limit <br />(2.3.5.7.11) | ||
| [[triforce]], [[blacksmith]], [[pajaric]], [[negric]] | | [[triforce]], [[blacksmith]], [[pajaric]], [[negric]] | ||
| [[orwell]], [[valentine]], [[mohajira]], [[porcupine]], [[hedgehog]], [[astrology]], [[vigintiduo]], [[augene]], [[nautilus]], [[catnip]], [[undevigintone]], [[injera]], [[keemun]], [[progress]], [[dominant]], [[meanenneadecal]], [[duodecim]] | | [[orwell]], [[valentine]], [[mohajira]], [[porcupine]], [[hedgehog]], [[astrology]], [[vigintiduo]], [[augene]], [[nautilus]], [[catnip]], [[undevigintone]], [[injera]], [[keemun]], [[progress]], [[dominant]], [[meanenneadecal]], [[duodecim]] | ||
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| [[miracle]], [[shrutar]], [[magic]], [[meanpop]], [[migration]], [[andromeda]], [[superpyth]] | | [[miracle]], [[shrutar]], [[magic]], [[meanpop]], [[migration]], [[andromeda]], [[superpyth]] | ||
|- | |- | ||
! 13-limit <br>(2 . 3 . 5 . 7 . 11 . 13) | ! 13-limit <br />(2.3.5.7.11.13) | ||
| [[negric]] | | [[negric]] | ||
| [[augene]], [[porcupine]], [[hedgehog]], [[triforce]], [[godzilla]], [[negri]], [[armodue]] | | [[augene]], [[porcupine]], [[hedgehog]], [[triforce]], [[godzilla]], [[negri]], [[armodue]] | ||
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| [[mirkat]], [[diaschismic]], [[miraculous]], [[andromeda]], [[superkleismic]], [[mothra]], [[mohajira]], [[undevigintone]], [[ogene]], [[nautilus]], [[negroni]], [[injera]] | | [[mirkat]], [[diaschismic]], [[miraculous]], [[andromeda]], [[superkleismic]], [[mothra]], [[mohajira]], [[undevigintone]], [[ogene]], [[nautilus]], [[negroni]], [[injera]] | ||
|- | |- | ||
! 17-limit <br>(2 . 3 . 5 . 7 . 11 . 13 . 17) | ! 17-limit <br />(2.3.5.7.11.13.17) | ||
| | | | ||
| [[lemba]]+, [[hedgehog]]+ | | [[lemba]]+, [[hedgehog]]+ | ||
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| [[mirkat]], [[miraculous]], [[lupercalia]]+, [[mohajira]], [[superpyth]]+, [[meantoid]], [[injera]], [[meanenneadecal]] | | [[mirkat]], [[miraculous]], [[lupercalia]]+, [[mohajira]], [[superpyth]]+, [[meantoid]], [[injera]], [[meanenneadecal]] | ||
|- | |- | ||
! 19-limit <br>(2 . 3 . 5 . 7 . 11 . 13 . 17 . 19) | ! 19-limit <br />(2.3.5.7.11.13.17.19) | ||
| | | | ||
| [[niner]]++ | | [[niner]]++ | ||
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| [[lupercalia]]+++, [[nautilus]]+++, [[negroni]]+++, [[injera]]+ | | [[lupercalia]]+++, [[nautilus]]+++, [[negroni]]+++, [[injera]]+ | ||
|- | |- | ||
! 2 . 3 . 5 . 7 . other n | ! 2.3.5.7.other n | ||
| [[negra]] | | [[negra]] | ||
| no-11 [[godzilla]], no-11 [[pajara]], no-11 [[duodecim]] | | no-11 [[godzilla]], no-11 [[pajara]], no-11 [[duodecim]] | ||
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| no-11 [[catakleismic]] | | no-11 [[catakleismic]] | ||
|- | |- | ||
! 2 . 3 . 5 . 11 <br>and its extensions | ! 2.3.5.11 <br />and its extensions | ||
| [[porkypine]], [[mavila]], [[dicot]] | | [[porkypine]], [[mavila]], [[dicot]] | ||
| [[orson]]+, [[tetracot]], [[mohaha]] | | [[orson]]+, [[tetracot]], [[mohaha]] | ||
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| [[escapade]] | | [[escapade]] | ||
|- | |- | ||
! 2 . 3 . 5 . other n | ! 2.3.5.other n | ||
| [[srutal archagall]], [[stutzel]] | | [[srutal archagall]], [[stutzel]] | ||
| [[sensipent]], [[nestoria]] | | [[sensipent]], [[nestoria]] | ||
| [[wuerschmidt]]<ref>Subgroup 2.3.5.23 version.</ref>, [[cata]] | | [[wuerschmidt]]<ref group="note">Subgroup 2.3.5.23 version.</ref>, [[cata]] | ||
| | | | ||
|- | |- | ||
! 2 . 3 . 7 | ! 2.3.7 | ||
| [[slendric]], [[archy]], [[bleu]], [[semaphore]] | | [[slendric]], [[archy]], [[bleu]], [[semaphore]] | ||
| [[stearnsmic clan|stearnsmic]], [[skwares]] | | [[stearnsmic clan|stearnsmic]], [[skwares]] | ||
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|- | |- | ||
! 2 . 3 . 7 . 11 <br>and its extensions | ! 2.3.7.11 <br />and its extensions | ||
| [[bleu]], [[supra]], [[semaphore]]+ | | [[bleu]], [[supra]], [[semaphore]]+ | ||
| [[skwares]], [[stearnsmic clan|stearnsmic]]+, [[suhajira]] | | [[skwares]], [[stearnsmic clan|stearnsmic]]+, [[suhajira]] | ||
| no-5 [[miracle]], [[radon]]^, [[hemif]]^<ref>^Hemif beats radon in 2.3.7.11, radon beats hemif in 2.3.7.11.13 (in damage not badness).</ref>, [[leapfrog]] | | 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]] | ||
| | | | ||
|- | |- | ||
! 2 . 3 . 7 . other n | ! 2.3.7.other n | ||
| [[baladic]], [[oceanfront]], no-5 [[negra]] | | [[baladic]], [[oceanfront]], no-5 [[negra]] | ||
| | | | ||
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| [[slendric]]+ | | [[slendric]]+ | ||
|- | |- | ||
! 2 . 3 . 11 <br>and its extensions | ! 2.3.11 <br />and its extensions | ||
| [[Rastmic_clan#Neutral|neutral]] (2.3.11 [[rastmic]]), [[namo]], [[paralimmal]], [[io]] | | [[Rastmic_clan#Neutral|neutral]] (2.3.11 [[rastmic]]), [[namo]], [[paralimmal]], [[io]] | ||
| [[tribilo]] (2.3.11 [[nexus]]), [[huxley]] | | [[tribilo]] (2.3.11 [[nexus]]), [[huxley]] | ||
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|- | |- | ||
! 2 . 3 . other n | ! 2.3.other n | ||
| [[barbados]], [[boethian]], [[semitonic]], [[superflat]], [[hydrothermal]] | | [[barbados]], [[boethian]], [[semitonic]], [[superflat]], [[hydrothermal]] | ||
| [[threedic]], [[pepperoni]] | | [[threedic]], [[pepperoni]] | ||
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|- | |- | ||
! 2 . 5 . 7 <br>and its extensions | ! 2.5.7 <br />and its extensions | ||
| [[didacus]], [[frostburn]], no-3 [[oodako]] | | [[didacus]], [[frostburn]], no-3 [[oodako]] | ||
| [[rainy]], [[mercy]], [[huntington]], [[llywelyn]], [[baldy]] | | [[rainy]], [[mercy]], [[huntington]], [[llywelyn]], [[baldy]] | ||
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|- | |- | ||
! 2 . 5 . other n | ! 2.5.other n | ||
| [[insect]], [[sulis]], [[wizz]], [[vengeance]], [[marveltri]], [[superquintal]], [[movila]] | | [[insect]], [[sulis]], [[wizz]], [[vengeance]], [[marveltri]], [[superquintal]], [[movila]] | ||
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|- | |- | ||
! 2 . 7 <br>and its extensions | ! 2.7 <br />and its extensions | ||
| [[orgone]], [[shipwreck]], [[stacks]], [[ultrakleismic]], [[machine]] | | [[orgone]], [[shipwreck]], [[stacks]], [[ultrakleismic]], [[machine]] | ||
| [[counterultrakleismic]], [[mechanism]], [[mabon]] | | [[counterultrakleismic]], [[mechanism]], [[mabon]] | ||
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| [[machine|apparatus]] | | [[machine|apparatus]] | ||
|- | |- | ||
! 3 . 5 . 7 <br>and its extensions | ! 3.5.7 <br />and its extensions | ||
| [[canopus]], [[BPS]], [[sirius]], [[arcturus]], [[dubhe]], [[Catalog of 3.5.7 subgroup rank two temperaments|vega]] | | [[canopus]], [[BPS]], [[sirius]], [[arcturus]], [[dubhe]], [[Catalog of 3.5.7 subgroup rank two temperaments|vega]] | ||
| [[izar]], [[mintra]] | | [[izar]], [[mintra]] | ||
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| [[erigone]] | | [[erigone]] | ||
|- | |- | ||
! 3 . 5 . other n | ! 3.5.other n | ||
| [[aldebaran]], [[deneb]], [[polaris]] | | [[aldebaran]], [[deneb]], [[polaris]] | ||
| | | | ||
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| [[alnilam]], [[fomalhaut]] | | [[alnilam]], [[fomalhaut]] | ||
|- | |- | ||
! 3 . 7 <br>and its extensions | ! 3.7 <br />and its extensions | ||
| [[mintaka]] (w.o. 13), [[keladic]] | | [[mintaka]] (w.o. 13), [[keladic]] | ||
| [[mebsuta]], [[minalzidar]] | | [[mebsuta]], [[minalzidar]] | ||
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|- | |- | ||
! 4 . n <br>and its extensions | ! 4.n <br />and its extensions | ||
| [[meanquad]], [[tetrahanson]], [[tetrameantone]], [[quarchy]], [[tetrominant]] | | [[meanquad]], [[tetrahanson]], [[tetrameantone]], [[quarchy]], [[tetrominant]] | ||
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|- | |- | ||
! 5 . n <br>and its extensions | ! 5.n <br />and its extensions | ||
| [[antipyth]], [[juggernaut]] | | [[antipyth]], [[juggernaut]] | ||
| | | | ||
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! >90 notes | ! >90 notes | ||
|- | |- | ||
! 5-limit <br>(2 . 3 . 5) | ! 5-limit <br />(2.3.5) | ||
| [[ennealimmal]], [[qintosec]], [[counterhanson]], [[undim]] | | [[ennealimmal]], [[qintosec]], [[counterhanson]], [[undim]] | ||
| [[tricot]], [[pental]] | | [[tricot]], [[pental]] | ||
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| | | | ||
|- | |- | ||
! 7-limit <br>(2 . 3 . 5 . 7) | ! 7-limit <br />(2.3.5.7) | ||
| [[ennealimmal]], [[tertiaseptal]], [[hemififths]], [[quadritikleismic]], [[grendel]], [[unidec]] | | [[ennealimmal]], [[tertiaseptal]], [[hemififths]], [[quadritikleismic]], [[grendel]], [[unidec]] | ||
| [[hendecatonic]] | | [[hendecatonic]] | ||
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| [[supermajor]], [[enneadecal]], [[term]] | | [[supermajor]], [[enneadecal]], [[term]] | ||
|- | |- | ||
! 11-limit <br>(2 . 3 . 5 . 7 . 11) | ! 11-limit <br />(2.3.5.7.11) | ||
| [[unidec]], [[tritikleismic]], [[hemithirds]], [[wizard]], [[diaschismic]] | | [[unidec]], [[tritikleismic]], [[hemithirds]], [[wizard]], [[diaschismic]] | ||
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| [[hemienneadecal]], [[hemiennealimmal]], [[abigail]], [[hemitert]], [[newt]], [[decoid]], [[vishnu]] | | [[hemienneadecal]], [[hemiennealimmal]], [[abigail]], [[hemitert]], [[newt]], [[decoid]], [[vishnu]] | ||
|- | |- | ||
! 13-limit <br>(2 . 3 . 5 . 7 . 11 . 13) | ! 13-limit <br />(2.3.5.7.11.13) | ||
| [[hemififths]], [[orwell]], [[magic]] | | [[hemififths]], [[orwell]], [[magic]] | ||
| [[mystery]], [[myna]], [[sensus]], [[meanpop]] | | [[mystery]], [[myna]], [[sensus]], [[meanpop]] | ||
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| [[abigail]], [[satin]], [[trinity]], [[newt]], [[acyuta]], [[deca]], [[quasiorwell]], [[decoid]], [[vulture]], [[hemiennealimmal]], [[Horwell_temperaments#Emkay|emkay]], [[countercata]] | | [[abigail]], [[satin]], [[trinity]], [[newt]], [[acyuta]], [[deca]], [[quasiorwell]], [[decoid]], [[vulture]], [[hemiennealimmal]], [[Horwell_temperaments#Emkay|emkay]], [[countercata]] | ||
|- | |- | ||
! 17-limit <br>(2 . 3 . 5 . 7 . 11 . 13 . 17) | ! 17-limit <br />(2.3.5.7.11.13.17) | ||
| [[leapday]], [[superkleismic]]+, [[meantonic]], [[huygens]] | | [[leapday]], [[superkleismic]]+, [[meantonic]], [[huygens]] | ||
| [[hendec]], [[marvolo]], [[diaschismic]], [[sensus]], [[andromeda]], [[modus]] | | [[hendec]], [[marvolo]], [[diaschismic]], [[sensus]], [[andromeda]], [[modus]] | ||
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| [[satin]], [[trinity]], [[octoid]], [[quincy]], [[mirkat]], [[ekadash]]+, [[quadritikleismic]], [[neominor]]+, [[ennealimnic]], [[sqrtphi]] | | [[satin]], [[trinity]], [[octoid]], [[quincy]], [[mirkat]], [[ekadash]]+, [[quadritikleismic]], [[neominor]]+, [[ennealimnic]], [[sqrtphi]] | ||
|- | |- | ||
! 19-limit <br>(2 . 3 . 5 . 7 . 11 . 13 . 17 . 19) | ! 19-limit <br />(2.3.5.7.11.13.17.19) | ||
| [[octacot]], [[andromeda]], [[meantonic]], [[huygens]] | | [[octacot]], [[andromeda]], [[meantonic]], [[huygens]] | ||
| [[hendec]]+, [[sensus]]+, [[crepuscular]]+, [[hitchcock]], [[modus]] | | [[hendec]]+, [[sensus]]+, [[crepuscular]]+, [[hitchcock]], [[modus]] | ||
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| [[satin]], [[trinity]], [[sqrtphi]]+, [[gizzard]]+, [[ketchup]], [[semisept]], [[cassandric]] | | [[satin]], [[trinity]], [[sqrtphi]]+, [[gizzard]]+, [[ketchup]], [[semisept]], [[cassandric]] | ||
|- | |- | ||
! 2 . 3 . 5 . 7 . other n | ! 2.3.5.7.other n | ||
| no-11 [[harry]], [[unicorn]] | | no-11 [[harry]], [[unicorn]] | ||
| no-11 [[buzzard]], no-11 [[orwell]] | | no-11 [[buzzard]], no-11 [[orwell]] | ||
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| no-11 [[ennealimmal]], no-11 [[decoid]], no-11 [[ennealimnic]], no-11 [[quadritikleismic]] | | 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 | ||
| no-7 [[qintosec]], [[pental]]+, no-7 [[maquila]], [[sensible]], [[ampersand]]+ | | no-7 [[qintosec]], [[pental]]+, no-7 [[maquila]], [[sensible]], [[ampersand]]+ | ||
| [[twentcufo]], no-7 [[emka]], no-7 [[gwazy]], no-7 [[rodan]], no-7 [[cataclysmic]], no-7 [[sfourth]] | | [[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]] | | no-7 [[hemienneadecal]], no-7 [[vulture]] | ||
|- | |- | ||
! 2 . 3 . 5 . other n | ! 2.3.5.other n | ||
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! 2 . 3 . 7 | ! 2.3.7 | ||
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! 2 . 3 . 7 . 11 <br>and its extensions | ! 2.3.7.11 <br />and its extensions | ||
| no-5 [[quanic]] | | no-5 [[quanic]] | ||
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! 2 . 3 . 7 . other n | ! 2.3.7.other n | ||
| [[hypnosis]] | | [[hypnosis]] | ||
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|- | |- | ||
! 2 . 3 . 11 <br>and its extensions | ! 2.3.11 <br />and its extensions | ||
| rank-2 [[pythrabian]] | | rank-2 [[pythrabian]] | ||
| rank-2 [[frameshift]] | | rank-2 [[frameshift]] | ||
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! 2 . 3 . other n | ! 2.3.other n | ||
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! 2 . 5 . 7 <br>and its extensions | ! 2.5.7 <br />and its extensions | ||
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| [[Subgroup temperaments#Daemotertiaschis|daemotertiaschis]] | | [[Subgroup temperaments#Daemotertiaschis|daemotertiaschis]] | ||
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! 2 . 5 . other n | ! 2.5.other n | ||
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! 2 . 7 <br>and its extensions | ! 2.7 <br />and its extensions | ||
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! 3 . 5 . 7 <br>and its extensions | ! 3.5.7 <br />and its extensions | ||
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! 3 . 5 . other n | ! 3.5.other n | ||
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! 3 . 7 <br>and its extensions | ! 3.7 <br />and its extensions | ||
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! 4 . n <br>and its extensions | ! 4.n <br />and its extensions | ||
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! 5 . n <br>and its extensions | ! 5.n <br />and its extensions | ||
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== Notes == | == Notes == | ||
<references group="note" /> | |||
[[Category:Lists of temperaments]] | [[Category:Lists of temperaments]] | ||