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 === | |||
'''The rows categorise temperaments by the [[just intonation subgroup]] they approximate.''' | '''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 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. | ||
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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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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 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. | ||
=== Columns === | |||
'''The columns categorise temperaments by the approximate number of notes-per-[[equave]] needed to reach all the temperament’s important intervals'''. | '''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. | 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. | ||
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If you see any temperaments listed in the wrong order, or see any temperaments in the wrong ‘approx. number of notes needed’ category, please move them to the correct position. | |||
If you know of a temperament that is recommended by a sizeable subset of the xen community but is not yet included here, please add it. | |||
Please do not add temperaments just for the sake of filling empty cells on the table. It’s okay for some cells to be empty. Only add temperaments if yourself, or at least a few other people, would recommend those temperaments. | |||
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. | |||
--> | |||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
| | |- | ||
! JI subgroup | ! JI subgroup | ||
! ~10 notes per equave | ! ~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 (temperament)|Helmholtz]], [[orson]], [[wuerschmidt]], [[sensipent]], [[compton]], [[valentine]], [[diaschismic]], [[tetracot]], [[passion]], [[superpyth]], [[ripple]] | ||
| [[kwazy]], [[luna]], [[vishnu]], [[parakleismic]], [[escapade]], [[amity]], [[gravity]], [[rodan]] | | [[kwazy]], [[luna]], [[vishnu]], [[parakleismic]], [[escapade]], [[amity]], [[gravity]], [[rodan]] | ||
| [[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]] | ||
| [[amity]], [[hemiwuerschmidt]], [[harry]], [[miracle]], [[garibaldi]], [[diaschismic]], [[sensi]] | | [[amity]], [[hemiwuerschmidt]], [[harry]], [[miracle]], [[garibaldi]], [[diaschismic]], [[sensi]] | ||
| [[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]] | ||
| [[nusecond]], [[modus]], [[lupercalia]], [[Meantone_family#Tridecimal_meantone|meantone]], [[winston]], [[pajara]], [[sensis]], [[ringo]], [[flattone]], [[darjeeling]], [[meanenneadecal]] | | [[nusecond]], [[modus]], [[lupercalia]], [[Meantone_family#Tridecimal_meantone|meantone]], [[winston]], [[pajara]], [[sensis]], [[ringo]], [[flattone]], [[darjeeling]], [[meanenneadecal]] | ||
| [[ | | [[miraculous]], [[leapday]], [[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]]+ | ||
| [[nusecond]]+, [[crepuscular]], [[winston]]+, [[pajara]], [[negroni]]+, [[sensis]]+, [[ringo]]+, [[pajarous]], [[augene]]+ | | [[nusecond]]+, [[crepuscular]], [[winston]]+, [[pajara]], [[negroni]]+, [[sensis]]+, [[ringo]]+, [[pajarous]], [[augene]]+ | ||
| | | [[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 | ||
| [[ | | [[porcupine]], [[mavila]], [[dicot]], [[flattone]] | ||
| [[orson]]+, [[tetracot]], [[mohaha]] | | [[orson]]+, [[tetracot]], [[mohaha]] | ||
| [[larry]] (no-7 [[gravity]]), [[countdown]], no-7 [[catalan]] | | [[larry]] (no-7 [[gravity]]), [[countdown]], no-7 [[catalan]] | ||
| [[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]] | ||
| | | no-5 no-11 [[liese]], no-11 [[skwares]] | ||
| | | | ||
| [[slendric]]+ | | [[slendric]]+ | ||
|- | |- | ||
! 2 . 3 . 11 <br>and its extensions | ! 2.3.11 <br>and its extensions | ||
| [[ | | [[neutral (temperament)|neutral]] (2.3.11 [[rastmic]]), [[namo]], [[paralimmal]], [[io]] | ||
| [[tribilo]] (2.3.11 [[nexus]]), [[huxley]] | | [[tribilo]] (2.3.11 [[nexus]]), [[huxley]] | ||
| | | | ||
| | | | ||
|- | |- | ||
! 2 . 3 . other n | ! 2.3.other ''n'' | ||
| [[barbados]], [[boethian]], [[semitonic]], [[superflat]], [[hydrothermal]] | | [[barbados]], [[boethian]], [[semitonic]], [[superflat]], [[hydrothermal]] | ||
| [[threedic]], [[pepperoni]] | | [[threedic]], [[pepperoni]] | ||
| [[ | | [[Subgroup temperaments #Historical|historical]] | ||
| | | | ||
|- | |- | ||
! 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]] | ||
| | | no-3 no-7 [[emka]], [[wizz]]+ | ||
| | | | ||
| | | | ||
|- | |- | ||
! 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]] ( | | [[mintaka]] (no-13), [[keladic]] | ||
| [[mebsuta]], [[minalzidar]] | | [[mebsuta]], [[minalzidar]] | ||
| [[mintaka]] (with 13) | | [[mintaka]] (with 13) | ||
| | | | ||
|- | |- | ||
! 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]], [[ | | [[ennealimmal]], [[quintosec]], [[counterhanson]], [[undim]] | ||
| [[ | | [[alphatricot]], [[quintile]] | ||
| [[minortone]], [[vavoom]] | | [[minortone]], [[vavoom]] | ||
| | | | ||
| | | | ||
|- | |- | ||
! 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]] | ||
| [[ | | [[diaschismic]], [[myna]], [[sensus]], [[meanpop]] | ||
| [[cassandra]] | | [[cassandra]], [[grosstone]] | ||
| [[widefourth]], [[octopus]], [[buzzard]], [[catakleismic]], [[rodan]], [[shrutar]] | | [[widefourth]], [[octopus]], [[mystery]], [[buzzard]], [[catakleismic]], [[rodan]], [[shrutar]] | ||
| [[abigail]], [[satin]], [[trinity]], [[newt]], [[acyuta]], [[deca]], [[quasiorwell]], [[decoid]], [[vulture]], [[hemiennealimmal]], [[ | | [[abigail]], [[satin]], [[trinity]], [[newt]], [[acyuta]], [[deca]], [[quasiorwell]], [[decoid]], [[vulture]], [[hemiennealimmal]], [[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]] | ||
| [[marvolo]], [[miraculous]]+ | | [[marvolo]], [[miraculous]]+ | ||
| [[ennealim]], [[bikleismic]], [[srutal]], [[valentino]]+ | | [[octopus]], [[ennealim]], [[bikleismic]], [[srutal]], [[valentino]]+ | ||
| [[newt|neonewt]]+, [[deca]]+, [[vulture]], [[satin]], [[stearnscape]]+, [[hemiennealimmal]], [[trinity]], [[quincy]], [[octoid]], [[sqrtphi]] | | [[newt|neonewt]]+, [[deca]]+, [[vulture]], [[satin]], [[stearnscape]]+, [[hemiennealimmal]], [[trinity]], [[quincy]], [[octoid]], [[sqrtphi]] | ||
|- | |- | ||
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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 [[ | | 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]] | | [[twentcufo]], no-7 [[emka]], no-7 [[gwazy]], no-7 [[rodan]], no-7 [[cataclysmic]], no-7 [[sfourth]] | ||
| | | | ||
| | | [[majvam]]+ | ||
| no-7 [[hemienneadecal]], no-7 [[vulture]] | | no-7 [[hemienneadecal]], no-7 [[vulture]] | ||
|- | |- | ||
! 2 . 3 . 5 . other n | ! 2.3.5.other ''n'' | ||
| | | | ||
| | | | ||
| | | | ||
| [[majvam]] | |||
| | | | ||
|- | |- | ||
! 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 | ||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
| [[Subgroup temperaments#Daemotertiaschis|daemotertiaschis]] | | [[Subgroup temperaments #Daemotertiaschis|daemotertiaschis]] | ||
|- | |- | ||
! 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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# '''[[Compton]] (51)''' | # '''[[Compton]] (51)''' | ||
# [[Ennealimmal]] (50) | # [[Ennealimmal]] (50) | ||
# [[Helmholtz]] (49) | # [[Helmholtz (temperament)|Helmholtz]] (49) | ||
# [[Dicot]] (47) | # [[Dicot]] (47) | ||
# [[Garibaldi]] (47) | # [[Garibaldi]] (47) | ||
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== Advanced reading == | == Advanced reading == | ||
* [[Tour of regular temperaments]]: a huge list of temperament families, many of which remain rarely-used and unexplored | * [[Tour of regular temperaments]]: a huge list of temperament families, many of which remain rarely-used and unexplored | ||
* [https://x31eq.com/catalog2.html x31eq Catalog of Regular Temperaments]: an even huger list by [[Graham Breed]] | |||
* [[Rank-3]] and [[rank-4]] temperaments: these are more complicated, rarely-used, types of temperaments | * [[Rank-3]] and [[rank-4]] temperaments: these are more complicated, rarely-used, types of temperaments | ||
* [[Equal-step tuning]]s (i.e. rank-1 temperaments) | * [[Equal-step tuning]]s (i.e. rank-1 temperaments) | ||
* More lists of temperaments: | |||
** [[Low harmonic entropy linear temperaments]] | |||
** [[Map of rank-2 temperaments]] | |||
** [[Ordered lists of ET rank two temperaments]] | |||
** and everything else in [[:Category:Lists of temperaments]] | |||
* A deprecated, archived in-development version of this page: [[User:BudjarnLambeth/Bird’s eye view of rank-2 temperaments]] | * A deprecated, archived in-development version of this page: [[User:BudjarnLambeth/Bird’s eye view of rank-2 temperaments]] | ||
== Notes == | == Notes == | ||
<references group="note" /> | |||
[[Category: | [[Category:Lists of temperaments]] | ||