@@ Line 4: / Line 4: @@
 == 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 regular temperament theory (RTT). Most would agree that a good temperament is ''efficient'', meaning it approximates some subset of [[just intonation]] relatively accurately with a relatively small number of notes. What they disagree on is ''how'' accurate is "relatively accurate", ''how'' small is "relatively small", and ''which'' JI subsets are interesting enough to be worth approximating.
-Most would agree that a good temperament is ''efficient'', meaning it approximates some subset of [[just intonation]] relatively accurately with a relatively small number of notes.
-What they disagree on is ''how'' accurate is "relatively accurate", ''how'' small is "relatively small", and ''which'' JI subsets are interesting enough to be worth approximating.
 For example:
+* '''Xenharmonicist A''' might argue that an error less than ~15 [[cents]] on most intervals, and less than 5 cents on the really important ones (like the perfect fifth and the octave), is accurate enough, and they might argue that 25 notes per [[equave]] is the most that is practical, any more than that is too cumbersome. They might argue that nobody can hear the harmonic effect of [[prime harmonics]] higher than 11, and they might argue that there is no real reason to use [[subgroup]]s that are missing primes 2 or 3, because those primes are so important to consonance.
+* '''Xenharmonicist B''' might argue that the error must be less than ~5 cents on almost all intervals, anything further out than that sounds out of tune to them. They might argue that it is perfectly possible to learn up to 50 notes per equave. They might argue that they can hear the subtle, delicate effect of prime harmonics up to 23, and they might argue that subgroups like 3.5.7.11 and 2.5.7.11 are the most fertile ground for new and exciting musical exploration.
+These are not the only possible stances, either: one could imagine a xenharmonicist C, xenharmonicist D, etc. Thousands of differing individual perspectives on what traits are important in a temperament.
-'''Xenharmonicist A''' might argue that an error less than ~15 [[cents]] on most intervals, and less than 5 cents on the really important ones (like the perfect fifth and the octave), is accurate enough.
+To gain more of a grasp on these debates, it may help to compare these temperaments to [[12edo]], a.k.a. the familiar 12-tone equal temperament which most modern music is tuned to by default. 12edo has, of course, 12 notes per equave, which makes it fairly small by temperament standards but not abnormally so. The most common theoretical approach to 12edo is to treat it as a 2.3.5-subgroup temperament, with similar accuracy to [[augmented (temperament)|augmented]]. The second most common approach is to interpret 12edo as a 2.3.17.19-subgroup temperament, with similar accuracy to [[semitonic]]. (Such a temperament would go in the ''2.3.other n'' row of the below tables). So that should provide a helpful point of comparison to measure these other temperaments against.
-And they might argue that 25 notes per [[equave]] is the most that is practical, any more than that is too cumbersome.
-They might argue that nobody can hear the harmonic effect of [[prime harmonics]] higher than 11.
-And they might argue that there's no real reason to use [[subgroup]]s that are missing primes 2 or 3, because those primes are so important to consonance.
-'''Xenharmonicist B''' might argue that the error must be less than ~5 cents on almost all intervals, anything further out than that sounds out of tune to them.
-They might argue that it's perfectly possible to learn up to 50 notes per equave.
-They might argue that they can hear the subtle, delicate effect of prime harmonics up to 23.
-And they might argue that subgroups like 3.5.7.11 and 2.5.7.11 are the most fertile ground for new and exciting musical exploration.
-These are not the only possible stances, either: One could imagine a Xenharmonicist C, Xenharmonicist D, etc. Thousands of differing individual perspectives on what traits are important in a temperament.
-To gain more of a grasp on these debates, it may help to compare these temperaments to [[12edo]], a.k.a. the familiar 12-tone equal temperament which most modern music is tuned to by default. 12edo has, of course, 12 notes per equave, which makes it fairly small by temperament standards (but not abnormally so).
-The most common theoretical approach to 12edo is to treat it as a 2.3.5 subgroup temperament, with similar accuracy to '''augmented'''.
-The second most common approach is to interpret 12edo as a 2.3.17.19 subgroup temperament, with similar accuracy to '''semitonic'''. (Such a temperament would go in the “''2.3.other n''” row of the below tables).
-So that should provide a helpful point of comparison to measure these other temperaments against.
 == How to read the tables ==
@@ Line 67: / Line 39: @@
 == Table of temperaments (5 to 45 notes per equave) ==
 The temperaments within each cell should be sorted by accuracy, with the lowest [[damage]] (highest accuracy) temperament listed first.
 <!--
 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.
@@ Line 76: / Line 47: @@
 -->
+=== Full prime limits ===
 {| class="wikitable center-all"
 |-
 ! JI subgroup
-! ~10 notes per equave<ref group="note">Number of notes per equave was estimated by multiplying the temperament’s [[graham complexity]] by 2.</ref>
+! ~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
-! ~30 notes
-! ~40 notes
 |-
 ! 5-limit <br>(2.3.5)
-| [[hanson]], [[misty]], [[magic]], [[meantone]], [[negri]], [[augmented (temperament)|diminished]], [[porcupine]], [[diminished (temperament)|diminished]], [[whitewood]], [[blackwood]], [[mavila]]
+| [[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]]
+| [[Helmholtz (temperament)|Helmholtz]], [[orson]], [[würschmidt]], [[sensipent]], [[compton]], [[valentine]], [[diaschismic]], [[tetracot]], [[passion]], [[superpyth]], [[ripple]]
-| [[kwazy]], [[luna]], [[vishnu]], [[parakleismic]], [[escapade]], [[amity]], [[gravity]], [[rodan]]
+| [[Luna]], [[vishnu]], [[parakleismic]], [[escapade]], [[amity]], [[misty]], [[gravity]], [[rodan]]
-| [[enneadecal]], [[gammic]], [[vulture]]
+| [[Enneadecal]], [[gammic]], [[vulture]]
 |-
 ! 7-limit <br>(2.3.5.7)
-| [[porcupine]], [[pajara]], [[keemun]], [[negri]], [[doublewide]], [[injera]], [[dominant (temperament)|dominant]], [[august]], [[diminished (temperament)|diminished]], [[blackwood]]
+| [[Dominant (temperament)|Dominant]], [[august]], [[blackwood]]
-| [[orwell]], [[valentine]], [[myna]], [[magic]], [[meantone]], [[mothra]], [[superpyth]], [[flattone]], [[liese]], [[beatles]], [[augene]], [[hedgehog]], [[nautilus]], [[catler]], [[godzilla]],  [[lemba]]
+| [[Magic]], [[meantone]], [[superpyth]], [[liese]], [[augene]], [[porcupine]], [[pajara]], [[negri]], [[keemun]], [[catler]], [[godzilla]], [[hedgehog]], [[injera]], [[nautilus]], [[diminished (temperament)|diminished]]
-| [[amity]], [[hemiwürschmidt]], [[harry]], [[miracle]], [[garibaldi]], [[diaschismic]], [[sensi]]
+| [[Garibaldi]], [[orwell]], [[sensi]], [[mothra]], [[flattone]], [[beatles]], [[doublewide]], [[lemba]]
-| [[misty]], [[unidec]], [[catakleismic]]
+| [[Catakleismic]], [[miracle]], [[valentine]], [[myna]], [[diaschismic]]
 |-
 ! 11-limit <br>(2.3.5.7.11)
-| [[triforce]], [[blackwood]], [[pajaric]], [[negric]]
+|
-| [[orwell]], [[valentine]], [[mohajira]], [[porcupine]], [[hedgehog]], [[astrology]], [[vigintiduo]], [[augene]], [[nautilus]], [[catnip]], [[undevigintone]], [[injera]], [[keemun]], [[progress]], [[dominant (temperament)|dominant]], [[meanenneadecal]], [[duodecim]]
+| [[Porcupine]], [[augene]], [[hedgehog]], [[catnip]], [[nautilus]], [[injera]], [[godzilla]], [[triforce]], [[progress]], [[meanenneadecal]], [[duodecim]], [[negric]], [[dominant (temperament)|dominant]], [[blackwood]], [[pajaric]]
-| [[mothra]], [[nusecond]], [[meantone]], [[squares]], [[quasisupra]], [[pajara]], [[telepathy]], [[suprapyth]], [[negroni]], [[porky]], [[fleetwood]], [[pajarous]], [[sensis]], [[flattone]], [[godzilla]], [[darjeeling]]
+| [[Orwell]], [[nusecond]], [[squares]], [[quasisupra]], [[pajara]], [[porky]], [[sensis]], [[telepathy]], [[suprapyth]], [[pajarous]], [[flattone]], [[keemun]], [[darjeeling]]
-| [[miracle]], [[shrutar]], [[magic]], [[meanpop]], [[migration]], [[andromeda]], [[superpyth]]
+| [[Miracle]], [[valentine]], [[shrutar]], [[magic]], [[andromeda]], [[mothra]], [[migration]], [[meantone]], [[mohajira]], [[superpyth]], [[undevigintone]], [[astrology]], [[vigintiduo]], [[negroni]], [[fleetwood]]
 |-
 ! 13-limit <br>(2.3.5.7.11.13)
-| [[negric]]
+|
-| [[augene]], [[porcupine]], [[hedgehog]], [[triforce]], [[godzilla]], [[negri]], [[armodue (temperament)|armodue]]
+| [[Porcupinefowl]], [[hedgehog]], [[triforce]], [[godzilla]], [[augene]], [[negric]], [[negri]], [[armodue (temperament)|armodue]]
-| [[nusecond]], [[modus]], [[lupercalia]], [[Meantone_family#Tridecimal_meantone|meantone]], [[winston]], [[pajara]], [[sensis]], [[ringo]], [[flattone]], [[darjeeling]], [[meanenneadecal]]
+| [[Winston]], [[sensis]], [[ringo]], [[flattone]], [[darjeeling]], [[meanenneadecal]], [[pajara]]
-| [[miraculous]], [[leapday]], [[andromeda]], [[superkleismic]], [[mothra]], [[mohajira]], [[undevigintone]], [[ogene]], [[nautilus]], [[negroni]], [[injera]]
+| [[Miraculous]], [[leapday]], [[superkleismic]], [[mothra]], [[nusecond]], [[modus]], [[lupercalia]], [[mohajira]], [[fokkertone]], [[undevigintone]], [[ogene]], [[negroni]], [[nautilus]], [[injera]]
 |-
 ! 17-limit <br>(2.3.5.7.11.13.17)
 |
-| [[lemba]]+, [[hedgehog]]+
+|
-| [[nusecond]]+, [[crepuscular]], [[winston]]+, [[pajara]], [[negroni]]+, [[sensis]]+, [[ringo]]+, [[pajarous]], [[augene]]+
+| [[Pajara]], [[pajarous]]
-| [[miraculous]], [[lupercalia]]+, [[mohajira]], [[superpyth]]+, [[meantoid]], [[injera]], [[meanenneadecal]]
+| [[Miraculous]], [[mohajira]], [[crepuscular]], [[injera]], [[meanenneadecal]]
 |-
 ! 19-limit <br>(2.3.5.7.11.13.17.19)
 |
-| [[niner]]++
+|
-| [[wilsec]], [[winston]]++, [[augene]]++, [[sensis]]++
+|
-| [[roman]]++, [[mohajira]], [[lupercalia]]++, [[superpyth]]++, [[negroni]]++, [[meanenneadecal]], [[ringo]]++, [[injera]], [[meantoid]]
+| [[Mohajira]], [[injera]], [[meanenneadecal]]
 |-
 ! Higher prime limits
@@ Line 124: / Line 96: @@
 |
 |
-| [[lupercalia]]+++, [[nautilus]]+++, [[negroni]]+++, [[injera]]+
+|
+|}
+=== Other subgroups ===
+Subgroups ''without'' a "2" ''don't have'' multiple of 2 intervals (eg the 2/1 octave, the 3/2 perfect fifth, the 5/4 major third).
+Subgroups ''without'' a "3" ''don't have'' multiple of 3 intervals (eg the 3/1 perfect twelfth, the 3/2 perfect fifth, the 5/3 major sixth).
+Subgroups ''without'' a "5" ''don't have'' multiple of 5 intervals (eg the 5/3 major sixth, the 5/4 major third, the 6/5 minor third).
+Subgroups ''with'' a "7", "11", or "other ''n''" include new [[xenharmonic]] consonant intervals that can't be found in common [[12edo]] tuning.
+{| class="wikitable center-all"
+|-
+! JI subgroup
+! ~5 notes per equave
+! ~10 notes
+! ~15 notes
+! ~20 notes
 |-
 ! 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]]
-| no-11 [[magic]], no-11 [[sensis]], no-11 [[meanpop]]
+| No-11 [[magic]], no-11 [[sensis]], no-11 [[meanpop]]
-| no-11 [[catakleismic]]
+| No-11 [[catakleismic]]
 |-
 ! 2.3.5.11 <br>and its extensions
-| [[porcupine]], [[mavila]], [[dicot]], [[flattone]]
+| [[Porcupine]], [[mavila]], [[dicot]], [[flattone]]
-| [[orson]]+, [[tetracot]], [[mohaha]]
+| [[Tetracot]], [[mohaha]]
-| [[larry]] (no-7 [[gravity]]), [[countdown]], no-7 [[catalan]]
+| [[Larry]], [[countdown]], no-7 [[catalan]]
-| [[escapade]]
+| [[Escapade]]
 |-
 ! 2.3.5.other ''n''
-| [[srutal archagall]], [[stutzel]]
+| [[Srutal archagall]], [[stutzel]]
-| [[sensipent]], [[nestoria]]
+| [[Sensipent]], [[nestoria]]
-| [[würschmidt]]<ref group="note">Subgroup 2.3.5.23 version.</ref>, [[cata]]
+| [[Würschmidt]]<ref group="note">Subgroup 2.3.5.23 version.</ref>, [[cata]]
 |
 |-
 ! 2.3.7
-| [[slendric]], [[archy]], [[bleu]], [[semaphore]]
+| [[Slendric]], [[archy]], [[bleu]], [[semaphore]]
-| [[stearnsmic clan|stearnsmic]], [[skwares]]
+| No-5 [[stearnsmic clan|stearnsmic]], [[skwares]]
-| [[hemif]], [[leapfrog]]
+| [[Hemif]], [[leapfrog]]
 |
 |-
 ! 2.3.7.11 <br>and its extensions
-| [[bleu]], [[supra]], [[semaphore]]+
+| [[Bleu]], [[supra]], [[semaphore]]+
-| [[skwares]], [[stearnsmic clan|stearnsmic]]+, [[suhajira]]
+| [[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]]
+| 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''
-| [[baladic]], [[oceanfront]], no-5 [[negra]]
+| [[Baladic]], [[oceanfront]], no-5 [[negra]]
-| no-5 no-11 [[liese]], no-11 [[skwares]]
+| No-5 no-11 [[liese]], no-11 [[skwares]]
+|
 |
-| [[slendric]]+
 |-
 ! 2.3.11 <br>and its extensions
-| [[neutral (temperament)|neutral]] (2.3.11 [[rastmic]]), [[namo]], [[paralimmal]], [[io]]
+| [[Neutral (temperament)|neutral]], [[namo]], [[paralimmal]], [[io]]
-| [[tribilo]] (2.3.11 [[nexus]]), [[huxley]]
+| [[Tribilo]], [[huxley]]
 |
 |
 |-
 ! 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
-| [[didacus]], [[frostburn]], no-3 [[oodako]]
+| [[Didacus]], [[frostburn]], no-3 [[oodako]], [[augment]]
-| [[rainy]], [[mercy]], [[huntington]], [[llywelyn]], [[baldy]]
+| [[Rainy]], [[mercy]], [[huntington]]
-| [[roulette]]
+| [[Llywelyn]], [[silver]], [[baldy]]
-|
+| [[Roulette]]
 |-
 ! 2.5.other ''n''
-| [[insect]], [[sulis]], [[wizz]], [[vengeance]], [[marveltri]], [[superquintal]], [[movila]]
+| [[Insect]], [[sulis]], [[wizz]], [[vengeance]], [[marveltri]], [[superquintal]], [[movila]]
-| no-3 no-7 [[emka]], [[wizz]]+
+| No-3 no-7 [[emka]]
 |
 |
 |-
 ! 2.7 <br>and its extensions
-| [[orgone]], [[shipwreck]], [[stacks]], [[ultrakleismic]], [[machine]]
+| [[Orgone]], [[shipwreck]], [[stacks]], [[ultrakleismic]], [[machine]]
-| [[counterultrakleismic]], [[mechanism]], [[mabon]]
+| [[Counterultrakleismic]], [[mechanism]], [[mabon]]
 |
-| [[machine|apparatus]]
+| [[Apparatus]]
 |-
 ! 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]], [[vega]]
-| [[izar]], [[mintra]]
+| [[Izar]], [[mintra]]
-| [[alhena]], [[remus]]
+| [[Alhena]], [[remus]]
-| [[erigone]]
+| [[Erigone]]
 |-
 ! 3.5.other ''n''
-| [[aldebaran]], [[deneb]], [[polaris]]
+| [[Aldebaran]], [[deneb]], [[polaris]]
 |
 |
-| [[alnilam]], [[fomalhaut]]
+| [[Alnilam]], [[fomalhaut]]
 |-
 ! 3.7 <br>and its extensions
-| [[mintaka]] (no-13), [[keladic]]
+| [[Mintaka]] (no-13), [[keladic]]
-| [[mebsuta]], [[minalzidar]]
+| [[Mebsuta]], [[minalzidar]]
-| [[mintaka]] (with 13)
+| [[Mintaka]] (with 13)
 |
 |-
 ! 4.''n'' <br>and its extensions
-| [[meanquad]], [[tetrahanson]], [[tetrameantone]], [[quarchy]], [[tetrominant]]
+| [[Meanquad]], [[tetrahanson]], [[tetrameantone]], [[quarchy]], [[tetrominant]]
+|
 |
-| [[fourwar]]
 |
 |-
 ! 5.''n'' <br>and its extensions
-| [[antipyth]], [[juggernaut]]
+| [[Antipyth]], [[juggernaut]]
 |
 |
@@ Line 223: / Line 213: @@
 |-
 ! Other subgroups
-| [[greeley]], [[halftone]], [[semiwolf]], [[auk]]
+| [[Greeley]], [[halftone]], [[semiwolf]], [[auk]]
 |
 |
@@ Line 234: / Line 224: @@
 |+
 ! JI subgroup
-! ~50 notes
+! ~25 notes
-! ~60 notes
+! ~30 notes
-! ~70 notes
+! ~35 notes
-! ~80 notes
+! ~40 notes
-! >90 notes
+! >45 notes
 |-
 ! 5-limit <br>(2.3.5)
-| [[ennealimmal]], [[quintosec]], [[counterhanson]], [[undim]]
+| [[Kwazy]], [[ennealimmal]], [[quintosec]], [[counterhanson]], [[undim]], [[quintile]]
-| [[alphatricot]], [[quintile]]
+| [[Alphatricot]]
-| [[minortone]], [[vavoom]]
+| [[Minortone]], [[vavoom]]
 |
 |
 |-
 ! 7-limit <br>(2.3.5.7)
-| [[ennealimmal]], [[tertiaseptal]], [[hemififths]], [[quadritikleismic]], [[grendel]], [[unidec]]
+| [[Hemififths]]
-| [[hendecatonic]]
+| [[Hemiwürschmidt]], [[unidec]]
-| [[sesquiquartififths]], [[quinmite]], [[parakleismic]]
+| [[Ennealimmal]], [[sesquiquartififths]], [[parakleismic]], [[amity]], [[harry]], [[misty]], [[hendecatonic (temperament)|hendecatonic]]
-| [[neptune]], [[gamera]], [[nessafof]], [[octoid]], [[septiquarter]]
+| [[Septiquarter]]
-| [[supermajor]], [[enneadecal]], [[term]]
+| [[Supermajor (temperament)|Supermajor]], [[enneadecal]], [[term]], [[neptune (temperament)|neptune]], [[tertiaseptal]], [[gamera]], [[quinmite]], [[nessafof]], [[octoid]], [[quadritikleismic]], [[grendel]]
 |-
 ! 11-limit <br>(2.3.5.7.11)
-| [[unidec]], [[tritikleismic]], [[hemithirds]], [[wizard]], [[diaschismic]]
+| [[Meanpop]]
-|
+| [[Unidec]], [[wizard]], [[diaschismic]]
-| [[quadritikleismic]], [[harry]]
+| [[Harry]], [[hemithirds]]
-| [[quasiorwell]], [[octoid]], [[sqrtphi]], [[hemiwürschmidt]], [[ennealimnic]], [[catakleismic]]
+| [[Tritikleismic]], [[hemiwürschmidt]]
-| [[hemienneadecal]], [[hemiennealimmal]], [[abigail]], [[hemitert]], [[newt]], [[decoid]], [[vishnu]]
+| [[Hemienneadecal]], [[hemiennealimmal]], [[abigail]], [[hemitert]], [[newt]], [[decoid]], [[vishnu]], [[quasiorwell]], [[octoid]], [[quadritikleismic]], [[sqrtphi]], [[ennealimnic]], [[catakleismic]]
 |-
 ! 13-limit <br>(2.3.5.7.11.13)
-| [[hemififths]], [[orwell]], [[magic]]
+| [[Hemififths]], [[andromeda]], [[magic]]
-| [[diaschismic]], [[myna]], [[sensus]], [[meanpop]]
+| [[Mystery]], [[myna]], [[sensus]], [[meanpop]]
-| [[cassandra]], [[grosstone]]
+| [[Cassandra]], [[diaschismic]], [[orwell]], [[grosstone]]
-| [[widefourth]], [[octopus]], [[mystery]], [[buzzard]], [[catakleismic]], [[rodan]], [[shrutar]]
+| [[Buzzard]], [[rodan]], [[shrutar]]
-| [[abigail]], [[satin]], [[trinity]], [[newt]], [[acyuta]], [[deca]], [[quasiorwell]], [[decoid]], [[vulture]], [[hemiennealimmal]], [[emkay]], [[countercata]]
+| [[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)
-| [[leapday]], [[superkleismic]]+, [[meantonic]], [[huygens]]
+| [[Leapday]], [[superkleismic]], [[fokkertone]]
-| [[hendec]], [[marvolo]], [[diaschismic]], [[sensus]], [[andromeda]], [[modus]]
+| [[Hendec]], [[sensus]], [[andromeda]], [[modus]]
-| [[comptone]]
+| [[Comptone]], [[diaschismic]]
-| [[heinz]], [[octopus]], [[lizard]], [[rodan]], [[echidna]], [[shrutar]]
+| [[Heinz]], [[octopus]], [[lizard]], [[marvolo]], [[rodan]], [[echidna]], [[shrutar]]
-| [[satin]], [[trinity]], [[octoid]], [[quincy]], [[mirkat]], [[ekadash]]+, [[quadritikleismic]], [[neominor]]+, [[ennealimnic]], [[sqrtphi]]
+| [[Satin]], [[trinity]], [[octoid]], [[quincy]], [[mirkat]], [[quadritikleismic]], [[ennealimnic]], [[sqrtphi]]
 |-
 ! 19-limit <br>(2.3.5.7.11.13.17.19)
-| [[octacot]], [[andromeda]], [[meantonic]], [[huygens]]
+| [[Fokkertone]], [[wilsec]]
-| [[hendec]]+, [[sensus]]+, [[crepuscular]]+, [[hitchcock]], [[modus]]
+| [[Hitchcock]], [[andromeda]]
-| [[marvolo]], [[miraculous]]+
+| [[Marvolo]]
-| [[octopus]], [[ennealim]], [[bikleismic]], [[srutal]], [[valentino]]+
+| [[Octopus]], [[ennealim]], [[bikleismic]], [[srutal]]
-| [[newt|neonewt]]+, [[deca]]+, [[vulture]], [[satin]], [[stearnscape]]+, [[hemiennealimmal]], [[trinity]], [[quincy]], [[octoid]], [[sqrtphi]]
+| [[Satin]], [[trinity]], [[hemiennealimmal]], [[quincy]], [[octoid]], [[sqrtphi]]
 |-
 ! Higher prime limits
-| [[winston]]+++, [[porky]]+++
 |
 |
-| [[srutaloo]], [[shrutar]]
+|
-| [[satin]], [[trinity]], [[sqrtphi]]+, [[gizzard]]+, [[ketchup]], [[semisept]], [[cassandric]]
+| [[Srutaloo]], [[shrutar]]
+| [[Satin]], [[trinity]], [[ketchup]], [[semisept]], [[cassandric]]
 |-
 ! 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]]
-| no-11 [[cassandra]]
+| No-11 [[cassandra]]
-| no-11 [[hemischis]]
+| No-11 [[hemischis]]
-| 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
-| no-7 [[quintosec]], [[quintile]]+, no-7 [[maquila]], [[sensible]], [[ampersand]]+
+| [[Quintosec]], no-7 [[maquila]], [[sensible]]
-| [[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''
@@ Line 307: / Line 297: @@
 |
 |
-| [[majvam]]
+| [[Majvam]]
 |
 |-
@@ Line 318: / Line 308: @@
 |-
 ! 2.3.7.11 <br>and its extensions
-| no-5 [[quanic]]
+| No-5 [[quanic]]
 |
 |
@@ Line 325: / Line 315: @@
 |-
 ! 2.3.7.other ''n''
-| [[hypnosis]]
+| [[Hypnosis]]
 |
 |
@@ Line 332: / Line 322: @@
 |-
 ! 2.3.11 <br>and its extensions
-| rank-2 [[pythrabian]]
+| Rank-2 [[pythrabian]]
-| rank-2 [[frameshift]]
+| Rank-2 [[frameshift]]
 |
 |
@@ Line 350: / Line 340: @@
 |
 |
-| [[Subgroup temperaments #Daemotertiaschis|daemotertiaschis]]
+| [[Daemotertiaschis]]
 |-
 ! 2.5.other ''n''
@@ Line 420: / Line 410: @@
 == Most linked-to rank-2 temperaments ==
-These were the top 99 rank-2 temperament pages with the most incoming links on the wiki on 27 Oct 2024. (When this section was written.)
+These are the top 105 rank-2 temperament pages with the most incoming links on the wiki as of 20 Oct 2026, about two years after this section was first written.
-# '''[[Meantone]] (313 links)'''
+# '''[[Meantone]] (540)'''
-# '''[[Porcupine]] (144)'''
+# '''[[Porcupine]] (223)'''
-# '''[[Superpyth]] (108)'''
+# '''[[Superpyth]] (183)'''
-# '''[[Magic]] (107)'''
+# '''[[Magic]] (164)'''
-# '''[[Mavila]] (97)'''
+# '''[[Mavila]] (135)'''
-# '''[[Orwell]] (81)'''
+# '''[[Orwell]] (127)'''
-# '''[[Miracle]] (78)'''
+# '''[[Miracle]] (125)'''
-# '''[[Pajara]] (76)'''
+# '''[[Blackwood]] (113)'''
-# '''[[Sensi]] (71)'''
+# '''[[Pajara]] (107)'''
-# '''[[Flattone]] (64)'''
+# '''[[Negri]] (106)'''
-# '''[[Amity]] (59)'''
+# '''[[Slendric]] (102)'''
-# '''[[Mohajira]] (59)'''
+# '''[[Sensi]] (101)'''
-# '''[[Negri]] (59)'''
+# '''[[Flattone]] (99)'''
-# '''[[Blackwood]] (58)'''
+# '''[[Tetracot]] (95)'''
-# '''[[Tetracot]] (56)'''
+# '''[[Garibaldi]] (93)'''
-# '''[[Valentine]] (53)'''
+# '''[[Diaschismic]] (91)'''
-# '''[[Wuerschmidt]] (53)'''
+# '''[[Valentine]] (90)'''
-# '''[[Slendric]] (52)'''
+# '''[[Würschmidt]] (86)'''
-# '''[[Compton]] (51)'''
+# '''[[Mohajira]] (83)'''
-# '''[[Ennealimmal]] (50)'''
+# '''[[Compton]] (78)'''
-# [[Helmholtz (temperament)|Helmholtz]] (49)
+# [[Amity]] (73)
-# [[Dicot]] (47)
+# [[Dicot]] (70)
-# [[Garibaldi]] (47)
+# [[Diminished (temperament)|Diminished]] (68)
-# [[Hanson]] (45)
+# [[Ennealimmal]] (67)
-# [[Catakleismic]] (44)
+# [[Archy]] (66)
-# [[Diaschismic]] (43)
+# [[Father]] (65)
-# [[Hemififths]] (42)
+# [[Catakleismic]] (64)
-# [[Myna]] (41)
+# [[Mothra]] (64)
-# [[Father]] (40)
+# [[Godzilla]] (62)
-# [[Squares]] (40)
+# [[Hemififths]] (62)
-# [[Rodan]] (39)
+# [[Squares]] (62)
-# [[Semaphore]] (39)
+# [[Semaphore]] (60)
-# [[Augmented]] (38)
+# [[Myna]] (59)
-# [[Diminished]] (38)
+# [[Hanson]] (58)
-# [[Srutal]] (38)
+# [[Rodan]] (58)
-# [[Godzilla]] (37)
+# [[Kleismic]] (57) (already listed as ''hanson'')
-# [[Harry]] (37)
+# [[Schismic]] (57)
-# [[Injera]] (37)
+# [[Augmented (temperament)|Augmented]] (56)
-# [[Diasem]] (36)
+# [[Injera]] (56)
-# [[Enneadecal]] (35)
+# [[Whitewood]] (56)
-# [[Orgone]] (34)
+# [[Harry]] (52)
-# [[Parakleismic]] (34)
+# [[Didacus]] (50)
-# [[Hedgehog]] (33)
+# [[Buzzard]] (49)
-# [[Luna]] (33)
+# [[Cassandra]] (49)
-# [[Octacot]] (33)
+# [[Octacot]] (49)
-# [[Augene]] (32)
+# [[Superkleismic]] (48)
-# [[Dominant]] (32)
+# [[Dominant (temperament)|Dominant]] (47)
-# [[Hemithirds]] (32)
+# [[Augene]] (46)
-# [[Keemun]] (32)
+# [[Helmholtz (temperament)|Helmholtz]] (46) (already listed as ''schismic'')
-# [[Lemba]] (32)
+# [[Hemiwürschmidt]] (46)
-# [[Mothra]] (32)
+# [[Keemun]] (46)
-# [[Whitewood]] (32)
+# [[Liese]] (44)
-# [[Archy]] (31)
+# [[Vishnu]] (44)
-# [[Liese]] (31)
+# [[Orgone]] (43)
-# [[Bleu]] (29)
+# [[Parakleismic]] (43)
-# [[Vishnu]] (29)
+# [[Srutal]] (43)
-# [[Hemiwuerschmidt]] (28)
+# [[BPS]] (42)
-# [[Superkleismic]] (27)
+# [[Lemba]] (42)
-# [[Echidna]] (26)
+# [[Passion]] (42)
-# [[Orson]] (26)
+# [[Enneadecal]] (41)
-# [[Tertiaseptal]] (26)
+# [[Vulture]] (41)
-# [[Triforce]] (26)
+# [[Escapade]] (40)
-# [[Passion]] (25)
+# [[Hedgehog]] (40)
-# [[Tritonic]] (25)
+# [[Ripple]] (40)
-# [[Unidec]] (25)
+# [[Triforce]] (40)
-# [[Wizard]] (25)
+# [[Tritonic]] (40)
-# [[Buzzard]] (24)
+# [[Nautilus]] (39)
-# [[Cassandra]] (24)
+# [[Echidna]] (38)
-# [[Ripple]] (24)
+# [[Hemithirds]] (38)
-# [[Vulture]] (24)
+# [[Luna]] (37)
-# [[Armodue]] (23) (''disambiguation page'')
+# [[Muggles]] (37)
-# [[Atomic]] (23)
+# [[Bleu]] (36)
-# [[Bug]] (23)
+# [[August]] (35)
-# [[Escapade]] (23)
+# [[Pontiac]] (35)
-# [[Pontiac]] (23)
+# [[Wizard]] (35)
-# [[Ampersand]] (22)
+# [[Bohpier]] (34)
-# [[Bohpier]] (22)
+# [[Orson]] (34)
-# [[Mohaha]] (22)
+# [[Sensipent]] (34)
-# [[Parapyth]] (22)
+# [[Tritikleismic]] (34)
-# [[August]] (21)
+# [[Beatles]] (33)
-# [[Blacksmith]] (21)
+# [[Schismatic]] (33) (already listed as ''schismic'')
-# [[Kwazy]] (21)
+# [[Unidec]] (32)
-# [[Octoid]] (21)
+# [[Bug]] (31)
-# [[Tritikleismic]] (21)
+# [[Machine]] (31)
-# [[Kleismic]] (20)
+# [[Atomic]] (30)
-# [[Misty]] (20)
+# [[Gary]] (30)
-# [[Schismatic]] (20) (''already listed as “Helmholtz”'')
+# [[Leapday]] (30)
-# [[Shrutar]] (20)
+# [[Mohaha]] (30)
-# [[Sqrtphi]] (20)
+# [[Octoid]] (30)
-# [[Beatles]] (19)
+# [[Porky]] (30)
-# [[Didacus]] (19)
+# [[Unicorn]] (30)
-# [[Meanpop]] (19)
+# [[Decoid]] (29)
-# [[Arcturus]] (18)
+# [[Doublewide]] (29)
-# [[Gorgo]] (18)
+# [[Gravity]] (29)
-# [[Guiron]] (18)
+# [[Immunity]] (29)
-# [[Leapday]] (18)
+# [[Misty]] (29)
-# [[Mitonic]] (18)
+# [[Newt]] (29)
-# [[Nautilus]] (18)
+# [[Shrutar]] (29)
-# [[Sensipent]] (18)
+# [[Tertiaseptal]] (29)
+# [[Andromeda]] (28)
+# [[Ultrapyth]] (28)
 == A simpler overview ==
 For a more streamlined, strictly curated list of useful temperaments, see the following pages:
-* [[Middle Path table of five-limit rank two temperaments]]
+* [[Middle Path table of 5-limit rank-2 temperaments]]
-* [[Middle Path table of seven-limit rank two temperaments]]
+* [[Middle Path table of 7-limit rank-2 temperaments]]
-* [[Middle Path table of eleven-limit rank two temperaments]]
+* [[Middle Path table of 11-limit rank-2 temperaments]]
-For a description of what the temperaments on the above pages are like, and how those temperaments were chosen, read Paul Erlich’s ''Middle Path'' essay:
+For a description of what the temperaments on the above pages are like, and how those temperaments were chosen, read Paul Erlich's ''Middle Path'' essay:
 * ''[[A Middle Path]]''

Survey of efficient temperaments by subgroup: Difference between revisions

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