@@ Line 39: / 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 48: / Line 47: @@
 -->
+=== Full prime limits ===
 {| class="wikitable center-all"
 |-
@@ Line 57: / Line 57: @@
 |-
 ! 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]]
-| [[kwazy]], [[luna]], [[vishnu]], [[parakleismic]], [[escapade]], [[amity]], [[gravity]], [[rodan]]
+| [[kwazy]], [[luna]], [[vishnu]], [[parakleismic]], [[escapade]], [[amity]], [[misty]], [[gravity]], [[rodan]]
 | [[enneadecal]], [[gammic]], [[vulture]]
 |-
@@ Line 77: / Line 77: @@
 | [[negric]]
 | [[augene]], [[porcupine]], [[hedgehog]], [[triforce]], [[godzilla]], [[negri]], [[armodue (temperament)|armodue]]
-| [[nusecond]], [[modus]], [[lupercalia]], [[Meantone_family#Tridecimal_meantone|meantone]], [[winston]], [[pajara]], [[sensis]], [[ringo]], [[flattone]], [[darjeeling]], [[meanenneadecal]]
+| [[nusecond]], [[modus]], [[lupercalia]], [[fokkertone]], [[winston]], [[pajara]], [[sensis]], [[ringo]], [[flattone]], [[darjeeling]], [[meanenneadecal]]
 | [[miraculous]], [[leapday]], [[andromeda]], [[superkleismic]], [[mothra]], [[mohajira]], [[undevigintone]], [[ogene]], [[nautilus]], [[negroni]], [[injera]]
 |-
@@ Line 84: / Line 84: @@
 | [[lemba]]+, [[hedgehog]]+
 | [[nusecond]]+, [[crepuscular]], [[winston]]+, [[pajara]], [[negroni]]+, [[sensis]]+, [[ringo]]+, [[pajarous]], [[augene]]+
-| [[miraculous]], [[lupercalia]]+, [[mohajira]], [[superpyth]]+, [[meantoid]], [[injera]], [[meanenneadecal]]
+| [[miraculous]], [[lupercalia]]+, [[mohajira]], [[superpyth]]+, [[fokkertone]]+, [[injera]], [[meanenneadecal]]
 |-
 ! 19-limit <br>(2.3.5.7.11.13.17.19)
@@ Line 90: / Line 90: @@
 | [[niner]]++
 | [[wilsec]], [[winston]]++, [[augene]]++, [[sensis]]++
-| [[roman]]++, [[mohajira]], [[lupercalia]]++, [[superpyth]]++, [[negroni]]++, [[meanenneadecal]], [[ringo]]++, [[injera]], [[meantoid]]
+| [[roman]]++, [[mohajira]], [[lupercalia]]++, [[superpyth]]++, [[negroni]]++, [[meanenneadecal]], [[ringo]]++, [[injera]], [[fokkertone]]++
 |-
 ! Higher prime limits
@@ Line 97: / Line 97: @@
 |
 | [[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
+! ~10 notes per equave
+! ~20 notes
+! ~30 notes
+! ~40 notes
 |-
 ! 2.3.5.7.other ''n''
@@ Line 221: / Line 239: @@
 ! 7-limit <br>(2.3.5.7)
 | [[ennealimmal]], [[tertiaseptal]], [[hemififths]], [[quadritikleismic]], [[grendel]], [[unidec]]
-| [[hendecatonic]]
+| [[hendecatonic (temperament)|hendecatonic]]
 | [[sesquiquartififths]], [[quinmite]], [[parakleismic]]
 | [[neptune]], [[gamera]], [[nessafof]], [[octoid]], [[septiquarter]]
-| [[supermajor]], [[enneadecal]], [[term]]
+| [[supermajor (temperament)|supermajor]], [[enneadecal]], [[term]]
 |-
 ! 11-limit <br>(2.3.5.7.11)
@@ Line 241: / Line 259: @@
 |-
 ! 17-limit <br>(2.3.5.7.11.13.17)
-| [[leapday]], [[superkleismic]]+, [[meantonic]], [[huygens]]
+| [[leapday]], [[superkleismic]]+, [[fokkertone]]+, [[fokkertone]]
 | [[hendec]], [[marvolo]], [[diaschismic]], [[sensus]], [[andromeda]], [[modus]]
 | [[comptone]]
@@ Line 248: / Line 266: @@
 |-
 ! 19-limit <br>(2.3.5.7.11.13.17.19)
-| [[octacot]], [[andromeda]], [[meantonic]], [[huygens]]
+| [[octacot]], [[andromeda]], [[fokkertone]]+, [[fokkertone]]
 | [[hendec]]+, [[sensus]]+, [[crepuscular]]+, [[hitchcock]], [[modus]]
 | [[marvolo]], [[miraculous]]+
@@ Line 392: / 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 23 Oct 2025, about one year after this section was first written.
-# '''[[Meantone]] (313 links)'''
+# '''[[Meantone]] (479)'''
-# '''[[Porcupine]] (144)'''
+# '''[[Porcupine]] (195)'''
-# '''[[Superpyth]] (108)'''
+# '''[[Superpyth]] (162)'''
-# '''[[Magic]] (107)'''
+# '''[[Magic]] (153)'''
-# '''[[Mavila]] (97)'''
+# '''[[Mavila]] (127)'''
-# '''[[Orwell]] (81)'''
+# '''[[Miracle]] (112)'''
-# '''[[Miracle]] (78)'''
+# '''[[Orwell]] (111)'''
-# '''[[Pajara]] (76)'''
+# '''[[Blackwood]] (95)'''
-# '''[[Sensi]] (71)'''
+# '''[[Flattone]] (95)'''
-# '''[[Flattone]] (64)'''
+# '''[[Sensi]] (92)'''
-# '''[[Amity]] (59)'''
+# '''[[Pajara]] (91)'''
-# '''[[Mohajira]] (59)'''
+# '''[[Slendric]] (89)'''
-# '''[[Negri]] (59)'''
+# '''[[Valentine]] (87)'''
-# '''[[Blackwood]] (58)'''
+# '''[[Würschmidt]] (86)'''
-# '''[[Tetracot]] (56)'''
+# '''[[Negri]] (84)'''
-# '''[[Valentine]] (53)'''
+# '''[[Tetracot]] (82)'''
-# '''[[Wuerschmidt]] (53)'''
+# '''[[Mohajira]] (79)'''
-# '''[[Slendric]] (52)'''
+# '''[[Compton]] (70)'''
-# '''[[Compton]] (51)'''
+# '''[[Amity]] (69)'''
-# '''[[Ennealimmal]] (50)'''
+# '''[[Diaschismic]] (69)'''
-# [[Helmholtz (temperament)|Helmholtz]] (49)
+# [[Garibaldi]] (68)
-# [[Dicot]] (47)
+# [[Dicot]] (64)
-# [[Garibaldi]] (47)
+# [[Ennealimmal]] (60)
-# [[Hanson]] (45)
+# [[Father]] (60)
-# [[Catakleismic]] (44)
+# [[Diminished (temperament)|Diminished]] (59)
-# [[Diaschismic]] (43)
+# [[Mothra]] (58)
-# [[Hemififths]] (42)
+# [[Myna]] (57)
-# [[Myna]] (41)
+# [[Rodan]] (57)
-# [[Father]] (40)
+# [[Catakleismic]] (57)
-# [[Squares]] (40)
+# [[Godzilla]] (56)
-# [[Rodan]] (39)
+# [[Hanson]] (56)
-# [[Semaphore]] (39)
+# [[Squares]] (55)
-# [[Augmented]] (38)
+# [[Hemififths]] (54)
-# [[Diminished]] (38)
+# [[Injera]] (53)
-# [[Srutal]] (38)
+# [[Octacot]] (53)
-# [[Godzilla]] (37)
+# [[Semaphore]] (52)
-# [[Harry]] (37)
+# [[Harry]] (52)
-# [[Injera]] (37)
+# [[Archy]] (50)
-# [[Diasem]] (36)
+# [[Augmented (temperament)|Augmented]] (50)
-# [[Enneadecal]] (35)
+# [[Helmholtz (temperament)|Helmholtz]] (48)
-# [[Orgone]] (34)
+# [[Superkleismic]] (46)
-# [[Parakleismic]] (34)
+# [[Augene]] (46)
-# [[Hedgehog]] (33)
+# [[Keemun]] (46)
-# [[Luna]] (33)
+# [[Whitewood]] (43)
-# [[Octacot]] (33)
+# [[Buzzard]] (43)
-# [[Augene]] (32)
+# [[Orgone]] (42)
-# [[Dominant]] (32)
+# [[Dominant (temperament)|Dominant]] (42)
-# [[Hemithirds]] (32)
+# [[Kleismic]] (42) (already listed as ''hanson'')
-# [[Keemun]] (32)
+# [[Liese]] (42)
-# [[Lemba]] (32)
+# [[Didacus]] (41)
-# [[Mothra]] (32)
+# [[Hemiwürschmidt]] (41)
-# [[Whitewood]] (32)
+# [[Parakleismic]] (41)
-# [[Archy]] (31)
+# [[Vishnu]] (40)
-# [[Liese]] (31)
+# [[Enneadecal]] (40)
-# [[Bleu]] (29)
+# [[Hemithirds]] (40)
-# [[Vishnu]] (29)
+# [[Lemba]] (40)
-# [[Hemiwuerschmidt]] (28)
+# [[Srutal]] (39)
-# [[Superkleismic]] (27)
+# [[Hedgehog]] (39)
-# [[Echidna]] (26)
+# [[Luna]] (38)
-# [[Orson]] (26)
+# [[Triforce]] (38)
-# [[Tertiaseptal]] (26)
+# [[Echidna]] (37)
-# [[Triforce]] (26)
+# [[Ripple]] (36)
-# [[Passion]] (25)
+# [[Tritonic]] (36)
-# [[Tritonic]] (25)
+# [[Escapade]] (36)
-# [[Unidec]] (25)
+# [[Passion]] (35)
-# [[Wizard]] (25)
+# [[Schismic]] (35) (already listed as ''helmholtz'')
-# [[Buzzard]] (24)
+# [[Nautilus]] (34)
-# [[Cassandra]] (24)
+# [[Bleu]] (34)
-# [[Ripple]] (24)
+# [[Vulture]] (33)
-# [[Vulture]] (24)
+# [[Wizard]] (33)
-# [[Armodue]] (23) (''disambiguation page'')
+# [[Orson]] (32)
-# [[Atomic]] (23)
+# [[Schismatic]] (32) (already listed as ''helmholtz'')
-# [[Bug]] (23)
+# [[Unidec]] (31)
-# [[Escapade]] (23)
+# [[Muggles]] (30)
-# [[Pontiac]] (23)
+# [[Sensipent]] (30)
-# [[Ampersand]] (22)
+# [[Tritikleismic]] (30)
-# [[Bohpier]] (22)
+# [[Unicorn]] (30)
-# [[Mohaha]] (22)
+# [[Beatles]] (29)
-# [[Parapyth]] (22)
+# [[Bohpier]] (29)
-# [[August]] (21)
+# [[Machine]] (29)
-# [[Blacksmith]] (21)
+# [[Shrutar]] (29)
-# [[Kwazy]] (21)
+# [[Tertiaseptal]] (29)
-# [[Octoid]] (21)
+# [[Misty]] (28)
-# [[Tritikleismic]] (21)
+# [[Mohaha]] (28)
-# [[Kleismic]] (20)
+# [[Pontiac]] (28)
-# [[Misty]] (20)
+# [[Porky]] (28)
-# [[Schismatic]] (20) (''already listed as “Helmholtz”'')
+# [[Semisept]] (28)
-# [[Shrutar]] (20)
+# [[August]] (28)
-# [[Sqrtphi]] (20)
+# [[Bug]] (28)
-# [[Beatles]] (19)
+# [[Doublewide]] (28)
-# [[Didacus]] (19)
+# [[Cassandra]] (27)
-# [[Meanpop]] (19)
+# [[Decimal]] (27)
-# [[Arcturus]] (18)
+# [[Immunity]] (26)
-# [[Gorgo]] (18)
+# [[Octoid]] (26)
-# [[Guiron]] (18)
+# [[Supermajor]] (26) (disambiguation page)
-# [[Leapday]] (18)
+# [[Quadritikleismic]] (25)
-# [[Mitonic]] (18)
+# [[Ultrapyth]] (25)
-# [[Nautilus]] (18)
+# [[Gorgo]] (25)
-# [[Sensipent]] (18)
+# [[Leapday]] (25)
+# [[Atomic]] (24)
+# [[Decoid]] (24)
+# [[Gravity]] (24)
+# [[Guiron]] (24)
+# [[Quartonic]] (24)
+# [[Sqrtphi]] (24)
 == 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