Survey of efficient temperaments by subgroup: Difference between revisions
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== Table of temperaments (5 to 45 notes per equave) == | == 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. | The temperaments within each cell should be sorted by accuracy, with the lowest [[damage]] (highest accuracy) temperament listed first. | ||
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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 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. | ||
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=== Full prime limits === | |||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|- | |- | ||
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|- | |- | ||
! 5-limit <br>(2.3.5) | ! 5-limit <br>(2.3.5) | ||
| [[hanson | | [[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]] | | [[kwazy]], [[luna]], [[vishnu]], [[parakleismic]], [[escapade]], [[amity]], [[misty]], [[gravity]], [[rodan]] | ||
| [[enneadecal]], [[gammic]], [[vulture]] | | [[enneadecal]], [[gammic]], [[vulture]] | ||
|- | |- | ||
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| [[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]]+, [[ | | [[miraculous]], [[lupercalia]]+, [[mohajira]], [[superpyth]]+, [[fokkertone]]+, [[injera]], [[meanenneadecal]] | ||
|- | |- | ||
! 19-limit <br>(2.3.5.7.11.13.17.19) | ! 19-limit <br>(2.3.5.7.11.13.17.19) | ||
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| [[niner]]++ | | [[niner]]++ | ||
| [[wilsec]], [[winston]]++, [[augene]]++, [[sensis]]++ | | [[wilsec]], [[winston]]++, [[augene]]++, [[sensis]]++ | ||
| [[roman]]++, [[mohajira]], [[lupercalia]]++, [[superpyth]]++, [[negroni]]++, [[meanenneadecal]], [[ringo]]++, [[injera]], [[ | | [[roman]]++, [[mohajira]], [[lupercalia]]++, [[superpyth]]++, [[negroni]]++, [[meanenneadecal]], [[ringo]]++, [[injera]], [[fokkertone]]++ | ||
|- | |- | ||
! Higher prime limits | ! Higher prime limits | ||
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| | | | ||
| [[lupercalia]]+++, [[nautilus]]+++, [[negroni]]+++, [[injera]]+ | | [[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'' | ! 2.3.5.7.other ''n'' | ||
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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 (temperament)|hendecatonic]] | ||
| [[sesquiquartififths]], [[quinmite]], [[parakleismic]] | | [[sesquiquartififths]], [[quinmite]], [[parakleismic]] | ||
| [[neptune]], [[gamera]], [[nessafof]], [[octoid]], [[septiquarter]] | | [[neptune]], [[gamera]], [[nessafof]], [[octoid]], [[septiquarter]] | ||
| [[supermajor]], [[enneadecal]], [[term]] | | [[supermajor (temperament)|supermajor]], [[enneadecal]], [[term]] | ||
|- | |- | ||
! 11-limit <br>(2.3.5.7.11) | ! 11-limit <br>(2.3.5.7.11) | ||
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== Most linked-to rank-2 temperaments == | == Most linked-to rank-2 temperaments == | ||
These are the top | 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]] (479)''' | # '''[[Meantone]] (479)''' | ||
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# [[Archy]] (50) | # [[Archy]] (50) | ||
# [[Augmented (temperament)|Augmented]] (50) | # [[Augmented (temperament)|Augmented]] (50) | ||
# [[Helmholtz (temperament)|Helmholtz]] (48) | |||
# [[Superkleismic]] (46) | # [[Superkleismic]] (46) | ||
# [[Augene]] (46) | # [[Augene]] (46) | ||
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# [[Escapade]] (36) | # [[Escapade]] (36) | ||
# [[Passion]] (35) | # [[Passion]] (35) | ||
# [[Schismic]] (35) | # [[Schismic]] (35) (already listed as ''helmholtz'') | ||
# [[Nautilus]] (34) | # [[Nautilus]] (34) | ||
# [[Bleu]] (34) | # [[Bleu]] (34) | ||
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# [[Wizard]] (33) | # [[Wizard]] (33) | ||
# [[Orson]] (32) | # [[Orson]] (32) | ||
# [[Schismatic]] (32) (already listed as '' | # [[Schismatic]] (32) (already listed as ''helmholtz'') | ||
# [[Unidec]] (31) | # [[Unidec]] (31) | ||
# [[Muggles]] (30) | # [[Muggles]] (30) | ||