Survey of efficient temperaments by subgroup: Difference between revisions
→Most linked-to rank-2 temperaments: helmholtz was missing |
m →Other subgroups: typo |
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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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=== Other subgroups === | === 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" | {| class="wikitable center-all" | ||
|- | |- | ||
! JI subgroup | ! JI subgroup | ||
! ~10 notes per equave | ! ~10 notes per equave | ||
! ~20 notes | ! ~20 notes | ||
! ~30 notes | ! ~30 notes | ||
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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]] | ||