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| Remember, these are just my ugly, messy notes, and it will look much nicer on the finished page. | | Remember, these are just my ugly, messy notes, and it will look much nicer on the finished page. |
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| I'm only sharing these WIP notes so that everyone can see the numbers that I'm looking at. | | I'm only sharing these WIP notes so that everyone can see the numbers that I'm looking at and see how far along things are. |
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| So far, I have used 1.5 x graham complexity and 2 x graham complexity to assess every singe 5lim and 7lim temperament on the table.
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| IMPORTANT NOTE: | | IMPORTANT NOTE: |
| RIGHT NOW THE TEMPERAMENTS IN EACH SUBSECTION ARE SORTED BY BADNESS. | | RIGHT NOW THE TEMPERAMENTS IN EACH SUBSECTION ARE SORTED BY BADNESS. |
| I AM AWARE THAT THIS IS VERY SILLY.
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| I WILL RE-SORT THEM BY ACCURACY, NOT BADNESS, IN THE FINAL VERSION. | | I WILL RE-SORT THEM BY ACCURACY, NOT BADNESS, IN THE FINAL VERSION. |
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| List entry format:
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| * Temperament name (1.5 x [[graham complexity]], 2 x graham complexity, [[badness]] to 2 sig fig - copied from wiki temperament pages)
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| | Number of notes recommended is estimated as 2 x graham complexity. |
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| How to calculate graham complexity: | | How to calculate graham complexity: |
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| | {| class="wikitable center-all" |
| | |+ |
| | ! JI subgroup |
| | ! ~10 notes per equave |
| | ! ~20 notes |
| | ! ~30 notes |
| | ! ~40 notes |
| | ! ~50 notes |
| | ! >60 notes |
| | |- |
| | ! 5-limit <br>(2 . 3 . 5) |
| | | [[meantone]], [[hanson]], [[augmented]], [[porcupine]], [[magic]], [[mavila]], [[dimipent]], [[blackwood]], [[negri]], [[misty]], [[whitewood]] |
| | | [[wuerschmidt]], [[orson]], [[helmholtz]], [[sensipent]], [[diaschismic], [[tetracot]], [[compton]], [[valentine]], [[superpyth]], [[ripple]], [[passion]] |
| | | [[kwazy]], [[luna]], [[amity]], [[vishnu]], [[parakleismic]], [[gravity]] |
| | | |
| | | [[ennealimmal]] |
| | | [[minortone]] |
| | |- |
| | ! 7-limit <br>(2 . 3 . 5 . 7) |
| | | [[pajara]], [[dominant]], [[diminished]], [[blacksmith]], [[august]], [[negri]], [[keemun]], [[injera]], [[porcupine]], [[doublewide]], [[inflated]], [[triforce]], [[superpelog]], [[shrutar]] |
| | | [[meantone]], [[magic]], [[orwell]], [[augene]], [[myna]], [[godzilla], [[valentine]], [[superpyth]], [[mothra]], [[flattone]], [[opossum]], [[hedgehog]], [[beatles]], [[liese]], [[catler]], [[nautilus]], [[schism]], [[lemba]] |
| | | [[miracle]], [[hemiwuerschmidt]], [[garibaldi]], [[amity]], [[sensi]], [[harry]], [[diaschismic]] |
| | | [[catakleismic]], [[misty]], [[unidec]] |
| | | [[ennealimmal]], [[tertiaseptal]], [[hemififths]] |
| | | [[enneadecal]], [[Ragismic_microtemperaments#Supermajor|supermajor]], [[sesquiquartififths]], [[pontiac]], [[parakleismic]], [[trinity]] |
| | |- |
| | ! 11-limit <br>(2 . 3 . 5 . 7 . 11) |
| | | [[august]], [[pajaric]], [[triforce]], [[blacksmith]] |
| | | [[orwell]], [[valentine]], [[augene]], [[meanenneadecal]], [[porcupine]], [[opossum]], [[hedgehog]], [[dominant]], [[nautilus]], [[mohajira]], [[catnip]], [[keemun]], [[superpelog]], [[duodecim]], [[negric]], [[progress]], [[injera]], [[undevigintone]], [[astrology]], [[vigintiduo]] |
| | | [[meantone]], [[pajara]], [[squares]], [[nusecond]], [[telepathy]], [[porky]], [[darjeeling]], [[pajarous]], [[sensis]], [[godzilla]], [[quasisupra]], [[suprapyth]], [[flattone]], [[fleetwood]], [[negroni]], [[mothra]] |
| | | [[miracle]], [[magic]], [[meanpop]], [[andromeda]], [[superpyth]], [[migration]], [[shrutar] |
| | | [[unidec]], [[hemithirds]], [[tritikleismic]], [[diaschismic]] |
| | | [[hemiennealimmal]], [[hemienneadecal]], [[vishnu]], [[harry]], [[quasiorwell]], [[wizard]], [[hemiwuerschmidt]], [[catakleismic]], [[ennealimnic]], [[sqrtphi]], [[ennealimmal]], [[cassandra]], [[trinity]] |
| | |- |
| | ! 13-limit <br>(2 . 3 . 5 . 7 . 11 . 13) |
| | | ~10 notes per equave |
| | | ~20 notes |
| | | ~30 notes |
| | | ~40 notes |
| | | ~50 notes |
| | | >60 notes |
| | |- |
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| THE EXCLAMATION MARKS
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| (!!!!!!) Indicates a temperament that seems like its number-of-notes estimate is way too low, and it might be an example some potential weakness or anomaly in the counting method.
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| == THE LIST WITH 2.0X GRAHAM COMPLEXITY ==
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| == 5LIM ==
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| ~10 NOTES/EQUAVE
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| * [[Meantone]] (6, 8, 0.0074)
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| * [[Hanson]] (9, 12, 0.013)
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| * [[Augmented]] (4.5, 6, 0.022)
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| * [[Vishnu]] (10.5, 14, 0.031) (!!!!!!)
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| * [[Porcupine]] (7.5, 10, 0.031)
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| * [[Magic]] (7.5, 10, 0.039)
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| * [[Mavila]] (6, 8, 0.040)
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| * [[Dimipent]] (6, 8, 0.047)
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| * [[Blackwood]] (7.5, 10, 0.064)
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| * [[Negri]] (10.5, 14, 0.087)
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| * [[Misty]] (7.5, 10, 0.11)
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| * [[Whitewood]] (10.5, 14, 0.16)
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| ~20 NOTES/EQUAVE
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| * [[Wuerschmidt]] (12, 16, 0.041)
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| * [[Orson]] (15, 20, 0.041)
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| * [[Helmholtz]] (12, 16, 0.0043)
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| * [[Sensipent]] (13.5, 18, 0.035)
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| * [[Diaschismic]] (12, 16, 0.038)
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| * [[Tetracot]] (13.5, 18, 0.049)
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| * [[Compton]] (18, 24, 0.094_
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| * [[Valentine]] (13.5, 18, 0.12)
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| * [[Superpyth]] (13.5, 18, 0.14)
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| * [[Ripple]] (12, 16, 0.14)
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| * [[Passion]] (13.5, 18, 0.17)
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| ~30 NOTES/EQUAVE
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| * [[Kwazy]] (19.5, 26, 0.014)
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| * [[Luna]] (22.5, 30, 0.021)
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| * [[Amity]] (19.5, 26, 0.022)
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| * [[Parakleismic]] (21, 28, 0.043)
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| * [[Gravity]] (25.5, 34, 0.093)
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| ~40 NOTES/EQUAVE
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| ~50 NOTES/EQUAVE
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| * [[Ennealimmal]] (40.5, 54, ??)
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| >60 NOTES/EQUAVE
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| * [[Minortone]] (52.5, 70, 0.030)
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| == 7LIM ==
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| ~10 NOTES/EQUAVE
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| * [[Pajara]] (6, 8, 0.020)
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| * [[Dominant]] (3, 4, 0.021)
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| * [[Diminished]] (6, 8, 0.022)
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| * [[Blacksmith]] (7.5, 10, 0.026)
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| * [[August]] (9, 12, 0.026)
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| * [[Negri]] (6, 8, 0.026)
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| * [[Keemun]] (9, 12, 0.027)
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| * [[Injera]] (9, 12, 0.031)
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| * [[Porcupine]] (9, 12, 0.041)
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| * [[Doublewide]] (9, 12, 0.043)
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| * [[Inflated]] (9, 12, 0.055)
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| * [[Superpelog]] (9, 12, 0.058)
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| * [[Shrutar]] (14, 0.19)
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| ~20 NOTES/EQUAVE
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| * [[Meantone]] (15, 20, 0.014)
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| * [[Magic]] (18, 24, 0.019)
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| * [[Orwell]] (16.5, 22, 0.021)
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| * [[Augene]] (13.5, 18, 0.025)
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| * [[Myna]] (15, 20, 0.027)
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| * [[Godzilla]] (12, 16, 0.027)
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| * [[Valentine]] (18, 24, 0.031)
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| * [[Superpyth]] (13.5, 18, 0.032)
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| * [[Mothra]] (18, 24, 0.037)
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| * [[Flattone]] (13.5, 18, 0.039)
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| * [[Opossum]] (13.5, 18, 0.041)
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| * [[Hedgehog]] (15, 20, 0.044)
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| * [[Beatles]] (13.5, 18, 0.046)
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| * [[Liese]] (16.5, 22, 0.047)
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| * [[Catler]] (18, 24, 0.050)
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| * [[Triforce]] (13.5, 18, 0.055)
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| * [[Nautilus]] (15, 20, 0.057)
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| * [[Schism]] (12, 16, 0.057)
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| * [[Lemba]] (12, 16, 0.062)
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| ~30 NOTES/EQUAVE
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| * [[Miracle]] (19.5, 26, 0.017)
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| * [[Hemiwuerschmidt]] (24, 32, 0.020)
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| * [[Garibaldi]] (22.5, 30, 0.022)
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| * [[Amity]] (25.5, 34, 0.024)
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| * [[Sensi]] (19.5, 26, 0.026)
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| * [[Harry]] (25.5, 34, 0.034)
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| * [[Diaschismic]] (27, 36, 0.038)
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| ~40 NOTES/EQUAVE
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| * [[Catakleismic]] (33, 44, 0.022)
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| * [[Misty]] (30, 40, 0.037)
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| * [[Unidec]] (33, 44 0.038)
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| ~50 NOTES/EQUAVE
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| * [[Ennealimmal]] (40.5, 54, 0.0036)
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| * [[Tertiaseptal]] (40.5, 54, 0.013)
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| * [[Hemififths]] (37.5, 50, 0.022)
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| >60 NOTES/EQUAVE
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| * [[Enneadecal]] (85.5, 114, 0.011)
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| * [[Ragismic_microtemperaments#Supermajor|Supermajor]] (112.5, 150, 0.011)
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| * [[Seqsquiquartififths]] (54, 72, 0.011)
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| * [[Pontiac]] (70.5, 94, 0.014)
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| * [[Parakleismic]] (52.5, 70, 0.027)
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| * [[Trinity]] (151.5, 202, 0.12)
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| == THE LIST WITH 1.5X GRAHAM COMPLEXITY ==
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| == 5LIM ==
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| ~10 NOTES/EQUAVE
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| * [[Helmholtz]] (12, 16, 0.0043)
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| * [[Meantone]] (6, 8, 0.0074)
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| * [[Hanson]] (9, 12, 0.013)
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| * [[Augmented]] (4.5, 6, 0.022)
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| * [[Vishnu]] (10.5, 14, 0.031) (!!!!!!)
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| * [[Porcupine]] (7.5, 10, 0.031)
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| * [[Sensipent]] (13.5, 18, 0.035)
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| * [[Diaschismic]] (12, 16, 0.038)
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| * [[Magic]] (7.5, 10, 0.039)
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| * [[Mavila]] (6, 8, 0.040)
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| * [[Wuerschmidt]] (12, 16, 0.041)
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| * [[Dimipent]] (6, 8, 0.047)
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| * [[Tetracot]] (13.5, 18, 0.049)
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| * [[Blackwood]] (7.5, 10, 0.064)
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| * [[Negri]] (10.5, 14, 0.087)
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| * [[Misty]] (7.5, 10, 0.11)
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| * [[Valentine]] (13.5, 18, 0.12)
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| * [[Superpyth]] (13.5, 18, 0.14)
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| * [[Ripple]] (12, 16, 0.14)
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| * [[Whitewood]] (10.5, 14, 0.16)
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| * [[Passion]] (13.5, 18, 0.17)
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| ~20 NOTES/EQUAVE
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| * [[Luna]] (22.5, 30, 0.021)
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| * [[Amity]] (19.5, 26, 0.022)
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| * [[Orson]] (15, 20, 0.041)
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| * [[Parakleismic]] (21, 28, 0.043)
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| * [[Compton]] (18, 24, 0.094)
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| ~30 NOTES/EQUAVE
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| * [[Kwazy]] (19.5, 26, 0.014)
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| * [[Gravity]] (25.5, 34, 0.093)
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| ~40 NOTES/EQUAVE
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| * [[Ennealimmal]] (40.5, 54, ??)
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| ~50 NOTES/EQUAVE
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| * [[Minortone]] (52.5, 70, 0.030)
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| >60 NOTES/EQUAVE
| | STILL YET TO BE RE-SORTED: |
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| == 7LIM ==
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| ~10 NOTES/EQUAVE
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| * [[Pajara]] (6, 8, 0.020)
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| * [[Dominant]] (3, 4, 0.021)
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| * [[Diminished]] (6, 8, 0.022)
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| * [[Augene]] (13.5, 18, 0.025)
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| * [[Blacksmith]] (7.5, 10, 0.026)
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| * [[August]] (9, 12, 0.026)
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| * [[Negri]] (6, 8, 0.026)
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| * [[Godzilla]] (12, 16, 0.027)
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| * [[Keemun]] (9, 12, 0.027)
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| * [[Injera]] (9, 12, 0.031)
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| * [[Superpyth]] (13.5, 18, 0.032)
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| * [[Flattone]] (13.5, 18, 0.039)
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| * [[Porcupine]] (9, 12, 0.041)
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| * [[Opossum]] (13.5, 18, 0.041)
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| * [[Doublewide]] (9, 12, 0.043)
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| * [[Beatles]] (13.5, 18, 0.046)
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| * [[Triforce]] (13.5, 18, 0.055)
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| * [[Inflated]] (9, 12, 0.055)
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| * [[Schism]] (12, 16, 0.057)
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| * [[Superpelog]] (9, 12, 0.058)
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| * [[Lemba]] (12, 16, 0.062)
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| * [[Shrutar]] (14, 0.19)
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| ~20 NOTES/EQUAVE
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| * [[Meantone]] (15, 20, 0.014)
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| * [[Miracle]] (19.5, 26, 0.017)
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| * [[Magic]] (18, 24, 0.019)
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| * [[Hemiwuerschmidt]] (24, 32, 0.020)
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| * [[Orwell]] (16.5, 22, 0.021)
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| * [[Garibaldi]] (22.5, 30, 0.022)
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| * [[Sensi]] (19.5, 26, 0.026)
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| * [[Myna]] (15, 20, 0.027)
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| * [[Valentine]] (18, 24, 0.031)
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| * [[Mothra]] (18, 24, 0.037)
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| * [[Hedgehog]] (15, 20, 0.044)
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| * [[Liese]] (16.5, 22, 0.047)
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| * [[Catler]] (18, 24, 0.050)
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| * [[Nautilus]] (15, 20, 0.057)
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| ~30 NOTES/EQUAVE
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| * [[Catakleismic]] (33, 44, 0.022)
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| * [[Amity]] (25.5, 34, 0.024)
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| * [[Harry]] (25.5, 34, 0.034)
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| * [[Misty]] (30, 40, 0.037)
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| * [[Diaschismic]] (27, 36, 0.038)
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| * [[Unidec]] (33, 44 0.038)
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| ~40 NOTES/EQUAVE
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| * [[Ennealimmal]] (40.5, 54, 0.0036)
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| * [[Tertiaseptal]] (40.5, 54, 0.013)
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| * [[Hemififths]] (37.5, 50, 0.022)
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| ~50 NOTES/EQUAVE
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| * [[Seqsquiquartififths]] (54, 72, 0.011)
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| * [[Parakleismic]] (52.5, 70, 0.027)
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| >60 NOTES/EQUAVE
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| * [[Enneadecal]] (85.5, 114, 0.011)
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| * [[Ragismic_microtemperaments#Supermajor|Supermajor]] (112.5, 150, 0.011)
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| * [[Pontiac]] (70.5, 94, 0.014)
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| * [[Trinity]] (151.5, 202, 0.12)
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| STILL TO-DO:
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| |-
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| ! 11-limit <br>(2 . 3 . 5 . 7 . 11)
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| | [[superpelog]], [[blacksmith]], [[opossum]], [[pajaric]], [[august]]
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| | [[mohajira]], [[superpyth]], [[quasisupra]], [[pajara]], [[telepathy]], [[suprapyth]], [[porcupine]], [[negroni]], [[porky]], [[hedgehog]], [[fleetwood]], [[pajarous]], [[astrology]], [[vigintiduo]], [[augene]], [[sensis]], [[nautilus]], [[catnip]], [[undevigintone]], [[injera]], [[flattone]], [[godzilla]], [[darjeeling]], [[keemun]], [[progress]], [[dominant]], [[triforce]], [[negric]], [[meanenneadecal]], [[duodecim]]
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| | [[hemiwuerschmidt]], [[miracle]], [[cassandra]], [[diaschismic]], [[valentine]], [[shrutar]], [[orwell]], [[magic]], [[meanpop]], [[migration]], [[nusecond]], [[andromeda]], [[mothra]], [[squares]], [[meantone]]
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| | [[unidec]], [[harry]], [[sqrtphi]], [[tritikleismic]], [[hemiwuerschmidt]], [[ennealimnic]], [[hemithirds]], [[catakleismic]], [[wizard]]
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| | [[hemienneadecal]], [[hemiennealimmal]], [[ennealimmal]], [[vishnu]], [[quasiorwell]], [[trinity]]
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| |- | | |- |
| ! 13-limit <br>(2 . 3 . 5 . 7 . 11 . 13) | | ! 13-limit <br>(2 . 3 . 5 . 7 . 11 . 13) |