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| https://en.xen.wiki/w/User:BudjarnLambeth/Sandbox
| | '''This is a working out sandbox page, not a content page.''' |
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| 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.
| | == Sandbox == |
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| | {{Harmonics in cet|33.547|columns=13|intervals=prime}} |
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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.
| | {{Harmonics in cet|33.426|columns=13|intervals=prime}} |
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| | {{Harmonics in cet|33.368|columns=13|intervals=prime}} |
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| | {{Harmonics in cet|33.361|columns=13|intervals=prime}} |
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| | . |
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| | . |
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| <pre>
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| IMPORTANT NOTE:
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| RIGHT NOW THE TEMPERAMENTS IN EACH SUBSECTION ARE SORTED BY BADNESS.
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| 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.
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| | {{Harmonics in cet|33.333|columns=13|intervals=prime}} |
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| | . |
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| ANOTHER IMPORTANT NOTE:
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| THE FINAL PAGE WILL NOT BE FORMATTED AS AN UGLY LIST LIKE THIS.
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| IT WILL BE FORMATTED AS A TABLE EXACTLY THE SAME LOOK AND FEEL AS BEFORE.
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| THIS IS JUST AN UGLY WORK-IN-PROGRESS.
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| | . |
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| | {{Harmonics in cet|33.302|columns=13|intervals=prime}} |
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| List entry format:
| | {{Harmonics in cet|33.286|columns=13|intervals=prime}} |
| * 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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| | {{Harmonics in cet|33.152|columns=13|intervals=prime}} |
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| How to calculate graham complexity:
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| 1. Subtract the smallest number in the second row of the temperament's mapping, from the largest
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| 2. Multiply the result by the number of periods per equave
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| | . |
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| | . |
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| | {{Harmonics in equal|1|8|7 |columns=18}} |
| | {{Harmonics in equal|1|9|8 |columns=18}} |
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| | . |
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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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| | {{Harmonics in equal|1|10|9 |columns=18}} |
| | {{Harmonics in equal|1|11|10 |columns=18}} |
| | {{Harmonics in equal|1|12|11 |columns=18}} |
| | {{Harmonics in equal|1|13|12 |columns=18}} |
| | {{Harmonics in equal|1|14|13 |columns=18}} |
| | {{Harmonics in equal|1|15|14 |columns=18}} |
| | {{Harmonics in equal|1|16|15 |columns=18}} |
| | {{Harmonics in equal|1|17|16 |columns=18}} |
| | {{Harmonics in equal|1|18|17 |columns=18}} |
| | {{Harmonics in equal|1|19|18 |columns=18}} |
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| | . |
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| | . |
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| | {{Harmonics in equal|1|20|19 |columns=18}} |
| | {{Harmonics in equal|1|21|20 |columns=18}} |
| | {{Harmonics in equal|1|22|21 |columns=18}} |
| | {{Harmonics in equal|1|23|22 |columns=18}} |
| | {{Harmonics in equal|1|24|23 |columns=18}} |
| | {{Harmonics in equal|1|25|24 |columns=18}} |
| | {{Harmonics in equal|1|26|25 |columns=18}} |
| | {{Harmonics in equal|1|27|26 |columns=18}} |
| | {{Harmonics in equal|1|28|27 |columns=18}} |
| | {{Harmonics in equal|1|29|28 |columns=18}} |
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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
| | {{Harmonics in equal|1|30|29 |columns=18}} |
| * [[Wuerschmidt]] (12, 16, 0.041)
| | {{Harmonics in equal|1|31|30 |columns=18}} |
| * [[Orson]] (15, 20, 0.041)
| | {{Harmonics in equal|1|32|31 |columns=18}} |
| * [[Helmholtz]] (12, 16, 0.0043)
| | {{Harmonics in equal|1|33|32 |columns=18}} |
| * [[Sensipent]] (13.5, 18, 0.035)
| | {{Harmonics in equal|1|34|33 |columns=18}} |
| * [[Diaschismic]] (12, 16, 0.038)
| | {{Harmonics in equal|1|35|34 |columns=18}} |
| * [[Tetracot]] (13.5, 18, 0.049)
| | {{Harmonics in equal|1|36|35 |columns=18}} |
| * [[Compton]] (18, 24, 0.094_
| | {{Harmonics in equal|1|37|36 |columns=18}} |
| * [[Valentine]] (13.5, 18, 0.12)
| | {{Harmonics in equal|1|38|37 |columns=18}} |
| * [[Superpyth]] (13.5, 18, 0.14)
| | {{Harmonics in equal|1|39|38 |columns=18}} |
| * [[Ripple]] (12, 16, 0.14)
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| * [[Passion]] (13.5, 18, 0.17)
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| ~30 NOTES/EQUAVE
| | <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> |
| * [[Kwazy]] (19.5, 26, 0.014)
| | <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> |
| * [[Luna]] (22.5, 30, 0.021)
| | <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> |
| * [[Amity]] (19.5, 26, 0.022)
| | <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> |
| * [[Parakleismic]] (21, 28, 0.043)
| | Page end. |
| * [[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 | |
| * [[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 | |
| * [[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 | |
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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 | |
| * [[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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| |-
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| ! 13-limit <br>(2 . 3 . 5 . 7 . 11 . 13)
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| | [[mohajira]], [[winston]], [[pajara]], [[undevigintone]], [[superpyth]], [[sensis]], [[negroni]], [[nautilus]], [[ogene]], [[ringo]], [[flattone]], [[injera]], [[augene]], [[darjeeling]], [[meanenneadecal]], [[porcupine]], [[hedgehog]], [[triforce]], [[godzilla]], [[negric]], [[negri]],[[Mavila_family#Armodue|armodue]], [[blacksmith]]
| |
| | [[cassandra]], [[diaschismic]], [[myna]], [[orwell]], [[shrutar]], [[miraculous]], [[sensus]], [[meanpop]], [[andromeda]], [[magic]], [[superkleismic]], [[mothra]], [[nusecond]], [[modus]], [[lupercalia]], [[meantone]]
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| | [[hemiwuerschmidt]], [[mirkat]], [[harry]], [[sqrtphi]], [[tritikleismic]], [[countercata]], [[hemiseven]], [[catakleismic]]
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| | [[semihemiennealimmal]], [[abigail]], [[ennealimmia]], [[decoid]], [[hemiennealimmal]], [[trinity]], [[enneadecal]], [[octoid]]
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| |-
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| ! 17-limit <br>(2 . 3 . 5 . 7 . 11 . 13 . 17)
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| | [[mohajira]], [[injera]], [[meanenneadecal]], [[pajara]]
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| | [[diaschismic]], [[echidna]], [[shrutar]], [[sensus]], [[miraculous]], [[andromeda]], [[modus]]
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| | [[mirkat]], [[harry]], [[sqrtphi]], [[tritikleismic]], [[countercata]], [[hemiseven]]
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| | [[trinity]], [[hemiennealimmal]], [[ennealimmal]], [[octoid]]
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| |-
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| ! 19-limit <br>(2 . 3 . 5 . 7 . 11 . 13 . 17 . 19)
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| | [[mohajira]], [[injera]], [[meanenneadecal]], [[marvolo]]
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| | [[shrutar]], [[andromeda]], [[modus]], [[hitchcock]]
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| | [[sqrtphi]], [[ketchup]]
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| | [[trinity]], [[hemiennealimmal]], [[ennealimmal]], [[octoid]]
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| |-
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| ! Higher prime limits
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| | [[marvolo]]
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| | [[srutal]], [[shrutar]], [[hitchcock]]
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| | [[decistearn]], [[ketchup]]
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| | [[trinity]], [[satin]]
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| |-
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| ! 2 . 3 . 5 . 7 . other n
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| |
| |
| | no-11 [[magic]], no-11 [[sensis]], no-11 [[meanpop]], [[negra]]
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| | no-11 [[catakleismic]], no-11 [[cassandra]], [[unicorn]]
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| | no-11 [[decoid]], no-11 [[hemischis]], no-11 [[tritikleismic]]
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| | no-11 [[ennealimmal]]
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| |-
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| ! 2 . 3 . 5 . 11 <br>and its extensions
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| | [[mavila]]
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| | [[sensible]], [[mohaha]], [[porkypine]]
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| | [[tetracot]]
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| | [[larry]] (2.3.5.11 [[gravity]])
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| |
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| |-
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| ! 2 . 3 . 5 . other n
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| | [[stützel]]
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| | [[nestoria]], [[cata]], [[sensipent]], [[srutal archagall]]
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| | [[wuerschmidt]] (2.3.5.23)
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| |-
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| ! 2 . 3 . 7
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| | [[archy]], [[semaphore]]
| |
| | [[bleu]]
| |
| | [[slendric]]
| |
| | no-5 [[hemififths]]
| |
| |
| |
| |-
| |
| ! 2 . 3 . 7 . 11 <br>and its extensions
| |
| | [[semaphore]]
| |
| | [[skwares]], [[bleu]], [[suhajira]], [[supra]]
| |
| | no-5 [[miracle]], [[hemififths]], [[slendric]], [[radon]]
| |
| |
| |
| |
| |
| |-
| |
| ! 2 . 3 . 7 . other n
| |
| | no-5 [[negra]]
| |
| | [[baladic]]
| |
| | [[oceanfront]]
| |
| | [[hypnosis]]
| |
| |
| |
| |-
| |
| ! 2 . 3 . 11 <br>and its extensions
| |
| | [[paralimmal]], [[huxley]], [[io]]
| |
| | 2.3.11 [[pythrabian]], [[neutral]] (2.3.11 [[rastmic]]), [[namo]]
| |
| | [[tribilo]] (2.3.11 [[nexus]])
| |
| |
| |
| | 2.3.11 [[frameshift]]
| |
| |-
| |
| !2 . 3 . other n
| |
| | [[barbados]], [[superflat]], [[hydrothermal]], [[dog]]
| |
| | [[threedic]], [[semitonic]]
| |
| | [[boethian]], [[pepperoni]]
| |
| | [[historical]]
| |
| |
| |
| |-
| |
| ! 2 . 5 . 7 <br>and its extensions
| |
| | no-3 [[oodako]], no-3 [[pajara]]
| |
| | [[didacus]], [[llywelyn]]
| |
| | [[rainy]], [[mercy]], [[frostburn]], [[baldy]]
| |
| | [[Subgroup temperaments#Daemotertiaschis|daemotertiaschis]]
| |
| | [[ostara]]
| |
| |-
| |
| ! 2 . 5 . other n
| |
| | [[movila]]
| |
| | [[wizz]], [[vengeance]], [[marveltri]], [[superquintal]], [[trader]]
| |
| | [[insect]], [[sulis]]
| |
| |
| |
| |
| |
| |-
| |
| ! 2 . 7 <br>and its extensions
| |
| | [[ultrakleismic]], [[shipwreck]], [[mabon]], [[demon]], [[machine]]
| |
| | [[orgone]], [[counterultrakleismic]], [[machine|apparatus]]
| |
| | [[stacks]], [[machine|mechanism]]
| |
| |
| |
| |
| |
| |-
| |
| ! 3 . 5 . 7 <br>and its extensions
| |
| | [[canopus]], [[BPS]], [[sirius]], [[arcturus]], [[vega]]
| |
| | [[mintra]] (3.5.7.11), [[dubhe]] (3.5.7.17)
| |
| | [[miaplacidus]], [[mintra]] (3.5.7.11.13)
| |
| | [[izar]], [[BPS|athena]]
| |
| |
| |
| |-
| |
| !3 . 5 . other n
| |
| | [[polaris]], [[aldebaran]]
| |
| | [[deneb]]
| |
| | [[No-twos subgroup temperaments#Fomalhaut|fomalhaut]]
| |
| | [[alnilam]]
| |
| |
| |
| |-
| |
| ! 3 . 7 <br>and its extensions
| |
| | [[mintaka]] (3.7.11), [[keladic]]
| |
| | [[mintaka]] (3.7.11.13), [[minalzidar]]
| |
| | [[mebsuta]]
| |
| |
| |
| |
| |
| |-
| |
| ! 4 . n <br>and its extensions
| |
| | [[tetrameantone]], [[quarchy]]
| |
| | [[tetrahanson]], [[meanquad]]
| |
| | [[Subgroup temperaments#Fourwar|fourwar]]
| |
| |
| |
| |
| |
| |-
| |
| ! 5 . n <br>and its extensions
| |
| | [[juggernaut]]
| |
| | [[antipyth]]
| |
| |
| |
| |
| |
| |
| |
| |-
| |
| ! Other subgroups
| |
| | [[halftone]], [[semiwolf]], [[auk]]
| |
| | [[greeley]]
| |
| |
| |
| |
| |
| |
| |
| |}
| |
| </pre> | |