User:BudjarnLambeth/Sandbox

https://en.xen.wiki/w/User:BudjarnLambeth/Sandbox

Remember, these are just my ugly, messy notes, and it will look much nicer on the finished page.

I'm only sharing these WIP notes so that everyone can see the numbers that I'm looking at.

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.

IMPORTANT NOTE: 
RIGHT NOW THE TEMPERAMENTS IN EACH SUBSECTION ARE SORTED BY BADNESS.
I AM AWARE THAT THIS IS VERY SILLY.
I WILL RE-SORT THEM BY ACCURACY, NOT BADNESS, IN THE FINAL VERSION.




ANOTHER IMPORTANT NOTE:
THE FINAL PAGE WILL NOT BE FORMATTED AS AN UGLY LIST LIKE THIS.
IT WILL BE FORMATTED AS A TABLE EXACTLY THE SAME LOOK AND FEEL AS BEFORE.
THIS IS JUST AN UGLY WORK-IN-PROGRESS.




List entry format:
* Temperament name (1.5 x [[graham complexity]], 2 x graham complexity, [[badness]] to 2 sig fig - copied from wiki temperament pages)


How to calculate graham complexity:
1. Subtract the smallest number in the second row of the temperament's mapping, from the largest
2. Multiply the result by the number of periods per equave









THE EXCLAMATION MARKS

(!!!!!!) 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.









== THE LIST WITH 2.0X GRAHAM COMPLEXITY ==


== 5LIM ==

~10 NOTES/EQUAVE
* [[Meantone]] (6, 8, 0.0074)
* [[Hanson]] (9, 12, 0.013)
* [[Augmented]] (4.5, 6, 0.022)
* [[Vishnu]] (10.5, 14, 0.031) (!!!!!!)
* [[Porcupine]] (7.5, 10, 0.031)
* [[Magic]] (7.5, 10, 0.039)
* [[Mavila]] (6, 8, 0.040)
* [[Dimipent]] (6, 8, 0.047)
* [[Blackwood]] (7.5, 10, 0.064)
* [[Negri]] (10.5, 14, 0.087)
* [[Misty]] (7.5, 10, 0.11)
* [[Whitewood]] (10.5, 14, 0.16)

~20 NOTES/EQUAVE
* [[Wuerschmidt]] (12, 16, 0.041)
* [[Orson]] (15, 20, 0.041)
* [[Helmholtz]] (12, 16, 0.0043)
* [[Sensipent]] (13.5, 18, 0.035)
* [[Diaschismic]] (12, 16, 0.038)
* [[Tetracot]] (13.5, 18, 0.049)
* [[Compton]] (18, 24, 0.094_
* [[Valentine]] (13.5, 18, 0.12)
* [[Superpyth]] (13.5, 18, 0.14)
* [[Ripple]] (12, 16, 0.14)
* [[Passion]] (13.5, 18, 0.17)

~30 NOTES/EQUAVE
* [[Kwazy]] (19.5, 26, 0.014)
* [[Luna]] (22.5, 30, 0.021)
* [[Amity]] (19.5, 26, 0.022)
* [[Parakleismic]] (21, 28, 0.043)
* [[Gravity]] (25.5, 34, 0.093)

~40 NOTES/EQUAVE

~50 NOTES/EQUAVE
* [[Ennealimmal]] (40.5, 54, ??)

>60 NOTES/EQUAVE
* [[Minortone]] (52.5, 70, 0.030)


== 7LIM == 

~10 NOTES/EQUAVE
* [[Pajara]] (6, 8, 0.020)
* [[Dominant]] (3, 4, 0.021)
* [[Diminished]] (6, 8, 0.022)
* [[Blacksmith]] (7.5, 10, 0.026)
* [[August]] (9, 12, 0.026)
* [[Negri]] (6, 8, 0.026)
* [[Keemun]] (9, 12, 0.027)
* [[Injera]] (9, 12, 0.031)
* [[Porcupine]] (9, 12, 0.041)
* [[Doublewide]] (9, 12, 0.043)
* [[Inflated]] (9, 12, 0.055)
* [[Superpelog]] (9, 12, 0.058)
* [[Shrutar]] (14, 0.19)

~20 NOTES/EQUAVE
* [[Meantone]] (15, 20, 0.014)
* [[Magic]] (18, 24, 0.019)
* [[Orwell]] (16.5, 22, 0.021)
* [[Augene]] (13.5, 18, 0.025) 
* [[Myna]] (15, 20, 0.027)
* [[Godzilla]] (12, 16, 0.027) 
* [[Valentine]] (18, 24, 0.031)
* [[Superpyth]] (13.5, 18, 0.032) 
* [[Mothra]] (18, 24, 0.037)
* [[Flattone]] (13.5, 18, 0.039) 
* [[Opossum]] (13.5, 18, 0.041) 
* [[Hedgehog]] (15, 20, 0.044)
* [[Beatles]] (13.5, 18, 0.046) 
* [[Liese]] (16.5, 22, 0.047)
* [[Catler]] (18, 24, 0.050)
* [[Triforce]] (13.5, 18, 0.055) 
* [[Nautilus]] (15, 20, 0.057)
* [[Schism]] (12, 16, 0.057) 
* [[Lemba]] (12, 16, 0.062) 

~30 NOTES/EQUAVE
* [[Miracle]] (19.5, 26, 0.017) 
* [[Hemiwuerschmidt]] (24, 32, 0.020) 
* [[Garibaldi]] (22.5, 30, 0.022) 
* [[Amity]] (25.5, 34, 0.024)
* [[Sensi]] (19.5, 26, 0.026) 
* [[Harry]] (25.5, 34, 0.034)
* [[Diaschismic]] (27, 36, 0.038)

~40 NOTES/EQUAVE
* [[Catakleismic]] (33, 44, 0.022) 
* [[Misty]] (30, 40, 0.037) 
* [[Unidec]] (33, 44 0.038) 

~50 NOTES/EQUAVE
* [[Ennealimmal]] (40.5, 54, 0.0036) 
* [[Tertiaseptal]] (40.5, 54, 0.013) 
* [[Hemififths]] (37.5, 50, 0.022) 

>60 NOTES/EQUAVE
* [[Enneadecal]] (85.5, 114, 0.011)
* [[Ragismic_microtemperaments#Supermajor|Supermajor]] (112.5, 150, 0.011)
* [[Seqsquiquartififths]] (54, 72, 0.011) 
* [[Pontiac]] (70.5, 94, 0.014)
* [[Parakleismic]] (52.5, 70, 0.027) 
* [[Trinity]] (151.5, 202, 0.12)







== THE LIST WITH 1.5X GRAHAM COMPLEXITY ==


== 5LIM ==

~10 NOTES/EQUAVE
* [[Helmholtz]] (12, 16, 0.0043)
* [[Meantone]] (6, 8, 0.0074)
* [[Hanson]] (9, 12, 0.013)
* [[Augmented]] (4.5, 6, 0.022)
* [[Vishnu]] (10.5, 14, 0.031) (!!!!!!)
* [[Porcupine]] (7.5, 10, 0.031)
* [[Sensipent]] (13.5, 18, 0.035)
* [[Diaschismic]] (12, 16, 0.038)
* [[Magic]] (7.5, 10, 0.039)
* [[Mavila]] (6, 8, 0.040)
* [[Wuerschmidt]] (12, 16, 0.041)
* [[Dimipent]] (6, 8, 0.047)
* [[Tetracot]] (13.5, 18, 0.049)
* [[Blackwood]] (7.5, 10, 0.064)
* [[Negri]] (10.5, 14, 0.087)
* [[Misty]] (7.5, 10, 0.11)
* [[Valentine]] (13.5, 18, 0.12)
* [[Superpyth]] (13.5, 18, 0.14)
* [[Ripple]] (12, 16, 0.14)
* [[Whitewood]] (10.5, 14, 0.16)
* [[Passion]] (13.5, 18, 0.17)

~20 NOTES/EQUAVE
* [[Luna]] (22.5, 30, 0.021)
* [[Amity]] (19.5, 26, 0.022)
* [[Orson]] (15, 20, 0.041)
* [[Parakleismic]] (21, 28, 0.043)
* [[Compton]] (18, 24, 0.094)

~30 NOTES/EQUAVE
* [[Kwazy]] (19.5, 26, 0.014)
* [[Gravity]] (25.5, 34, 0.093)

~40 NOTES/EQUAVE
* [[Ennealimmal]] (40.5, 54, ??)

~50 NOTES/EQUAVE
* [[Minortone]] (52.5, 70, 0.030)

>60 NOTES/EQUAVE


== 7LIM == 

~10 NOTES/EQUAVE
* [[Pajara]] (6, 8, 0.020)
* [[Dominant]] (3, 4, 0.021)
* [[Diminished]] (6, 8, 0.022)
* [[Augene]] (13.5, 18, 0.025) 
* [[Blacksmith]] (7.5, 10, 0.026)
* [[August]] (9, 12, 0.026)
* [[Negri]] (6, 8, 0.026)
* [[Godzilla]] (12, 16, 0.027) 
* [[Keemun]] (9, 12, 0.027)
* [[Injera]] (9, 12, 0.031)
* [[Superpyth]] (13.5, 18, 0.032) 
* [[Flattone]] (13.5, 18, 0.039) 
* [[Porcupine]] (9, 12, 0.041)
* [[Opossum]] (13.5, 18, 0.041) 
* [[Doublewide]] (9, 12, 0.043)
* [[Beatles]] (13.5, 18, 0.046) 
* [[Triforce]] (13.5, 18, 0.055) 
* [[Inflated]] (9, 12, 0.055)
* [[Schism]] (12, 16, 0.057) 
* [[Superpelog]] (9, 12, 0.058)
* [[Lemba]] (12, 16, 0.062) 
* [[Shrutar]] (14, 0.19)

~20 NOTES/EQUAVE
* [[Meantone]] (15, 20, 0.014)
* [[Miracle]] (19.5, 26, 0.017) 
* [[Magic]] (18, 24, 0.019)
* [[Hemiwuerschmidt]] (24, 32, 0.020) 
* [[Orwell]] (16.5, 22, 0.021)
* [[Garibaldi]] (22.5, 30, 0.022) 
* [[Sensi]] (19.5, 26, 0.026) 
* [[Myna]] (15, 20, 0.027)
* [[Valentine]] (18, 24, 0.031)
* [[Mothra]] (18, 24, 0.037)
* [[Hedgehog]] (15, 20, 0.044)
* [[Liese]] (16.5, 22, 0.047)
* [[Catler]] (18, 24, 0.050)
* [[Nautilus]] (15, 20, 0.057)

~30 NOTES/EQUAVE
* [[Catakleismic]] (33, 44, 0.022) 
* [[Amity]] (25.5, 34, 0.024)
* [[Harry]] (25.5, 34, 0.034)
* [[Misty]] (30, 40, 0.037) 
* [[Diaschismic]] (27, 36, 0.038)
* [[Unidec]] (33, 44 0.038) 

~40 NOTES/EQUAVE
* [[Ennealimmal]] (40.5, 54, 0.0036) 
* [[Tertiaseptal]] (40.5, 54, 0.013) 
* [[Hemififths]] (37.5, 50, 0.022) 

~50 NOTES/EQUAVE
* [[Seqsquiquartififths]] (54, 72, 0.011) 
* [[Parakleismic]] (52.5, 70, 0.027) 

>60 NOTES/EQUAVE
* [[Enneadecal]] (85.5, 114, 0.011)
* [[Ragismic_microtemperaments#Supermajor|Supermajor]] (112.5, 150, 0.011)
* [[Pontiac]] (70.5, 94, 0.014)
* [[Trinity]] (151.5, 202, 0.12)















STILL TO-DO:

|-
! 11-limit <br>(2 . 3 . 5 . 7 . 11)
| [[superpelog]], [[blacksmith]], [[opossum]], [[pajaric]], [[august]]
| [[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]]
| [[hemiwuerschmidt]], [[miracle]], [[cassandra]], [[diaschismic]], [[valentine]], [[shrutar]], [[orwell]], [[magic]], [[meanpop]], [[migration]], [[nusecond]], [[andromeda]], [[mothra]], [[squares]], [[meantone]]
| [[unidec]], [[harry]], [[sqrtphi]], [[tritikleismic]], [[hemiwuerschmidt]], [[ennealimnic]], [[hemithirds]], [[catakleismic]], [[wizard]]
| [[hemienneadecal]], [[hemiennealimmal]], [[ennealimmal]], [[vishnu]], [[quasiorwell]], [[trinity]]
|-
! 13-limit <br>(2 . 3 . 5 . 7 . 11 . 13)
| 
| [[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]]
| [[hemiwuerschmidt]], [[mirkat]], [[harry]], [[sqrtphi]], [[tritikleismic]], [[countercata]], [[hemiseven]], [[catakleismic]]
| [[semihemiennealimmal]], [[abigail]], [[ennealimmia]], [[decoid]], [[hemiennealimmal]], [[trinity]], [[enneadecal]], [[octoid]]
|-
! 17-limit <br>(2 . 3 . 5 . 7 . 11 . 13 . 17)
| 
| [[mohajira]], [[injera]], [[meanenneadecal]], [[pajara]]
| [[diaschismic]], [[echidna]], [[shrutar]], [[sensus]], [[miraculous]], [[andromeda]], [[modus]]
| [[mirkat]], [[harry]], [[sqrtphi]], [[tritikleismic]], [[countercata]], [[hemiseven]]
| [[trinity]], [[hemiennealimmal]], [[ennealimmal]], [[octoid]]
|-
! 19-limit <br>(2 . 3 . 5 . 7 . 11 . 13 . 17 . 19)
| 
| [[mohajira]], [[injera]], [[meanenneadecal]], [[marvolo]]
| [[shrutar]], [[andromeda]], [[modus]], [[hitchcock]]
| [[sqrtphi]], [[ketchup]]
| [[trinity]], [[hemiennealimmal]], [[ennealimmal]], [[octoid]]
|-
! Higher prime limits
| 
| [[marvolo]]
| [[srutal]], [[shrutar]], [[hitchcock]]
| [[decistearn]], [[ketchup]]
| [[trinity]], [[satin]]
|-
! 2 . 3 . 5 . 7 . other n
| 
| no-11 [[magic]], no-11 [[sensis]], no-11 [[meanpop]], [[negra]]
| no-11 [[catakleismic]], no-11 [[cassandra]], [[unicorn]]
| no-11 [[decoid]], no-11 [[hemischis]], no-11 [[tritikleismic]]
| no-11 [[ennealimmal]]
|-
! 2 . 3 . 5 . 11 <br>and its extensions
| [[mavila]]
| [[sensible]], [[mohaha]], [[porkypine]]
| [[tetracot]]
| [[larry]] (2.3.5.11 [[gravity]])
| 
|-
! 2 . 3 . 5 . other n
| [[stützel]]
| [[nestoria]], [[cata]], [[sensipent]], [[srutal archagall]]
| [[wuerschmidt]] (2.3.5.23)
| 
| 
|-
! 2 . 3 . 7
| [[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]]
| 
| 
| 
|}