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https://en.xen.wiki/w/User:BudjarnLambeth/Sandbox
'''This is a working out sandbox page, not a content page.'''


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 and see how far along things are.
== Sandbox ==
{{Harmonics in cet|33.547|columns=13|intervals=prime}}


{{Harmonics in cet|33.426|columns=13|intervals=prime}}


{{Harmonics in cet|33.368|columns=13|intervals=prime}}


{{Harmonics in cet|33.361|columns=13|intervals=prime}}




.




<pre>
.
IMPORTANT NOTE:
RIGHT NOW THE TEMPERAMENTS IN EACH SUBSECTION ARE SORTED BY BADNESS.
I WILL RE-SORT THEM BY ACCURACY, NOT BADNESS, IN THE FINAL VERSION.




{{Harmonics in cet|33.333|columns=13|intervals=prime}}




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.




.




{{Harmonics in cet|33.302|columns=13|intervals=prime}}


{{Harmonics in cet|33.286|columns=13|intervals=prime}}


Number of notes recommended is estimated as 2 x graham complexity.
{{Harmonics in cet|33.152|columns=13|intervals=prime}}


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


.




.




{{Harmonics in equal|1|8|7 |columns=18}}
{{Harmonics in equal|1|9|8 |columns=18}}




.




.


{| class="wikitable center-all"
 
|+
{{Harmonics in equal|1|10|9 |columns=18}}
! JI subgroup
{{Harmonics in equal|1|11|10 |columns=18}}
! ~10 notes per equave
{{Harmonics in equal|1|12|11 |columns=18}}
! ~20 notes
{{Harmonics in equal|1|13|12 |columns=18}}
! ~30 notes
{{Harmonics in equal|1|14|13 |columns=18}}
! ~40 notes
{{Harmonics in equal|1|15|14 |columns=18}}
! ~50 notes
{{Harmonics in equal|1|16|15 |columns=18}}
! ~60 notes
{{Harmonics in equal|1|17|16 |columns=18}}
! ~70 notes
{{Harmonics in equal|1|18|17 |columns=18}}
! ~80 notes
{{Harmonics in equal|1|19|18 |columns=18}}
! >90 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]]
 
|
{{Harmonics in equal|1|20|19 |columns=18}}
| [[minortone]], [[vavoom]]
{{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}}
! 7-limit <br>(2 . 3 . 5 . 7)
{{Harmonics in equal|1|25|24 |columns=18}}
| [[pajara]], [[dominant]], [[diminished]], [[blacksmith]], [[august]], [[negri]], [[keemun]], [[injera]], [[porcupine]], [[doublewide]], [[inflated]], [[triforce]], [[superpelog]], [[shrutar]]
{{Harmonics in equal|1|26|25 |columns=18}}
| [[meantone]], [[magic]], [[orwell]], [[augene]], [[myna]], [[godzilla], [[valentine]], [[superpyth]], [[mothra]], [[flattone]], [[opossum]], [[hedgehog]], [[beatles]], [[liese]], [[catler]], [[nautilus]], [[schism]], [[lemba]]
{{Harmonics in equal|1|27|26 |columns=18}}
| [[miracle]], [[hemiwuerschmidt]], [[garibaldi]], [[amity]], [[sensi]], [[harry]], [[diaschismic]]
{{Harmonics in equal|1|28|27 |columns=18}}
| [[catakleismic]], [[misty]], [[unidec]]
{{Harmonics in equal|1|29|28 |columns=18}}
| [[ennealimmal]], [[tertiaseptal]], [[hemififths]]
 
|  
 
| [[sesquiquartififths]], [[parakleismic]]
.
|
 
| [[enneadecal]], [[Ragismic_microtemperaments#Supermajor|supermajor]], [[pontiac]], [[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]]
{{Harmonics in equal|1|30|29 |columns=18}}
| [[meantone]], [[pajara]], [[squares]], [[nusecond]], [[telepathy]], [[porky]], [[darjeeling]], [[pajarous]], [[sensis]], [[godzilla]], [[quasisupra]], [[suprapyth]], [[flattone]], [[fleetwood]], [[negroni]], [[mothra]]
{{Harmonics in equal|1|31|30 |columns=18}}
| [[miracle]], [[magic]], [[meanpop]], [[andromeda]], [[superpyth]], [[migration]], [[shrutar]
{{Harmonics in equal|1|32|31 |columns=18}}
| [[unidec]], [[wizard]], [[hemithirds]], [[tritikleismic]], [[diaschismic]]
{{Harmonics in equal|1|33|32 |columns=18}}
|  
{{Harmonics in equal|1|34|33 |columns=18}}
| [[harry]]
{{Harmonics in equal|1|35|34 |columns=18}}
| [[quasiorwell]], [[catakleismic]], [[ennealimnic]], [[hemiwuerschmidt]], [[sqrtphi]], [[cassandra]]
{{Harmonics in equal|1|36|35 |columns=18}}
| [[hemiennealimmal]], [[hemienneadecal]], [[vishnu]], [[trinity]]
{{Harmonics in equal|1|37|36 |columns=18}}
|-
{{Harmonics in equal|1|38|37 |columns=18}}
! 13-limit <br>(2 . 3 . 5 . 7 . 11 . 13)
{{Harmonics in equal|1|39|38 |columns=18}}
| [[negric]] 0.0202
 
| [[negri]] 0.0178, [[Mavila_family#Armodue|armodue]] 0.0194, [[opossum]] 0.0194, [[triforce]] 0.0203, [[blacksmith]] 0.0205, [[augene]] 0.0208, [[lupercalia]] 0.0213, [[porcupine]] 0.0213, [[hedgehog]] 0.0215, [[godzilla]] 0.0225
<br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br>
| [[meantone]] 0.0180, [[winston]] 0.0199, sensis 0.0200, [[meanenneadecal]] 0.0212, [[darjeeling]] 0.0214, flattone]] 0223, [[ringo]] 0.226, [[nusecond]] 0.0233, [[modus]] 0.0238, [[pajara]] 0.0276
<br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br>
| [[mirkat]] 0.0186, [[miraculous]] 0.0187, [[andromeda]] 0.0207, [[superkleismic]] 0.0215, [[injera]] 0.0216, [[nautilus]] 0.223, [[undevigintone]] 0.0229, [[ogene]] 0.229, [[mohajira]] 0.0234, [[mothra]] 0.0240, [[superpyth]] 0.0247, [[negroni]] 0.0353, [[diaschismic]] 0.0379
<br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br>
| [[orwell]] 0.0197, [[magic]] 0.0215
<br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br>
| [[myna]] 0.0171, [[sensus]] 0.0207, [[meanpop]] 0.0209
Page end.
| [[cassandra]] 0.0207
| [[catakleismic]] 0.0169, [[shrutar]] 0.0794
| [[abigail]] 0.00886, [[hemiennealimmal]] 0.0125, [[harry]] 0.0130, [[semihemiennealimmal]] 0.0132, [[decoid]] 0.0134, [[trinity]] 0.0264
|-
! 17-limit <br>(2 . 3 . 5 . 7 . 11 . 13 . 17)
|  
|  
| [[pajara]] 0.0209
| [[mirkat]] 0.0118, [[miraculous]] 0.0171, [[mohajira]] 0.0173, [[injera]] 0.0184, [[meanenneadecal]] 0.0230
|  
| [[sensus]] 0.0162, [[diaschismic]] 0.0164, [[modus]] 0.0215, [[andromeda]] 0.0234
|  
| [[echidna]] 0.0203, [[shrutar]] 0.0494
| [[harry]] 0.0127, [[sqrtphi]] 0.0130, [[tritikleismic]] 0.0136, [[octoid]] 0.0143, [[trinity]] 0.0256
|-
! 19-limit <br>(2 . 3 . 5 . 7 . 11 . 13 . 17 . 19)
|  
|  
|
| [[injera]] 0.0151, [[mohajira]] 0.0173,  [[meanenneadecal]] 0.0203, [[shrutar]] 0.0442
| [[andromeda]] 0.0192
| [[hitchcock]] 0.0175, [[modus]] 0.0179
| [[marvolo]] 999.999
|
| [[sqrtphi]] 0.0147, [[octoid]] 0.0160, [[ketchup]] 0.0182, [[trinity]] 0.0184
|-
! Higher prime limits
| ~10 notes per equave
| ~20 notes
| ~30 notes
| ~40 notes
| ~50 notes
| ~60 notes
| ~70 notes
| [[shrutar]] 0.0351
| [[satin]] 0.0122, [[ketchup]] 0.0140, [[trinity]] 0.0143, [[decistearn]] 0.0917
|-
! 2 . 3 . 5 . 7 . other n
| [[negra] ???,
|  
| no-11 [[sensis]] 0.0200, no-11 [[meanpop]] 0.0209, no-11 [[magic]] 0.0215,
| no-11 [[catakleismic]]!0.0118
| [[unicorn]] 0.0409
|  
| no-11 [[cassandra]] 0.0207
| no-11 [[hemischis]] 0.0208
| no-11 [[decoid]] 0.0135, no-11 [[ennealimmal]] 0.0294
|-
! 2 . 3 . 5 . 11 . other n
| [[porkypine]], [[mavila]]
| [[tetracot]], [[mohaha]]
| [[larry]] (2.3.5.11 gravity)
|  
| [[sensible]]
|  
|  
|  
|  
|-
! 2 . 3 . 5 . other n
| [[srutal archagall]], [[stutzel]]
| [[nestoria]], [[sensipent]]
| [[cata]], [[wuerschmidt]] (2.3.5.23)
|  
|  
|  
|  
|  
|  
|-
! 2 . 3 . 7
| [[slendric]], [[bleu]], [[archy]], [[semaphore]]
| [[skwares]]
| no-5 [[hemififths]]
|
|
|
|
|  
|  
|-
! 2 . 3 . 7 . 11 <br>and its extensions
| [[bleu]], [[supra]]
| [[skwares]], [[suhajira]],
| [[radon]], no-5 [[miracle]], no-5 [[hemififths]]
|  
|  
|  
|  
|  
|  
|-
! 2 . 3 . 7 . other n
| [[baladic]], [[oceanfront]], no-5 [[negra]]
|  
|  
|  
| [[hypnosis]]
|  
|  
|  
|  
|-
! 2 . 3 . 11 <br>and its extensions
| [[Rastmic_clan#Neutral|neutral] (2.3.11 [[rastmic]]), [[namo]], [[paralimmal]], [[io]]
| [[tribilo]] (2.3.11 [[nexus]]), [[huxley]]
|  
|  
| 2.3.11 [[pythrabian]]
| 2.3.11 [[frameshift]]
|  
|  
|  
|-
! 2 . 3 . other n
| [[boethian]], [[barbados]], [[superflat]], [[semitonic]], [[hydrothermal]], [[dog]]
| [[threedic]], [[pepperoni]]
| [[Subgroup_temperaments#Historical|historical]]
|  
|  
|  
|  
|
|
|-
! 2 . 5 . 7 <br>and its extensions
| [[didacus]], [[frostburn]], no-3 [[oodako]]
| [[baldy]], [[rainy]], [[llywelyn]], [[mercy]]
|
|
|
|
|
|
| [[Subgroup temperaments#Daemotertiaschis|daemotertiaschis]]
|-
! 2 . 5 . other n
| [[movila]], [[insect]], [[superquintal]], [[wizz]], [[trader]], [[vengeance]], [[marveltri]], [[sulis]]
|
|
|
|
|
|
|
|
|-
! 2 . 7 <br>and its extensions
| [[orgone]], [[machine]], [[stacks]], [[ultrakleismic]], [[shipwreck]], [[demon]]
| [[machine|mechanism]], [[counterultrakleismic]], [[mabon]]
|
| [[machine|apparatus]]
|
|
|
|
|
|-
! 3 . 5 . 7 <br>and its extensions
| [[canopus]], [[BPS]], [[sirius]], [[arcturus]], [[https://en.xen.wiki/w/Catalog_of_3.5.7_subgroup_rank_two_temperaments|vega]], [[dubhe]] (3.5.7.17)
| [[izar]], [[mintra]] (3.5.7.11)
| [[No-twos_subgroup_temperaments#Alhena|alhena]]
|
|
|
|
|
|
|-
! 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]]
| [[mebsuta]], [[minalzidar]]
| [[mintaka]] (3.7.11.13)
|
|
|
|
|
|
|-
! 4 . n <br>and its extensions
| [[tetrahanson]], [[meanquad]], [[tetrominant]], [[tetrameantone]], [[quarchy]]
|
| [[Subgroup temperaments#Fourwar|fourwar]]
|
|
|
|
|
|
|-
! 5 . n <br>and its extensions
| [[antipyth]], [[juggernaut]]
|
|
|
|
|
|
|
|
|-
! Other subgroups
| [[greeley]], [[halftone]], [[semiwolf]], [[auk]]
|
|
|
|
|
|
|
|
|}
</pre>
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