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== Scales ==
; 12-tone 7edo&5edo
This scale is designed to be mapped to the key of C on a conventional piano keyboard, with 7edo on the white keys, and 5edo on black:
* 5 2 3 4 1 5 1 4 3 2 5 0


Remember, these are just my ugly, messy notes, and it will look much nicer on the finished page.
; 24-tone blackwood&greenwood
You can have two pianos/keyboards, one 68.6 [[cents]] sharp of the other, both tuned to the 12-tone 7edo&5edo scale. The combined black keys across both keyboards will be [[blackwood]][10] and the white keys will be [[greenwood]][14].
* 3 2 0 2 1 2 2 1 1 1 3 1 1 1 2 2 1 2 0 2 3 0 2 0


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.
; 20-tone blackwood&greenwood
Removing the duplicates from the previous scale (perhaps for use on other instruments beside keyboard) gives this 20-tone scale, which includes both blackwood[10] and greenwood[14] as subsets.
* 3 2 2 1 2 2 1 1 1 3 1 1 1 2 2 1 2 2 3 2


; Muggles[19]
Of all the regular temperaments available in 35edo, [[muggles]] approximates [[just intonation]] the most closely. Here is the muggles[19] [[MOS scale]]:
* 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 1 2 2 2


; Ripple[23]
This [[modmos]] of ripple[12] sounds sort of like the familiar [[12edo]]:
* 3 3 3 2 3 3 3 4 2 3 3 3
And it can be extended out to the ripple[23] [MOS scale]] which adds many [[7-limit]] intervals:
* 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1


; [[MOS scale]]s
* [[Greenwood]][7]/[[whitewood]][7]: 5 5 5 5 5 5 5 (''a.k.a. [[7edo]]; an [[equiheptatonic]] scale'')
* [[Greenwood]][14]: 3 2 3 2 3 2 3 2 3 2 3 2 3 2
* [[Greenwood]][21]: 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2
* [[Muggles]][5] (a.k.a. sub-diatonic): 9 4 9 9 4
* [[Muggles]][13]: 2 2 5 2 2 2 5 2 2 2 5 2 2
* [[Muggles]][16]: 2 2 3 2 2 2 2 2 3 2 2 2 2 3 2 2
* [[Muggles]][19]: 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 1 2 2 2
* [[Ripple]][12]: 3 3 3 3 3 3 3 3 2 3 3 3
* [[Ripple]][23]: 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1
* [[Secund]][17]: 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3
* [[Whitewood]][14]: 1 4 1 4 1 4 1 4 1 4 1 4 1 4
* [[Whitewood]][21]: 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1
* [[Blackwood]][5]: 7 7 7 7 7 (''a.k.a. [[5edo]]; an [[equipentatonic]] scale; [[slendro]]-like; works with all three blackwood tunings'')
* [[Blackwood|5/4-blackwood]][10]: 4 3 4 3 4 3 4 3 4 3
* [[Blackwood|5/4-blackwood]][15]: 3 1 3 3 1 3 3 1 3 3 1 3 3 1 3
* [[Blackwood|5/4-blackwood]][25]: 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1
* [[Blackwood|6/5-blackwood]][10]: 2 5 2 5 2 5 2 5 2 5
* [[Blackwood|6/5-blackwood]][15]: 2 3 2 2 3 2 2 3 2 2 3 2 2 3 2
* [[Blackwood|6/5-blackwood]][20]: 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2
{| class="wikitable mw-collapsible mw-collapsed"
|+Secund[17] subsets
|''Contains [[Template:Idiosyncratic|idiosyncratic terms]].''


*[[Antipental blues]]: 8 7 1 4 8 7
* Antipental blues maj 6th: 8 7 1 4 7 1 7
* Antipental blues neutral 7th: 8 7 1 4 8 3 4
* Antipental blues maj 7th: 8 7 1 4 8 4 3
* Antipental blues harmonic: 8 7 1 4 3 9 3
* [[Pelog]]-like heptatonic: 3 5 7 5 3 8 4 (''Phrygian-like'')
* Pelog-like pentatonic: 3 5 12 3 12
* Secund chance ([[modmos]] of secund[8]): 4 7 4 1 4 4 7 4
* Secund-tempered rotated [[5afdo]]: 7 4 9 8 7
* Secund-tempered [[6afdo]]: 8 7 5 7 4 4
* Undecimal Mixolydian: 7 4 4 5 7 1 7
* Undecimal minor hexatonic: 7 1 7 5 8 7
* Undecimal quasi-equipentatonic: 7 8 5 8 7
* 12 from secund[17]: 7 1 3 4 1 4 3 4 1 3 1 3
|}


{| class="wikitable mw-collapsible mw-collapsed"
|+6/5-blackwood[20] subsets
|''Contains [[Template:Idiosyncratic|idiosyncratic terms]].''


*Blackwood meta-Hirajoshi: 2 3 4 2 5 7 2 12
** ''Blackwood pseudo-Akebono neutral: 5 9 7 2 12''
** ''Blackwood pseudo-Akebono supermajor: 7 7 7 2 12''
** ''Blackwood pseudo-Hirajoshi: 2 12 7 2 12''
** ''Blackwood pseudo-[[pelog]]: 5 4 12 2 12''
* Blackwood meta-partial: 4 3 2 2 3 7 7 7
** ''Blackwood-tempered [[5afdo]]: 7 4 10 7 7''
** ''Mechanical (from [[16afdo]]): 9 2 10 7 7''
** ''Starship (from [[68ifdo]]'', see [[ifdo]]''): 4 7 3 7 7 7''
** ''Volcanic (from [[16afdo]]): 4 7 10 7 7''
* Meta-monsoon: 7 4 3 2 5 9 5
** ''Monsoon (from [[47zpi]]): 7 7 7 9 5''
** ''Monsoon otonal: 7 9 5 9 5''
** ''Monsoon major: 11 5 5 9 5''
* Blackwood neutral nonatonic: 4 7 3 2 5 4 5 2 3
* Blackwood undecimal harmonic: 4 8 4 5 4 5 5
* Dungeon (from [[30afdo]]): 11 3 7 2 12
* Moonbeam (from [[16afdo]]): 7 2 12 12 2
* Underpass (from [[10afdo]]): 9 12 5 4 5
* 12 from 6/5-blackwood[20]: 4 3 2 2 3 7 2 3 2 2 3 2
|}


<pre>
{| class="wikitable mw-collapsible mw-collapsed"
IMPORTANT NOTE:
|+Ripple[23] subsets
RIGHT NOW THE TEMPERAMENTS IN EACH SUBSECTION ARE SORTED BY BADNESS.
|''Contains [[Template:Idiosyncratic|idiosyncratic terms]].''
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.
 
 
 


* Clear pond (ripple[12] [[modmos]]): 3 3 3 2 3 3 3 4 2 3 3 3
** Lydian: 6 5 6 3 6 6 3
** Major: 6 5 3 6 6 6 3
** Mixolydian: 6 5 3 6 6 3 6
** Dorian: 6 3 5 6 6 3 6
** Minor: 6 3 5 6 4 5 6
** Phrygian: 3 6 5 6 4 5 6
** Locrian: 3 6 5 3 7 5 6
** Harmonic minor: 6 3 5 6 4 8 3
** Melodic minor: 6 3 5 6 6 6 3
** Major pentatonic: 6 8 6 6 9
** Minor pentatonic: 9 5 6 9 6
** Minor blues: 9 5 3 3 9 6
** Minor blues heptatonic: 9 5 3 3 6 3 6
** Akebono I: 6 3 11 6 9
* Hirajoshi: 6 3 11 3 12
* Subminor hexatonic: 6 2 6 6 9 6
* Subminor pentatonic: 8 6 6 9 6
* Subminor blues: 8 6 3 3 9 6
* Subminor blues heptatonic: 8 6 3 3 6 3 6
|}


 
; Other scales
Number of notes recommended is estimated as 2 x graham complexity.
* Amulet{{idiosyncratic}}, approximated from [[magic]] in [[25edo]]: 3 1 3 3 1 3 4 3 3 1 3 4 3
 
* Fourfourths{{idio}} ([[modmos]] of 7/6-blackwood[20]): 3 1 1 2 1 1 1 4 1 1 1 4 1 1 1 4 1 1 1 4
How to calculate graham complexity:
* Near-just rotated [[5afdo]]: 6 5 9 8 7
1. Subtract the smallest number in the second row of the temperament's mapping, from the largest
* Near-just [[6afdo]]: 8 7 5 6 5 4
2. Multiply the result by the number of periods per equave
 
 
 
 
 
 
 
 
 
 
{| class="wikitable center-all"
|+
! JI subgroup
! ~10 notes per equave
! ~20 notes
! ~30 notes
! ~40 notes
! ~50 notes
! ~60 notes
! ~70 notes
! ~80 notes
! >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]]
|
| [[minortone]], [[vavoom]]
|
|
|-
! 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]]
|
| [[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]]
| [[meantone]], [[pajara]], [[squares]], [[nusecond]], [[telepathy]], [[porky]], [[darjeeling]], [[pajarous]], [[sensis]], [[godzilla]], [[quasisupra]], [[suprapyth]], [[flattone]], [[fleetwood]], [[negroni]], [[mothra]]
| [[miracle]], [[magic]], [[meanpop]], [[andromeda]], [[superpyth]], [[migration]], [[shrutar]
| [[unidec]], [[wizard]], [[hemithirds]], [[tritikleismic]], [[diaschismic]]
|
| [[harry]]
| [[quasiorwell]], [[catakleismic]], [[ennealimnic]], [[hemiwuerschmidt]], [[sqrtphi]], [[cassandra]]
| [[hemiennealimmal]], [[hemienneadecal]], [[vishnu]], [[trinity]]
|-
! 13-limit <br>(2 . 3 . 5 . 7 . 11 . 13)
| [[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
| [[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
| [[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
| [[orwell]] 0.0197, [[magic]] 0.0215
| [[myna]] 0.0171, [[sensus]] 0.0207, [[meanpop]] 0.0209
| [[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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