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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.
; 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


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.
; 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
|}


{| class="wikitable mw-collapsible mw-collapsed"
|+Ripple[23] subsets
|''Contains [[Template:Idiosyncratic|idiosyncratic terms]].''


<pre>
* Clear pond (ripple[12] [[modmos]]): 3 3 3 2 3 3 3 4 2 3 3 3
List entry format:
** Lydian: 6 5 6 3 6 6 3
* Temperament name (1.5 x [[graham complexity]], 2 x graham complexity, [[badness]] to 2 sig fig - copied from wiki temperament pages)
** Major: 6 5 3 6 6 6 3
 
** Mixolydian: 6 5 3 6 6 3 6
 
** Dorian: 6 3 5 6 6 3 6
How to calculate graham complexity:
** Minor: 6 3 5 6 4 5 6
1. Subtract the smallest number in the second row of the temperament's mapping, from the largest
** Phrygian: 3 6 5 6 4 5 6
2. Multiply the result by the number of periods per equave
** 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
''To-do: Re-sort the temperaments in each clump by [[damage]], instead of by badness.''
** 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
(!!!!!!) Indicates a temperament was manually moved to a different 'note count' category because the clumsy note count gave a very strange result.
* Hirajoshi: 6 3 11 3 12
 
* Subminor hexatonic: 6 2 6 6 9 6
(^^^) Indicates temperament that would move to a lower section if 1.5x was used instead of 2x
* 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
 
|}
 
== 5LIM ==
 
~10 NOTES/EQUAVE
* [[Meantone]] (6, 8, 0.0074)
* [[Hanson]] (9, 12, 0.013)
* [[Augmented]] (4.5, 6, 0.022)
* [[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) (^^^)
* [[Vishnu]] (10.5, 14, 0.031) (!!!!!!)
* [[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
; Other scales
* [[Miracle]] (19.5, 26, 0.017) (^^^)
* Amulet{{idiosyncratic}}, approximated from [[magic]] in [[25edo]]: 3 1 3 3 1 3 4 3 3 1 3 4 3
* [[Hemiwuerschmidt]] (24, 32, 0.020) (^^^)
* 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
* [[Garibaldi]] (22.5, 30, 0.022) (^^^)
* Near-just rotated [[5afdo]]: 6 5 9 8 7
* [[Amity]] (25.5, 34, 0.024)
* Near-just [[6afdo]]: 8 7 5 6 5 4
* [[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)
 
 
 
 
|-
! 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]]
|
|
|
|}
</pre>
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