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'''This is a working out sandbox page, not a content page.'''
== 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


; 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


Between
; 20-tone blackwood&greenwood
0.0239167
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.
and
* 3 2 2 1 2 2 1 1 1 3 1 1 1 2 2 1 2 2 3 2
0.0239833


{| class="wikitable sortable"
; Muggles[19]
|+ style="font-size: 105%;" | List of Octave-Based Fine Measures (Logarithmic)
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
! Unit Name (Symbol):
 
! Divisions of Octave
; Ripple[23]
! Prime Factors
This [[modmos]] of ripple[12] sounds sort of like the familiar [[12edo]]:
! Origin / Significance
* 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:
| [[Eka]]
* 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1
| [[16edo|16]]
 
| 2<sup>4</sup>
; [[MOS scale]]s
| From Sanskrit ''eka'': one, unit; chromatic unit of Armodue 16edo Theory<ref>[http://www.armodue.com/risorse.htm Armodue: le risorse di un nuovo sistema musicale]</ref>.
* [[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
| [[Normal diesis]]
* [[Greenwood]][21]: 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2
| [[31edo|31]]
* [[Muggles]][5] (a.k.a. sub-diatonic): 9 4 9 9 4
| 31 (prime)
* [[Muggles]][13]: 2 2 5 2 2 2 5 2 2 2 5 2 2
| See the dedicated page.
* [[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
| [[Méride]]
* [[Ripple]][12]: 3 3 3 3 3 3 3 3 2 3 3 3
| [[43edo|43]]
* [[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
| 43 (prime)
* [[Secund]][17]: 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3
| Proposed by [[Joseph Sauveur]], as 7 heptaméride units<ref name="measure">[http://www.huygens-fokker.org/docs/measures.html Stichting Huygens-Fokker: Logarithmic Interval Measures]</ref><ref>[http://tonalsoft.com/enc/m/meride.aspx Tonalsoft | ''Méride / 43-ed2 / 43-edo / 43-ET / 43-tone equal-temperament'']</ref>.
* [[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
| [[Holdrian comma]]
* [[Blackwood]][5]: 7 7 7 7 7 (''a.k.a. [[5edo]]; an [[equipentatonic]] scale; [[slendro]]-like; works with all three blackwood tunings'')
| [[53edo|53]]
* [[Blackwood|5/4-blackwood]][10]: 4 3 4 3 4 3 4 3 4 3
| 53 (prime)
* [[Blackwood|5/4-blackwood]][15]: 3 1 3 3 1 3 3 1 3 3 1 3 3 1 3
| See the dedicated page.
* [[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
| [[Holdrian comma|Mercator’s old comma]]
* [[Blackwood|6/5-blackwood]][15]: 2 3 2 2 3 2 2 3 2 2 3 2 2 3 2
| [[55edo|55]]
* [[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
| 5 x 11
{| class="wikitable mw-collapsible mw-collapsed"
| Not to be confused with [[Mercator's comma]].
|+Secund[17] subsets
|-
|''Contains [[Template:Idiosyncratic|idiosyncratic terms]].''
| [[Decitone]]
 
| [[60edo|60]]
*[[Antipental blues]]: 8 7 1 4 8 7
| 2<sup>2</sup> × 3 × 5
* 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
| [[Morion]]
* Antipental blues harmonic: 8 7 1 4 3 9 3
| [[72edo|72]]
* [[Pelog]]-like heptatonic: 3 5 7 5 3 8 4 (''Phrygian-like'')
| 2<sup>3</sup> × 3<sup>2</sup>
* Pelog-like pentatonic: 3 5 12 3 12
| See the dedicated page.
* Secund chance ([[modmos]] of secund[8]): 4 7 4 1 4 4 7 4
|-
* Secund-tempered rotated [[5afdo]]: 7 4 9 8 7
| [[Farab]]
* Secund-tempered [[6afdo]]: 8 7 5 7 4 4
| [[144edo|144]]
* Undecimal Mixolydian: 7 4 4 5 7 1 7
| 2<sup>4</sup> × 3<sup>2</sup>
* Undecimal minor hexatonic: 7 1 7 5 8 7
| 1/12 of [[12edo]] semitone; Proposed by [[al-Farabi]] in 10th century<ref name="measure"/><ref>[http://tonalsoft.com/enc/f/farab.aspx Tonalsoft | ''Farab''].</ref>.
* Undecimal quasi-equipentatonic: 7 8 5 8 7
|-
* 12 from secund[17]: 7 1 3 4 1 4 3 4 1 3 1 3
| [[Mem]]
|}
| [[205edo|205]]
 
| 5 × 41
{| class="wikitable mw-collapsible mw-collapsed"
| Unit used by H-Pi Instruments<ref name="measure"/><ref>[http://musictheory.zentral.zone/huntsystem1.html H-Pi Instruments | Hunt Theoretical System]</ref><ref>[http://tonalsoft.com/enc/m/mem.aspx Tonalsoft | ''Mem, 205-edo'']</ref>.
|+6/5-blackwood[20] subsets
|-
|''Contains [[Template:Idiosyncratic|idiosyncratic terms]].''
| [[Tredek]]
 
| [[270edo|270]]
*Blackwood meta-Hirajoshi: 2 3 4 2 5 7 2 12
| 2 × 3<sup>3</sup> × 5
** ''Blackwood pseudo-Akebono neutral: 5 9 7 2 12''
| Proposed by [[Joseph Monzo]] (2013)<ref>[http://tonalsoft.com/enc/t/tredek.aspx Tonalsoft | ''Tredek, 270-edo'']</ref>.
** ''Blackwood pseudo-Akebono supermajor: 7 7 7 2 12''
|-
** ''Blackwood pseudo-Hirajoshi: 2 12 7 2 12''
| [[Savart]]*
** ''Blackwood pseudo-[[pelog]]: 5 4 12 2 12''
| [[300edo|300]]
* Blackwood meta-partial: 4 3 2 2 3 7 7 7
| 2<sup>2</sup> × 3 × 5<sup>2</sup>
** ''Blackwood-tempered [[5afdo]]: 7 4 10 7 7''
| [[Alexander Wood]]'s definition of the Savart<ref>''[https://books.google.com.au/books?id=NWZ8CgAAQBAJ&lpg=PT50&vq=savart&pg=PT51 The Physics of Music]'', Alexander Wood, 1944.</ref>, containing [[12edo]]. 
** ''Mechanical (from [[16afdo]]): 9 2 10 7 7''
|-
** ''Starship (from [[68ifdo]]'', see [[ifdo]]''): 4 7 3 7 7 7''
| [[Heptaméride]] / [[eptaméride]] / [[savart]]*
** ''Volcanic (from [[16afdo]]): 4 7 10 7 7''
| [[301edo|301]]
* Meta-monsoon: 7 4 3 2 5 9 5
| 7 × 43
** ''Monsoon (from [[47zpi]]): 7 7 7 9 5''
| 301 ≃ 1,000 × log<sub>10</sub>2; 1/7 of Méride unit; proposed by Joseph Sauveur (1701), advocated by [[Félix Savart]]<ref name="measure"/><ref>[http://tonalsoft.com/enc/h/heptameride.aspx Tonalsoft | ''Heptaméride'']</ref>.
** ''Monsoon otonal: 7 9 5 9 5''
|-
** ''Monsoon major: 11 5 5 9 5''
| [[Gene]]
* Blackwood neutral nonatonic: 4 7 3 2 5 4 5 2 3
| [[311edo|311]]
* Blackwood undecimal harmonic: 4 8 4 5 4 5 5
| 311 (prime)
* Dungeon (from [[30afdo]]): 11 3 7 2 12
| Proposed by Joseph Monzo (2007)<ref>[http://tonalsoft.com/enc/g/gene.aspx Tonalsoft | ''Gene, 311-edo'']</ref>.
* Moonbeam (from [[16afdo]]): 7 2 12 12 2
|-
* Underpass (from [[10afdo]]): 9 12 5 4 5
| [[Dröbisch Angle]]
* 12 from 6/5-blackwood[20]: 4 3 2 2 3 7 2 3 2 2 3 2
| [[360edo|360]]
|}
| 2<sup>3</sup> × 3<sup>2</sup> × 5
 
| Proposed as ''angle'' by [[Moritz Dröbisch]] in the 19th century, later by [[Andrew Pikler]] as the current name in ''Logarithmic Frequency Systems'' (1966)<ref name="measure"/>.
{| class="wikitable mw-collapsible mw-collapsed"
|-
|+Ripple[23] subsets
| [[Squb]]
|''Contains [[Template:Idiosyncratic|idiosyncratic terms]].''
| [[494edo|494]]
 
| 2 × 13 × 19
* Clear pond (ripple[12] [[modmos]]): 3 3 3 2 3 3 3 4 2 3 3 3
| {{Citation needed}}
** Lydian: 6 5 6 3 6 6 3
|-
** Major: 6 5 3 6 6 6 3
| Great [[iring]] / [[centitone]]
** Mixolydian: 6 5 3 6 6 3 6
| [[500edo|500]]
** Dorian: 6 3 5 6 6 3 6
| 2<sup>2</sup> × 5<sup>3</sup>
** Minor: 6 3 5 6 4 5 6
| {{Citation needed}}
** Phrygian: 3 6 5 6 4 5 6
|-
** Locrian: 3 6 5 3 7 5 6
| Dexl
** Harmonic minor: 6 3 5 6 4 8 3
| [[540edo|540]]
** Melodic minor: 6 3 5 6 6 6 3
| 2<sup>2</sup> × 3<sup>3</sup> × 5
** Major pentatonic: 6 8 6 6 9
| Proposed by Joseph Monzo (2023)<ref>[http://tonalsoft.com/enc/d/dexl.aspx Tonalsoft | ''Dexl, 540-edo'']</ref>.
** Minor pentatonic: 9 5 6 9 6
|-
** Minor blues: 9 5 3 3 9 6
| [[Iring]] / [[centitone]]
** Minor blues heptatonic: 9 5 3 3 6 3 6
| [[600edo|600]]
** Akebono I: 6 3 11 6 9
| 2<sup>3</sup> × 3 × 5<sup>2</sup>
* Hirajoshi: 6 3 11 3 12
| [[Relative cent]] of [[6edo]] ([[12edo]] tone); Proposed by [[Widogast Iring]] (1898), later by [[Joseph Yasser]] as a "centitone" (1932)<ref name="measure"/><ref>[http://www.tonalsoft.com/enc/c/centitone.aspx Tonalsoft | ''Centitone, iring'']</ref>.
* Subminor hexatonic: 6 2 6 6 9 6
|-
* Subminor pentatonic: 8 6 6 9 6
| [[Skisma]] (Sk)
* Subminor blues: 8 6 3 3 9 6
| [[612edo|612]]
* Subminor blues heptatonic: 8 6 3 3 6 3 6
| 2<sup>2</sup> × 3<sup>2</sup> × 17
| Edo representation of [[Sagittal notation|Sagittal]]'s Ultra (Herculean) precision level JI notation (58eda), where it is known as an "ultrina"<ref name="measure"/><ref>[http://tonalsoft.com/enc/s/sk.aspx Tonalsoft | ''Sk, 612-edo'']</ref>.
|-
| [[Delfi]]
| [[665edo|665]]
| 5 × 7 × 19
| <ref name="measure"/>
|-
| Small [[iring]] / [[centitone]]
| [[700edo|700]]
| 2<sup>2</sup> × 5<sup>2</sup> x 7
| {{Citation needed}}
|-
| [[Woolhouse]]
| [[730edo|730]]
| 2 × 5 × 73
| Proposed by [[Wesley S.B. Woolhouse]] (1835)<ref>[https://archive.org/details/essayonmusicali00woolgoog/page/n34/mode/2up ''Essay on musical intervals, harmonics, and the temperament of the musical scale, &c''], Wesley S.B. Woolhouse. </ref>.
|-
| [[Millioctave]] (moct)
| [[1000edo|1000]]
| 2<sup>3</sup> × 5<sup>3</sup>
| See the dedicated page.  
|-
| [[Cent]] (¢)
| 1200
| 2<sup>4</sup> × 3 × 5<sup>2</sup>
| See the dedicated page.
|-
| Greater muon
| [[1224edo|1224]]
| 2<sup>3</sup> × 3<sup>2</sup> × 17
| {{Citation needed}}
|-
| Triangular cent
| [[1260edo|1260]]
| 2<sup>2</sup> × 3<sup>2</sup> × 5 × 7
| {{Citation needed}}
|-
| Pion
| [[1272edo|1272]]
| 2<sup>3</sup> × 3 × 53
| {{Citation needed}}
|-
| Pound
| [[1344edo|1344]]
| 2<sup>6</sup> × 3 × 7
| {{Citation needed}}
|-
| Neutron
| [[1392edo|1392]]
| 2<sup>4</sup> × 3 × 29
| {{Citation needed}}
|-
| Lesser muon
| [[1428edo|1428]]
| 2<sup>2</sup> × 3 × 7 × 17
| {{Citation needed}}
|-
| Decifarab
| [[1440edo|1440]]
| 2<sup>5</sup> × 3<sup>2</sup> × 5
| 1/10 of [[Farab]] unit<ref name="measure"/>.
|-
| Quadratic cent
| [[1452edo|1452]]
| 2<sup>2</sup> × 3 × 11<sup>2</sup>
| {{Citation needed}}
|-
| Ksion
| [[1476edo|1476]]
| 2<sup>2</sup> × 3<sup>2</sup> × 41
| {{Citation needed}}
|-
| Cubic cent
| [[1500edo|1500]]
| 2<sup>2</sup> × 3 × 5<sup>3</sup>
| {{Citation needed}}
|-
| Heptamu (7mu)
| [[1536edo|1536]]
| 2<sup>9</sup> × 3
| Seventh MIDI-resolution unit, 1/128 (1/(2<sup>7</sup>)) of [[12edo]] semitone<ref>[http://tonalsoft.com/enc/number/7mu.aspx Tonalsoft | ''7mu / heptamu'']</ref>
|-
| Rhoon
| [[1560edo|1560]]
| 2<sup>3</sup> × 3 × 5 × 13
| {{Citation needed}}
|-
| śata
| [[1600edo|1600]]
| 2<sup>6</sup> × 5<sup>2</sup>
| From Sanskrit ''śatam'': hundred; [[Relative cent]] of Armodue 16edo Theory{{Citation needed}}
|-
| Tile
| [[1632edo|1632]]
| 2<sup>5</sup> × 3 × 17
| {{Citation needed}}
|-
| [[Iota]]
| [[1700edo|1700]]
| 2<sup>2</sup> × 5<sup>2</sup> × 17
| [[Relative cent]] of [[17edo]]; proposed by [[Margo Schulter]] (2002) and [[George Secor]]<ref name="measure"/>.
|-
| [[Harmos]]
| [[1728edo|1728]]
| 2<sup>6</sup> × 3<sup>3</sup>
| 1728 = 12<sup>3</sup>; 1/144 of [[12edo]] semitone; Proposed by [[Paul Beaver]]<ref name="measure"/><ref name="equal">[http://tonalsoft.com/enc/e/equal-temperament.aspx Tonalsoft | ''Equal temperaments'']</ref>.
|-
| Hind śat / Indian cent
| 2200
| 2<sup>3</sup> × 11 × 5<sup>2</sup>
| {{Citation needed}}
|-
| [[Mina]]
| [[2460edo|2460]]
| 2<sup>2</sup> × 3 × 5 × 41
| Abbreviation of "schismina", edo representation of [[Sagittal notation|Sagittal]]'s Extreme (Olympian) precision level JI notation (233eda)<ref name="measure"/><ref>[http://tonalsoft.com/enc/m/mina.aspx Tonalsoft | ''Mina'']</ref>.
|-
| Centidiesis
| 3100
| 2<sup>2</sup> × 5<sup>2</sup> x 31
| {{Citation needed}}
|-
| Centiméride
| 4300
| 2<sup>2</sup> × 5<sup>2</sup> x 43
| {{Citation needed}}
|-
| [[Major tina]]
| [[8269edo|8269]]
| 8269 (prime)
| Proposed by [[Flora Canou]] (2021)<ref>[https://forum.sagittal.org/viewtopic.php?f=4&t=515 The Sagittal Forum | ''Definition of the tina reviewed'']</ref>.
|-
| [[Tina]]
| [[8539edo|8539]]
| 8539 (prime)
| Provides good approximations for 41-limit primes except 37; named by [[Dave Keenan]] and [[George Secor]]; edo representation of [[Sagittal notation|Sagittal]]'s Insane (Magrathean) precision level JI notation (809eda)<ref name="measure"/><ref>[http://tonalsoft.com/enc/t/tina.aspx Tonalsoft | ''Tina'']</ref>.
|-
| [[Purdal]]
| [[9900edo|9900]]
| 2<sup>2</sup> × 3<sup>2</sup> × 5<sup>2</sup> × 11
| [[Relative cent]] of [[99edo]]; Suggested by [[Osmiorisbendi]], advocated by [[Tútim Dennsuul Wafiil]]. See the dedicated page.
|-
| [[Türk sent]] / [[Turkish cent]]
| [[10600edo|10600]]
| 2<sup>3</sup> × 5<sup>2</sup> × 53
| [[Relative cent]] of [[106edo]], 1/200 of [[53edo]]; invented by [[M. Ekrem Karadeniz]] (1965), influenced by [[Abdülkadir Töre]]<ref name="measure"/><ref>[http://www.tonalsoft.com/enc/t/turk-sent.aspx Tonalsoft | ''Türk-sent'']</ref><ref>[http://www.ozanyarman.com/files/doctorate_thesis.pdf ''79-Tone Tuning & Theory for Turkish Maqam Music''], Ozan Yarman. </ref>.
|-
| [[Prima]]
| [[12276edo|12276]]
| 2<sup>2</sup> × 3<sup>2</sup> × 11 × 31
| Proposed by [[Erv Wilson]], [[Gene Ward Smith]] and [[Gavin Putland]]<ref name="measure"/>.
|-
| [[Jinn]]
| [[16808edo|16808]]
| 2<sup>3</sup> × 11 × 191
| See the dedicated page.
|-
| [[Jot]]
| [[30103edo|30103]]
| 30103 (prime)
| 30103 ≃ 100,000 × log<sub>10</sub>2; Proposed by [[Augustus de Morgan]] (1864)<ref name="measure"/><ref>[http://www.tonalsoft.com/enc/j/jot.aspx Tonalsoft | ''Jot'']</ref><ref name="equal"/>.
|-
| [[Imp]]
| [[31920edo|31920]]
| 2<sup>4</sup> × 3 × 5 × 7 × 19
| <ref name="measure"/>
|-
| [[Flu]]
| [[46032edo|46032]]
| 2<sup>4</sup> × 3 × 7 × 137
| Proposed by Gene Ward Smith (2005)<ref name="measure"/><ref>[http://tonalsoft.com/enc/f/flu.aspx Tonalsoft | ''Flu'']</ref>.
|-
| [[Normal atom]]
| [[78005edo|78005]]
| 5 × 15601
| Name proposed by Tristan Bay in 2023; 78005edo consistently maps Kirnberger's atom to 1 edostep and is a very strong 5-limit system. {{Citation needed}}
|-
| [[MIDI Tuning Standard unit]] (14mu)
| [[196608edo|196608]]
| 2<sup>16</sup> × 3
| Fourteenth MIDI-resolution unit, 1/16384 (1/(2<sup>14</sup>)) of [[12edo]] semitone<ref name="measure"/>.
|}
|}


Between
; Other scales
0.0239167
* Amulet{{idiosyncratic}}, approximated from [[magic]] in [[25edo]]: 3 1 3 3 1 3 4 3 3 1 3 4 3
and
* 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
0.0239833
* Near-just rotated [[5afdo]]: 6 5 9 8 7
* Near-just [[6afdo]]: 8 7 5 6 5 4
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