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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.
Between
0.0239167
and
0.0239833


 
{| class="wikitable sortable"
 
|+ style="font-size: 105%;" | List of Octave-Based Fine Measures (Logarithmic)
 
|-
 
! Unit Name (Symbol):
 
! Divisions of Octave
 
! Prime Factors
<pre>
! Origin / Significance
IMPORTANT NOTE:
|-
RIGHT NOW THE TEMPERAMENTS IN EACH SUBSECTION ARE SORTED BY BADNESS.
| [[Eka]]
I WILL RE-SORT THEM BY ACCURACY, NOT BADNESS, IN THE FINAL VERSION.
| [[16edo|16]]
 
| 2<sup>4</sup>
 
| 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>.  
 
|-
 
| [[Normal diesis]]
ANOTHER IMPORTANT NOTE:
| [[31edo|31]]
THE FINAL PAGE WILL NOT BE FORMATTED AS AN UGLY LIST LIKE THIS.
| 31 (prime)
IT WILL BE FORMATTED AS A TABLE EXACTLY THE SAME LOOK AND FEEL AS BEFORE.
| See the dedicated page.  
THIS IS JUST AN UGLY WORK-IN-PROGRESS.
|-
 
| [[Méride]]
 
| [[43edo|43]]
 
| 43 (prime)
 
| 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>.
 
|-
 
| [[Holdrian comma]]
Number of notes recommended is estimated as 2 x graham complexity.
| [[53edo|53]]
 
| 53 (prime)
How to calculate graham complexity:
| See the dedicated page.
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 temperaments in each cell are listed by damahe (least to most).
 
(^) = list item has not yet been ordered by damage
 
(^^^) = cell is currently ordered alphabetically, needs to be re-ordered by damage
 
(£££) = cell is currently ordered by badness, needs to be re-ordered by damage
 
(!!) = todo: check that none of the ones in this cell are extreme exotemperaments (>20 cents error on most intervals), remove them if they are
 
{| 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)
| [[Holdrian comma|Mercator’s old comma]]
| [[hanson]], [[magic]], [[meantone]], [[negri]], [[augmented]], [[porcupine]], [[dimipent]], [[mavila]], [[blackwood]], [[misty]](^), [[whitewood]](^)
| [[55edo|55]]
| [[helmhpltz]], [[orson]], [[wuerschmidt]], [[sensipent]], [[compton]], [[diaschismic]], [[tetracot]], [[passion]], [[superpyth]], [[ripple]], [[valentine]](^)
| 5 x 11
| [[luna]], [[vishnu]], [[amity]], [[gravity]](^), [[kwazy]](^), [[parakleismic]](^)
| Not to be confused with [[Mercator's comma]].
|
| [[ennealimmal]]
|  
| [[minortone]](^), [[vavoom]](^)
|
|
|-
|-
! 7-limit <br>(2 . 3 . 5 . 7)
| [[Decitone]]
| [[porcupine]], [[pajara]], [[keemun]], [[negri]], [[doublewide]], [[injera]], [[dominant]], [[august]], [[diminished]], [[blacksmith]]
| [[60edo|60]]
| [[orwell]], [[myna]], [[magic]], [[meantone]], [[mothra]], [[superpyth]], [[flattone]], [[liese], [[beatles]], [[augene]], [[hedgehog]], [[nautilus]], [[catler]], [[godzilla]],  [[lemba]], [[schism]](^), [[valentine]](^)
| 2<sup>2</sup> × 3 × 5
| [[miracle]], [[garibaldi]], [[sensi]], [[amity]](^), [[diaschismic]](^), [[harry]](^), [[hemiwuerschmidt]](^)
| [[catakleismic]], [[misty]], [[unidec]] (^^^)
| [[ennealimmal]], [[hemififths]], [[tertiaseptal]] (^^^)
|  
| [[parakleismic]], [[sesquiquartififths]] (^^^)
|
|
| [[enneadecal]], [[pontiac]],[[Ragismic_microtemperaments#Supermajor|supermajor]] (^^^)
|-
|-
! 11-limit <br>(2 . 3 . 5 . 7 . 11)
| [[Morion]]
| [[august]], [[blacksmith]], [[pajaric]], [[triforce]] (^^^)
| [[72edo|72]]
| [[orwell]], [[mohajira]], [[porcupine]], [[hedgehog]], [[astrology]], [[vigintiduo]], [[augene]], [[nautilus]], [[catnip]], [[undevigintone]], [[injera]], [[keemun]], [[progress]], [[dominant]], [[negric]], [[meanenneadecal]], [[duodecim]], [[opossum]], [[valentine]](^)
| 2<sup>3</sup> × 3<sup>2</sup>
| [[nusecond]], [[squares]], [[meantone]], [[quasisupra]], [[pajara]], [[telepathy]], [[suprapyth]], [[negroni]], [[porky]], [[fleetwood]], [[pajarous]], [[sensis]], [[flattone]], [[godzilla]], [[darjeeling]], [[mothra]](^)
| See the dedicated page.
| [[miracle]], [[magic]], [[meanpop]], [[migration]], [[andromeda]], [[superpyth]], [[shrutar]](^)
|-
| [[diaschismic]], [[hemithirds]], [[tritikleismic]], [[unidec]], [[wizard]] (^^^)
| [[Farab]]
|  
| [[144edo|144]]
| [[harry]]
| 2<sup>4</sup> × 3<sup>2</sup>
| [[cassandra]], [[catakleismic]], [[ennealimnic]], [[hemiwuerschmidt]], [[quasiorwell]],  [[sqrtphi]] (^^^)
| 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>.
| [[hemienneadecal]], [[hemiennealimmal]], [[trinity]], [[vishnu]] (^^^)
|-
| [[Mem]]
| [[205edo|205]]
| 5 × 41
| 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>.
|-
| [[Tredek]]
| [[270edo|270]]
| 2 × 3<sup>3</sup> × 5
| Proposed by [[Joseph Monzo]] (2013)<ref>[http://tonalsoft.com/enc/t/tredek.aspx Tonalsoft | ''Tredek, 270-edo'']</ref>.
|-
| [[Savart]]*
| [[300edo|300]]
| 2<sup>2</sup> × 3 × 5<sup>2</sup>
| [[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]]. 
|-
| [[Heptaméride]] / [[eptaméride]] / [[savart]]*
| [[301edo|301]]
| 7 × 43
| 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>.
|-
| [[Gene]]
| [[311edo|311]]
| 311 (prime)
| Proposed by Joseph Monzo (2007)<ref>[http://tonalsoft.com/enc/g/gene.aspx Tonalsoft | ''Gene, 311-edo'']</ref>.
|-
| [[Dröbisch Angle]]
| [[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"/>.
|-
| [[Squb]]
| [[494edo|494]]
| 2 × 13 × 19
| {{Citation needed}}
|-
| Great [[iring]] / [[centitone]]
| [[500edo|500]]
| 2<sup>2</sup> × 5<sup>3</sup>
| {{Citation needed}}
|-
| Dexl
| [[540edo|540]]
| 2<sup>2</sup> × 3<sup>3</sup> × 5
| Proposed by Joseph Monzo (2023)<ref>[http://tonalsoft.com/enc/d/dexl.aspx Tonalsoft | ''Dexl, 540-edo'']</ref>.
|-
| [[Iring]] / [[centitone]]
| [[600edo|600]]
| 2<sup>3</sup> × 3 × 5<sup>2</sup>
| [[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>.
|-
| [[Skisma]] (Sk)
| [[612edo|612]]
| 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>.
|-
|-
! 13-limit <br>(2 . 3 . 5 . 7 . 11 . 13)
| [[Delfi]]
| [[negric]]
| [[665edo|665]]
| [[negri]], [[Mavila_family#Armodue|armodue]], [[opossum]], [[triforce]], [[blacksmith]], [[augene]], [[lupercalia]], [[porcupine]], [[hedgehog]], [[godzilla]] (£££)
| 5 × 7 × 19
| [[meantone]], [[winston]], sensis, [[meanenneadecal]], [[darjeeling]], [[flattone]], [[ringo]], [[nusecond]], [[modus]], [[pajara]] (£££)
| <ref name="measure"/>
| [[mirkat]], [[miraculous]], [[andromeda]], [[superkleismic]], [[injera]], [[nautilus]] , [[undevigintone]], [[ogene]], [[mohajira]], [[mothra]], [[superpyth]], [[negroni]], [[diaschismic]] (£££)
| [[orwell]], [[magic]] (£££)
| [[myna]], [[sensus]], [[meanpop]] (£££)
| [[cassandra]]
| [[catakleismic]], [[shrutar]] (£££)
| [[abigail]], [[hemiennealimmal]], [[harry]], [[semihemiennealimmal]], [[decoid]], [[trinity]] (£££)
|-
|-
! 17-limit <br>(2 . 3 . 5 . 7 . 11 . 13 . 17)
| Small [[iring]] / [[centitone]]
|
| [[700edo|700]]
|
| 2<sup>2</sup> × 5<sup>2</sup> x 7
| [[pajara]]
| {{Citation needed}}
| [[mirkat]], [[miraculous]], [[mohajira]], [[injera]], [[meanenneadecal]] (£££)
|
| [[sensus]], [[diaschismic]], [[modus]], [[andromeda]] (£££)
|  
| [[echidna]], [[shrutar]] (£££)
| [[harry]], [[sqrtphi]], [[tritikleismic]], [[octoid]], [[trinity]] (£££)
|-
|-
! 19-limit <br>(2 . 3 . 5 . 7 . 11 . 13 . 17 . 19)
| [[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>.
| [[injera]], [[mohajira]],  [[meanenneadecal]], [[shrutar]] (£££)
| [[andromeda]]
| [[hitchcock]], [[modus]] (£££)
| [[marvolo]]
|
| [[sqrtphi]], [[octoid]], [[ketchup]], [[trinity]] (£££)
|-
|-
! Higher prime limits
| [[Millioctave]] (moct)
|
| [[1000edo|1000]]
|
| 2<sup>3</sup> × 5<sup>3</sup>
|
| See the dedicated page.
|
|
|
|
| [[shrutar]]
| [[satin]], [[ketchup]], [[trinity]] (£££)
|-
|-
! 2 . 3 . 5 . 7 . other n
| [[Cent]] (¢)
| [[negra]
| 1200
|
| 2<sup>4</sup> × 3 × 5<sup>2</sup>
| no-11 [[sensis]], no-11 [[meanpop]], no-11 [[magic]] (£££)
| See the dedicated page.
| no-11 [[catakleismic]]
| [[unicorn]]
|  
| no-11 [[cassandra]]
| no-11 [[hemischis]]
| no-11 [[decoid]], no-11 [[ennealimmal]] (£££)
|-
|-
! 2 . 3 . 5 . 11 . other n
| Greater muon
| [[mavila]], [[porkypine]] (^^^)
| [[1224edo|1224]]
| [[mohaha]], [[tetracot]] (^^^)
| 2<sup>3</sup> × 3<sup>2</sup> × 17
| [[larry]] (2.3.5.11 gravity)
| {{Citation needed}}
|
| [[sensible]]
|
|
|
|  
|-
|-
! 2 . 3 . 5 . other n
| Triangular cent
| [[srutal archagall]], [[stutzel]] (^^^)
| [[1260edo|1260]]
| [[nestoria]], [[sensipent]] (^^^)
| 2<sup>2</sup> × 3<sup>2</sup> × 5 × 7
| [[cata]], [[wuerschmidt]] (2.3.5.23) (^^^)
| {{Citation needed}}
|
|
|
|
|
|  
|-
|-
! 2 . 3 . 7
| Pion
| [[archy]], [[bleu]], [[semaphore]], [[slendric]] (^^^)
| [[1272edo|1272]]
| [[skwares]]
| 2<sup>3</sup> × 3 × 53
| no-5 [[hemififths]]
| {{Citation needed}}
|  
|  
|
|
|
|
|-
|-
! 2 . 3 . 7 . 11 <br>and its extensions
| Pound
| [[bleu]], [[supra]] (^^^)
| [[1344edo|1344]]
| [[skwares]], [[suhajira]] (^^^)
| 2<sup>6</sup> × 3 × 7
| no-5 [[miracle]], [[radon]], no-5 [[hemififths]] (^^^)
| {{Citation needed}}
|
|
|
|
|  
|  
|-
|-
! 2 . 3 . 7 . other n
| Neutron
| [[baladic]], no-5 [[negra]], [[oceanfront]] (^^^)
| [[1392edo|1392]]
|
| 2<sup>4</sup> × 3 × 29
|
| {{Citation needed}}
|  
| [[hypnosis]]
|  
|  
|
|
|-
|-
! 2 . 3 . 11 <br>and its extensions
| Lesser muon
| [[io]], [[namo], [[Rastmic_clan#Neutral|neutral] (2.3.11 [[rastmic]]), [[paralimmal]] (^^^) (!!)
| [[1428edo|1428]]
| [[huxley]], [[tribilo]] (2.3.11 [[nexus]]) (^^^)
| 2<sup>2</sup> × 3 × 7 × 17
|
| {{Citation needed}}
|
| 2.3.11 [[pythrabian]]
| 2.3.11 [[frameshift]]
|
|
|  
|-
|-
! 2 . 3 . other n
| Decifarab
| [[barbados]], [[boethian]], [[dog]], [[hydrothermal]], [[semitonic]], [[superflat]] (^^^) (!!)
| [[1440edo|1440]]
| [[pepperoni]], [[threedic]] (^^^)
| 2<sup>5</sup> × 3<sup>2</sup> × 5
| [[Subgroup_temperaments#Historical|historical]]
| 1/10 of [[Farab]] unit<ref name="measure"/>.
|
|
|
|
|
|
|-
|-
! 2 . 5 . 7 <br>and its extensions
| Quadratic cent
| [[didacus]], [[frostburn]], no-3 [[oodako]] (^^^) (!!)
| [[1452edo|1452]]
| [[baldy]], [[llywelyn]], [[mercy]], [[rainy]] (^^^)
| 2<sup>2</sup> × 3 × 11<sup>2</sup>
|
| {{Citation needed}}
|
|
|
|
|  
| [[Subgroup temperaments#Daemotertiaschis|daemotertiaschis]]
|-
|-
! 2 . 5 . other n
| Ksion
| [[insect]], [[marveltri]], [[movila]], [[sulis]], [[superquintal]], [[trader]], [[vengeance]], [[wizz]] (^^^) (!!)
| [[1476edo|1476]]
|
| 2<sup>2</sup> × 3<sup>2</sup> × 41
|
| {{Citation needed}}
|
|
|
|
|  
|  
|-
|-
! 2 . 7 <br>and its extensions
| Cubic cent
| [[demon]], [[machine]], [[orgone]], [[shipwreck]], [[stacks]], [[ultrakleismic]] (^^^) (!!)
| [[1500edo|1500]]
| [[counterultrakleismic]], [[mabon]], [[machine|mechanism]] (^^^)
| 2<sup>2</sup> × 3 × 5<sup>3</sup>
|
| {{Citation needed}}
| [[machine|apparatus]]
|
|
|
|  
|  
|-
|-
! 3 . 5 . 7 <br>and its extensions
| Heptamu (7mu)
| [[arcturus]], [[BPS]], [[canopus]], [[dubhe]] (3.5.7.17), [[sirius]], [[Catalog of 3.5.7 subgroup rank two temperaments|vega]] (^^^)
| [[1536edo|1536]]
| [[izar]], [[mintra]] (3.5.7.11) (^^^)
| 2<sup>9</sup> × 3
| [[No-twos_subgroup_temperaments#Alhena|alhena]]
| 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>
|
|
|
|
|
|
|-
|-
! 3 . 5 . other n
| Rhoon
| [[aldebaran]], [[deneb]], [[polaris]] (^^^)
| [[1560edo|1560]]
|
| 2<sup>3</sup> × 3 × 5 × 13
|  
| {{Citation needed}}
| [[alnilam]], [[No-twos subgroup temperaments#Fomalhaut|fomalhaut]] (^^^)
|
|
|
|  
|  
|-
|-
! 3 . 7 <br>and its extensions
| śata
| [[keladic]], [[mintaka]] (3.7.11) (^^^)
| [[1600edo|1600]]
| [[mebsuta]], [[minalzidar]] (^^^)
| 2<sup>6</sup> × 5<sup>2</sup>
| [[mintaka]] (3.7.11.13)
| From Sanskrit ''śatam'': hundred; [[Relative cent]] of Armodue 16edo Theory{{Citation needed}}
|
|
|
|
|
|
|-
|-
! 4 . n <br>and its extensions
| Tile
| [[meanquad]], [[tetrahanson]], [[tetrameantone]], [[tetrominant]], [[quarchy]] (^^^)
| [[1632edo|1632]]
|  
| 2<sup>5</sup> × 3 × 17
| [[Subgroup temperaments#Fourwar|fourwar]]
| {{Citation needed}}
|  
|  
|
|
|
|
|-
|-
! 5 . n <br>and its extensions
| [[Iota]]
| [[antipyth]], [[juggernaut]] (^^^)
| [[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"/>.
|
|
|
|
|
|
|-
|-
! Other subgroups
| [[Harmos]]
| [[auk]], [[greeley]], [[halftone]], [[semiwolf]] (^^^)
| [[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"/>.
|}
|}
</pre>
 
Between
0.0239167
and
0.0239833
Retrieved from "https://en.xen.wiki/w/User:BudjarnLambeth/Sandbox"