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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

Revision as of 07:09, 6 December 2024

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


Between 0.0239167 and 0.0239833

List of Octave-Based Fine Measures (Logarithmic)
Unit Name (Symbol): Divisions of Octave Prime Factors Origin / Significance
Eka 16 24 From Sanskrit eka: one, unit; chromatic unit of Armodue 16edo Theory[1].
Normal diesis 31 31 (prime) See the dedicated page.
Méride 43 43 (prime) Proposed by Joseph Sauveur, as 7 heptaméride units[2][3].
Holdrian comma 53 53 (prime) See the dedicated page.
Mercator’s old comma 55 5 x 11 Not to be confused with Mercator's comma.
Decitone 60 22 × 3 × 5
Morion 72 23 × 32 See the dedicated page.
Farab 144 24 × 32 1/12 of 12edo semitone; Proposed by al-Farabi in 10th century[2][4].
Mem 205 5 × 41 Unit used by H-Pi Instruments[2][5][6].
Tredek 270 2 × 33 × 5 Proposed by Joseph Monzo (2013)[7].
Savart* 300 22 × 3 × 52 Alexander Wood's definition of the Savart[8], containing 12edo.
Heptaméride / eptaméride / savart* 301 7 × 43 301 ≃ 1,000 × log102; 1/7 of Méride unit; proposed by Joseph Sauveur (1701), advocated by Félix Savart[2][9].
Gene 311 311 (prime) Proposed by Joseph Monzo (2007)[10].
Dröbisch Angle 360 23 × 32 × 5 Proposed as angle by Moritz Dröbisch in the 19th century, later by Andrew Pikler as the current name in Logarithmic Frequency Systems (1966)[2].
Squb 494 2 × 13 × 19 [citation needed]
Great iring / centitone 500 22 × 53 [citation needed]
Dexl 540 22 × 33 × 5 Proposed by Joseph Monzo (2023)[11].
Iring / centitone 600 23 × 3 × 52 Relative cent of 6edo (12edo tone); Proposed by Widogast Iring (1898), later by Joseph Yasser as a "centitone" (1932)[2][12].
Skisma (Sk) 612 22 × 32 × 17 Edo representation of Sagittal's Ultra (Herculean) precision level JI notation (58eda), where it is known as an "ultrina"[2][13].
Delfi 665 5 × 7 × 19 [2]
Small iring / centitone 700 22 × 52 x 7 [citation needed]
Woolhouse 730 2 × 5 × 73 Proposed by Wesley S.B. Woolhouse (1835)[14].
Millioctave (moct) 1000 23 × 53 See the dedicated page.
Cent (¢) 1200 24 × 3 × 52 See the dedicated page.
Greater muon 1224 23 × 32 × 17 [citation needed]
Triangular cent 1260 22 × 32 × 5 × 7 [citation needed]
Pion 1272 23 × 3 × 53 [citation needed]
Pound 1344 26 × 3 × 7 [citation needed]
Neutron 1392 24 × 3 × 29 [citation needed]
Lesser muon 1428 22 × 3 × 7 × 17 [citation needed]
Decifarab 1440 25 × 32 × 5 1/10 of Farab unit[2].
Quadratic cent 1452 22 × 3 × 112 [citation needed]
Ksion 1476 22 × 32 × 41 [citation needed]
Cubic cent 1500 22 × 3 × 53 [citation needed]
Heptamu (7mu) 1536 29 × 3 Seventh MIDI-resolution unit, 1/128 (1/(27)) of 12edo semitone[15]
Rhoon 1560 23 × 3 × 5 × 13 [citation needed]
śata 1600 26 × 52 From Sanskrit śatam: hundred; Relative cent of Armodue 16edo Theory[citation needed]
Tile 1632 25 × 3 × 17 [citation needed]
Iota 1700 22 × 52 × 17 Relative cent of 17edo; proposed by Margo Schulter (2002) and George Secor[2].
Harmos 1728 26 × 33 1728 = 123; 1/144 of 12edo semitone; Proposed by Paul Beaver[2][16].
Hind śat / Indian cent 2200 23 × 11 × 52 [citation needed]
Mina 2460 22 × 3 × 5 × 41 Abbreviation of "schismina", edo representation of Sagittal's Extreme (Olympian) precision level JI notation (233eda)[2][17].
Centidiesis 3100 22 × 52 x 31 [citation needed]
Centiméride 4300 22 × 52 x 43 [citation needed]
Major tina 8269 8269 (prime) Proposed by Flora Canou (2021)[18].
Tina 8539 8539 (prime) Provides good approximations for 41-limit primes except 37; named by Dave Keenan and George Secor; edo representation of Sagittal's Insane (Magrathean) precision level JI notation (809eda)[2][19].
Purdal 9900 22 × 32 × 52 × 11 Relative cent of 99edo; Suggested by Osmiorisbendi, advocated by Tútim Dennsuul Wafiil. See the dedicated page.
Türk sent / Turkish cent 10600 23 × 52 × 53 Relative cent of 106edo, 1/200 of 53edo; invented by M. Ekrem Karadeniz (1965), influenced by Abdülkadir Töre[2][20][21].
Prima 12276 22 × 32 × 11 × 31 Proposed by Erv Wilson, Gene Ward Smith and Gavin Putland[2].
Jinn 16808 23 × 11 × 191 See the dedicated page.
Jot 30103 30103 (prime) 30103 ≃ 100,000 × log102; Proposed by Augustus de Morgan (1864)[2][22][16].
Imp 31920 24 × 3 × 5 × 7 × 19 [2]
Flu 46032 24 × 3 × 7 × 137 Proposed by Gene Ward Smith (2005)[2][23].
Normal atom 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) 196608 216 × 3 Fourteenth MIDI-resolution unit, 1/16384 (1/(214)) of 12edo semitone[2].

Between 0.0239167 and 0.0239833

  1. ↑ Armodue: le risorse di un nuovo sistema musicale
  2. ↑ 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 Stichting Huygens-Fokker: Logarithmic Interval Measures
  3. ↑ Tonalsoft | Méride / 43-ed2 / 43-edo / 43-ET / 43-tone equal-temperament
  4. ↑ Tonalsoft | Farab.
  5. ↑ H-Pi Instruments | Hunt Theoretical System
  6. ↑ Tonalsoft | Mem, 205-edo
  7. ↑ Tonalsoft | Tredek, 270-edo
  8. ↑ The Physics of Music, Alexander Wood, 1944.
  9. ↑ Tonalsoft | Heptaméride
  10. ↑ Tonalsoft | Gene, 311-edo
  11. ↑ Tonalsoft | Dexl, 540-edo
  12. ↑ Tonalsoft | Centitone, iring
  13. ↑ Tonalsoft | Sk, 612-edo
  14. ↑ Essay on musical intervals, harmonics, and the temperament of the musical scale, &c, Wesley S.B. Woolhouse.
  15. ↑ Tonalsoft | 7mu / heptamu
  16. ↑ 16.0 16.1 Tonalsoft | Equal temperaments
  17. ↑ Tonalsoft | Mina
  18. ↑ The Sagittal Forum | Definition of the tina reviewed
  19. ↑ Tonalsoft | Tina
  20. ↑ Tonalsoft | Türk-sent
  21. ↑ 79-Tone Tuning & Theory for Turkish Maqam Music, Ozan Yarman.
  22. ↑ Tonalsoft | Jot
  23. ↑ Tonalsoft | Flu
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