User:BudjarnLambeth/Sandbox: Difference between revisions

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! Unit Name (Symbol):
! Unit Name (Symbol):
! Divisions of Octave
! Divisions of Octave
! Prime Factors
! Origin / Significance
|-
|-
| [[Eka]]
| [[Eka]]
| [[16edo|16]]
| [[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]]
| [[Normal diesis]]
| [[31edo|31]]
| [[31edo|31]]
| 31 (prime)
| See the dedicated page.
|-
|-
| [[Méride]]
| [[Méride]]
| [[43edo|43]]
| [[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]]
| [[Holdrian comma]]
| [[53edo|53]]
| [[53edo|53]]
| 53 (prime)
| See the dedicated page.
|-
|-
| [[Holdrian comma|Mercator’s old comma]]
| [[Holdrian comma|Mercator’s old comma]]
| [[55edo|55]]
| [[55edo|55]]
| 5 x 11
| Not to be confused with [[Mercator's comma]].
|-
|-
| [[Decitone]]
| [[Decitone]]
| [[60edo|60]]
| [[60edo|60]]
| 2<sup>2</sup> × 3 × 5
|
|-
|-
| [[Morion]]
| [[Morion]]
| [[72edo|72]]
| [[72edo|72]]
| 2<sup>3</sup> × 3<sup>2</sup>
| See the dedicated page.
|-
|-
| [[Farab]]
| [[Farab]]
| [[144edo|144]]
| [[144edo|144]]
| 2<sup>4</sup> × 3<sup>2</sup>
| 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>.
|-
|-
| [[Mem]]
| [[Mem]]
| [[205edo|205]]
| [[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]]
| [[Tredek]]
| [[270edo|270]]
| [[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]]*
| [[Savart]]*
| [[300edo|300]]
| [[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]]*
| [[Heptaméride]] / [[eptaméride]] / [[savart]]*
| [[301edo|301]]
| [[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]]
| [[Gene]]
| [[311edo|311]]
| [[311edo|311]]
| 311 (prime)
| Proposed by Joseph Monzo (2007)<ref>[http://tonalsoft.com/enc/g/gene.aspx Tonalsoft | ''Gene, 311-edo'']</ref>.
|-
|-
| [[Dröbisch Angle]]
| [[Dröbisch Angle]]
| [[360edo|360]]
| [[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]]
| [[Squb]]
| [[494edo|494]]
| [[494edo|494]]
| 2 × 13 × 19
| {{Citation needed}}
|-
|-
| Great [[iring]] / [[centitone]]
| Great [[iring]] / [[centitone]]
| [[500edo|500]]
| [[500edo|500]]
| 2<sup>2</sup> × 5<sup>3</sup>
| {{Citation needed}}
|-
|-
| Dexl
| Dexl
| [[540edo|540]]
| [[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]]
| [[Iring]] / [[centitone]]
| [[600edo|600]]
| [[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)
| [[Skisma]] (Sk)
| [[612edo|612]]
| [[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>.
|-
|-
| [[Delfi]]
| [[Delfi]]
| [[665edo|665]]
| [[665edo|665]]
| 5 × 7 × 19
| <ref name="measure"/>
|-
|-
| Small [[iring]] / [[centitone]]
| Small [[iring]] / [[centitone]]
| [[700edo|700]]
| [[700edo|700]]
| 2<sup>2</sup> × 5<sup>2</sup> x 7
| {{Citation needed}}
|-
|-
| [[Woolhouse]]
| [[Woolhouse]]
| [[730edo|730]]
| [[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)
| [[Millioctave]] (moct)
| [[1000edo|1000]]
| [[1000edo|1000]]
| 2<sup>3</sup> × 5<sup>3</sup>
| See the dedicated page.
|-
|-
| [[Cent]] (¢)
| [[Cent]] (¢)
| 1200
| 1200
| 2<sup>4</sup> × 3 × 5<sup>2</sup>
| See the dedicated page.
|-
|-
| Greater muon
| Greater muon
| [[1224edo|1224]]
| [[1224edo|1224]]
| 2<sup>3</sup> × 3<sup>2</sup> × 17
| {{Citation needed}}
|-
|-
| Triangular cent
| Triangular cent
| [[1260edo|1260]]
| [[1260edo|1260]]
| 2<sup>2</sup> × 3<sup>2</sup> × 5 × 7
| {{Citation needed}}
|-
|-
| Pion
| Pion
| [[1272edo|1272]]
| [[1272edo|1272]]
| 2<sup>3</sup> × 3 × 53
| {{Citation needed}}
|-
|-
| Pound
| Pound
| [[1344edo|1344]]
| [[1344edo|1344]]
| 2<sup>6</sup> × 3 × 7
| {{Citation needed}}
|-
|-
| Neutron
| Neutron
| [[1392edo|1392]]
| [[1392edo|1392]]
| 2<sup>4</sup> × 3 × 29
| {{Citation needed}}
|-
|-
| Lesser muon
| Lesser muon
| [[1428edo|1428]]
| [[1428edo|1428]]
| 2<sup>2</sup> × 3 × 7 × 17
| {{Citation needed}}
|-
|-
| Decifarab
| Decifarab
| [[1440edo|1440]]
| [[1440edo|1440]]
| 2<sup>5</sup> × 3<sup>2</sup> × 5
| 1/10 of [[Farab]] unit<ref name="measure"/>.
|-
|-
| Quadratic cent
| Quadratic cent
| [[1452edo|1452]]
| [[1452edo|1452]]
| 2<sup>2</sup> × 3 × 11<sup>2</sup>
| {{Citation needed}}
|-
|-
| Ksion
| Ksion
| [[1476edo|1476]]
| [[1476edo|1476]]
| 2<sup>2</sup> × 3<sup>2</sup> × 41
| {{Citation needed}}
|-
|-
| Cubic cent
| Cubic cent
| [[1500edo|1500]]
| [[1500edo|1500]]
| 2<sup>2</sup> × 3 × 5<sup>3</sup>
| {{Citation needed}}
|-
|-
| Heptamu (7mu)
| Heptamu (7mu)
| [[1536edo|1536]]
| [[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
| Rhoon
| [[1560edo|1560]]
| [[1560edo|1560]]
| 2<sup>3</sup> × 3 × 5 × 13
| {{Citation needed}}
|-
|-
| śata
| śata
| [[1600edo|1600]]
| [[1600edo|1600]]
| 2<sup>6</sup> × 5<sup>2</sup>
| From Sanskrit ''śatam'': hundred; [[Relative cent]] of Armodue 16edo Theory{{Citation needed}}
|-
|-
| Tile
| Tile
| [[1632edo|1632]]
| [[1632edo|1632]]
| 2<sup>5</sup> × 3 × 17
| {{Citation needed}}
|-
|-
| [[Iota]]
| [[Iota]]
| [[1700edo|1700]]
| [[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]]
| [[Harmos]]
| [[1728edo|1728]]
| [[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
| Hind śat / Indian cent
| 2200
| 2200
| 2<sup>3</sup> × 11 × 5<sup>2</sup>
| {{Citation needed}}
|-
|-
| [[Mina]]
| [[Mina]]
| [[2460edo|2460]]
| [[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
| Centidiesis
| 3100
| 3100
| 2<sup>2</sup> × 5<sup>2</sup> x 31
| {{Citation needed}}
|-
|-
| Centiméride
| Centiméride
| 4300
| 4300
| 2<sup>2</sup> × 5<sup>2</sup> x 43
| {{Citation needed}}
|-
|-
| [[Major tina]]
| [[Major tina]]
| [[8269edo|8269]]
| [[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]]
| [[Tina]]
| [[8539edo|8539]]
| [[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]]
| [[Purdal]]
| [[9900edo|9900]]
| [[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]]
| [[Türk sent]] / [[Turkish cent]]
| [[10600edo|10600]]
| [[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]]
| [[Prima]]
| [[12276edo|12276]]
| [[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]]
| [[Jinn]]
| [[16808edo|16808]]
| [[16808edo|16808]]
| 2<sup>3</sup> × 11 × 191
| See the dedicated page.
|-
|-
| [[Jot]]
| [[Jot]]
| [[30103edo|30103]]
| [[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]]
| [[Imp]]
| [[31920edo|31920]]
| [[31920edo|31920]]
| 2<sup>4</sup> × 3 × 5 × 7 × 19
| <ref name="measure"/>
|-
|-
| [[Flu]]
| [[Flu]]
| [[46032edo|46032]]
| [[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]]
| [[Normal atom]]
| [[78005edo|78005]]
| [[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)
| [[MIDI Tuning Standard unit]] (14mu)
| [[196608edo|196608]]
| [[196608edo|196608]]
| 2<sup>16</sup> × 3
| Fourteenth MIDI-resolution unit, 1/16384 (1/(2<sup>14</sup>)) of [[12edo]] semitone<ref name="measure"/>.
|}
|}


Revision as of 07:10, 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
Eka 16
Normal diesis 31
Méride 43
Holdrian comma 53
Mercator’s old comma 55
Decitone 60
Morion 72
Farab 144
Mem 205
Tredek 270
Savart* 300
Heptaméride / eptaméride / savart* 301
Gene 311
Dröbisch Angle 360
Squb 494
Great iring / centitone 500
Dexl 540
Iring / centitone 600
Skisma (Sk) 612
Delfi 665
Small iring / centitone 700
Woolhouse 730
Millioctave (moct) 1000
Cent (¢) 1200
Greater muon 1224
Triangular cent 1260
Pion 1272
Pound 1344
Neutron 1392
Lesser muon 1428
Decifarab 1440
Quadratic cent 1452
Ksion 1476
Cubic cent 1500
Heptamu (7mu) 1536
Rhoon 1560
śata 1600
Tile 1632
Iota 1700
Harmos 1728
Hind śat / Indian cent 2200
Mina 2460
Centidiesis 3100
Centiméride 4300
Major tina 8269
Tina 8539
Purdal 9900
Türk sent / Turkish cent 10600
Prima 12276
Jinn 16808
Jot 30103
Imp 31920
Flu 46032
Normal atom 78005
MIDI Tuning Standard unit (14mu) 196608

Between 0.0239167 and 0.0239833

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