Xenharmonic Wiki

User:BudjarnLambeth/Sandbox: Difference between revisions

← Older editNewer edit →
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,215 edits
mNo edit summary
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,215 edits
mNo edit summary
Line 12: Line 12:
! 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"/>.
|}
|}


Retrieved from "https://en.xen.wiki/w/User:BudjarnLambeth/Sandbox"