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==== Octave-based fine measures ====
==== Octave-based fine measures ====
The following table demonstrates a list of measures derived from the logarithmic division of the octave<ref>[http://www.huygens-fokker.org/docs/measures.html Stichting Huygens-Fokker: Logarithmic Interval Measures]</ref>:
The following table demonstrates a list of measures derived from the logarithmic division of the octave:


{| class="wikitable sortable"
{| class="wikitable sortable"
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| [[16edo|16]]
| [[16edo|16]]
| 2<sup>4</sup>
| 2<sup>4</sup>
| From Sanskrit ''eka'': one, unit; chromatic unit of Armodue 16edo Theory
| From Sanskrit ''eka'': one, unit; chromatic unit of Armodue 16edo Theory{{Citation needed}}.
|-
|-
| [[Normal diesis]]
| [[Normal diesis]]
| [[31edo|31]]
| [[31edo|31]]
| PRIME
| PRIME
|
| See the dedicated page.
|-
|-
| [[Méride]]
| [[Méride]]
| [[43edo|43]]
| [[43edo|43]]
| PRIME
| PRIME
| Proposed by [[Joseph Sauveur]], as 7 heptaméride units<ref>[http://tonalsoft.com/enc/m/meride.aspx Tonalsoft | ''Méride / 43-ed2 / 43-edo / 43-ET / 43-tone equal-temperament'']</ref>
| 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]]
| PRIME
| PRIME
|
| <ref name="measure"/>
|-
|-
| [[Morion]]
| [[Morion]]
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| [[144edo|144]]
| [[144edo|144]]
| 2<sup>4</sup> × 3<sup>2</sup>
| 2<sup>4</sup> × 3<sup>2</sup>
| 1/12 of [[12edo]] semitone; Proposed by al-Farabi in 10th century<ref>[http://tonalsoft.com/enc/f/farab.aspx Tonalsoft | ''Farab''].</ref>
| 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
| 5 × 41
| Unit used by H-Pi Instruments<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>
| 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]]
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| [[300edo|300]]
| [[300edo|300]]
| 2<sup>2</sup> × 3 × 5<sup>2</sup>
| 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>, compatible with [[12edo]] system
| [[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
| 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>[http://tonalsoft.com/enc/h/heptameride.aspx Tonalsoft | ''Heptaméride'']</ref>.  
| 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]]
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| [[360edo|360]]
| [[360edo|360]]
| 2<sup>3</sup> × 3<sup>2</sup> × 5
| 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).  
| 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]]
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| [[600edo|600]]
| [[600edo|600]]
| 2<sup>3</sup> × 3 × 5<sup>2</sup>
| 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>[http://www.tonalsoft.com/enc/c/centitone.aspx Tonalsoft | ''Centitone, iring'']</ref>.
| [[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]]
| [[Skisma]] (Sk)
| [[612edo|612]]
| [[612edo|612]]
| 2<sup>2</sup> × 3<sup>2</sup> × 17
| 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>[http://tonalsoft.com/enc/s/sk.aspx Tonalsoft | ''Sk, 612-edo'']</ref>.  
| 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
| 5 × 7 × 19
|
| <ref name="measure"/>
|-
|-
| Small [[iring]] / [[centitone]]
| Small [[iring]] / [[centitone]]
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| [[730edo|730]]
| [[730edo|730]]
| 2 × 5 × 73
| 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'']</ref>
| 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>
| 2<sup>3</sup> × 5<sup>3</sup>
| [[Wikipedia: Metric prefix|SI-prefix]] division of octave
| See the dedicated page.
|-
|-
| [[Cent]] (¢)
| [[Cent]] (¢)
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| [[1440edo|1440]]
| [[1440edo|1440]]
| 2<sup>5</sup> × 3<sup>2</sup> × 5
| 2<sup>5</sup> × 3<sup>2</sup> × 5
| 1/10 of [[Farab]] unit{{Citation needed}}
| 1/10 of [[Farab]] unit<ref name="measure"/>.
|-
|-
| Quadratic cent
| Quadratic cent
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| {{Citation needed}}
| {{Citation needed}}
|-
|-
| [[7mu]] or [[Heptamu]]
| [[Heptamu]] (7mu)
| [[1536edo|1536]]
| [[1536edo|1536]]
| 2<sup>9</sup> × 3
| 2<sup>9</sup> × 3
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| [[1\1700_octave|1700]]
| [[1\1700_octave|1700]]
| 2<sup>2</sup> × 5<sup>2</sup> × 17
| 2<sup>2</sup> × 5<sup>2</sup> × 17
| [[Relative cent]] of [[17edo]]; proposed by [[Margo Schulter]] (2002) and [[George Secor]]
| [[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>
| 2<sup>6</sup> × 3<sup>3</sup>
| 1728 = 12<sup>3</sup>; 1/144 of [[12edo]] semitone; Proposed by [[Paul Beaver]]<ref>[http://tonalsoft.com/enc/e/equal-temperament.aspx Tonalsoft | ''Equal temperaments'']</ref>
| 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
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| [[2460edo|2460]]
| [[2460edo|2460]]
| 2<sup>2</sup> × 3 × 5 × 41
| 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>[http://tonalsoft.com/enc/m/mina.aspx Tonalsoft | ''Mina'']</ref>
| 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
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| [[8539edo|8539]]
| [[8539edo|8539]]
| PRIME
| 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>[http://tonalsoft.com/enc/t/tina.aspx Tonalsoft | ''Tina'']</ref>.  
| 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
| 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]].  
| [[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
| 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>[http://www.tonalsoft.com/enc/t/turk-sent.aspx Tonalsoft | ''Türk-sent'']</ref><ref>''79-Tone Tuning & Theory for Turkish Maqam Music'', Ozan Yarman. </ref>
| [[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
| 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]]
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| [[30103edo|30103]]
| [[30103edo|30103]]
| PRIME
| PRIME
| 30103 ≃ 100,000 × log<sub>10</sub>2; Proposed by [[Augustus de Morgan]] (1864)<ref>[http://www.tonalsoft.com/enc/j/jot.aspx Tonalsoft | ''Jot'']</ref>
| 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
| 2<sup>4</sup> × 3 × 5 × 7 × 19
|
| <ref name="measure"/>
|-
|-
| [[Flu]]
| [[Flu]]
| [[46032edo|46032]]
| [[46032edo|46032]]
| 2<sup>4</sup> × 3 × 7 × 137
| 2<sup>4</sup> × 3 × 7 × 137
| Proposed by [[Gene Ward Smith]] (2005)<ref>[http://tonalsoft.com/enc/f/flu.aspx Tonalsoft | ''Flu'']</ref>
| Proposed by Gene Ward Smith (2005)<ref name="measure"/><ref>[http://tonalsoft.com/enc/f/flu.aspx Tonalsoft | ''Flu'']</ref>.
|-
|-
| [[MIDI Tuning Standard unit]] (14mu)
| [[MIDI Tuning Standard unit]] (14mu)
| [[196608edo|196608]]
| [[196608edo|196608]]
| 2<sup>16</sup> × 3
| 2<sup>16</sup> × 3
| Fourteenth MIDI-resolution unit, 1/16384 (1/(2<sup>14</sup>)) of [[12edo]] semitone
| Fourteenth MIDI-resolution unit, 1/16384 (1/(2<sup>14</sup>)) of [[12edo]] semitone<ref name="measure"/>.
|-
|-
| [[Mean free path]]
| [[Mean free path]]
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