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| {| class="wikitable sortable" | | {{Harmonics in cet|33.426|columns=13|intervals=prime}} |
| |+ style="font-size: 105%;" | List of Octave-Based Fine Measures (Logarithmic)
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| |-
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| ! Unit Name (Symbol):
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| ! Divisions of Octave
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| ! Prime Factors
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| ! Origin / Significance
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| |-
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| | [[Eka]]
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| | [[16edo|16]]
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| | 2<sup>4</sup>
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| | 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>.
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| |-
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| | [[Normal diesis]]
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| | [[31edo|31]]
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| | 31 (prime)
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| | See the dedicated page.
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| |-
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| | [[Méride]]
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| | [[43edo|43]]
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| | 43 (prime)
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| | 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>.
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| |-
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| | [[Holdrian comma]]
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| | [[53edo|53]]
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| | 53 (prime)
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| | See the dedicated page.
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| |-
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| | [[Holdrian comma|Mercator’s old comma]]
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| | [[55edo|55]]
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| | 5 x 11
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| | Not to be confused with [[Mercator's comma]].
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| |-
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| | [[Decitone]]
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| | [[60edo|60]]
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| | 2<sup>2</sup> × 3 × 5
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| |
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| |-
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| | [[Morion]]
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| | [[72edo|72]]
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| | 2<sup>3</sup> × 3<sup>2</sup>
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| | See the dedicated page.
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| |-
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| | [[Farab]]
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| | [[144edo|144]]
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| | 2<sup>4</sup> × 3<sup>2</sup>
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| | 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>.
| |
| |-
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| | [[Mem]]
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| | [[205edo|205]]
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| | 5 × 41
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| | 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>.
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| |-
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| | [[Tredek]]
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| | [[270edo|270]]
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| | 2 × 3<sup>3</sup> × 5
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| | Proposed by [[Joseph Monzo]] (2013)<ref>[http://tonalsoft.com/enc/t/tredek.aspx Tonalsoft | ''Tredek, 270-edo'']</ref>.
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| |-
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| | [[Savart]]*
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| | [[300edo|300]]
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| | 2<sup>2</sup> × 3 × 5<sup>2</sup>
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| | [[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]].
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| |-
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| | [[Heptaméride]] / [[eptaméride]] / [[savart]]*
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| | [[301edo|301]]
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| | 7 × 43
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| | 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>.
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| |-
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| | [[Gene]]
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| | [[311edo|311]]
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| | 311 (prime)
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| | Proposed by Joseph Monzo (2007)<ref>[http://tonalsoft.com/enc/g/gene.aspx Tonalsoft | ''Gene, 311-edo'']</ref>.
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| |- | |
| | [[Dröbisch Angle]]
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| | [[360edo|360]]
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| | 2<sup>3</sup> × 3<sup>2</sup> × 5
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| | 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"/>.
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| |-
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| | [[Squb]]
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| | [[494edo|494]]
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| | 2 × 13 × 19
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| | {{Citation needed}}
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| |-
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| | Great [[iring]] / [[centitone]]
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| | [[500edo|500]]
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| | 2<sup>2</sup> × 5<sup>3</sup>
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| | {{Citation needed}}
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| |-
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| | Dexl
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| | [[540edo|540]]
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| | 2<sup>2</sup> × 3<sup>3</sup> × 5
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| | Proposed by Joseph Monzo (2023)<ref>[http://tonalsoft.com/enc/d/dexl.aspx Tonalsoft | ''Dexl, 540-edo'']</ref>.
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| |-
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| | [[Iring]] / [[centitone]]
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| | [[600edo|600]]
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| | 2<sup>3</sup> × 3 × 5<sup>2</sup>
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| | [[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>.
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| |-
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| | [[Skisma]] (Sk)
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| | [[612edo|612]]
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| | 2<sup>2</sup> × 3<sup>2</sup> × 17
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| | 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>.
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| |-
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| | [[Delfi]]
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| | [[665edo|665]]
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| | 5 × 7 × 19
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| | <ref name="measure"/>
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| |-
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| | Small [[iring]] / [[centitone]]
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| | [[700edo|700]]
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| | 2<sup>2</sup> × 5<sup>2</sup> x 7
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| | {{Citation needed}}
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| |- | |
| | [[Woolhouse]]
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| | [[730edo|730]]
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| | 2 × 5 × 73
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| | 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>.
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| |-
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| | [[Millioctave]] (moct)
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| | [[1000edo|1000]]
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| | 2<sup>3</sup> × 5<sup>3</sup>
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| | See the dedicated page.
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| |-
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| | [[Cent]] (¢)
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| | 1200
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| | 2<sup>4</sup> × 3 × 5<sup>2</sup>
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| | See the dedicated page.
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| |-
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| | Greater muon
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| | [[1224edo|1224]]
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| | 2<sup>3</sup> × 3<sup>2</sup> × 17
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| | {{Citation needed}}
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| |-
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| | Triangular cent
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| | [[1260edo|1260]]
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| | 2<sup>2</sup> × 3<sup>2</sup> × 5 × 7
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| | {{Citation needed}}
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| |-
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| | Pion
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| | [[1272edo|1272]]
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| | 2<sup>3</sup> × 3 × 53
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| | {{Citation needed}}
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| |-
| |
| | Pound
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| | [[1344edo|1344]]
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| | 2<sup>6</sup> × 3 × 7
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| | {{Citation needed}}
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| |-
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| | Neutron
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| | [[1392edo|1392]]
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| | 2<sup>4</sup> × 3 × 29
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| | {{Citation needed}}
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| |-
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| | Lesser muon
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| | [[1428edo|1428]]
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| | 2<sup>2</sup> × 3 × 7 × 17
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| | {{Citation needed}}
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| |-
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| | Decifarab
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| | [[1440edo|1440]]
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| | 2<sup>5</sup> × 3<sup>2</sup> × 5
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| | 1/10 of [[Farab]] unit<ref name="measure"/>.
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| |-
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| | Quadratic cent
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| | [[1452edo|1452]]
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| | 2<sup>2</sup> × 3 × 11<sup>2</sup>
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| | {{Citation needed}}
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| |-
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| | Ksion
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| | [[1476edo|1476]]
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| | 2<sup>2</sup> × 3<sup>2</sup> × 41
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| | {{Citation needed}}
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| |-
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| | Cubic cent
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| | [[1500edo|1500]]
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| | 2<sup>2</sup> × 3 × 5<sup>3</sup>
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| | {{Citation needed}}
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| |-
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| | Heptamu (7mu)
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| | [[1536edo|1536]]
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| | 2<sup>9</sup> × 3
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| | 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>
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| |-
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| | Rhoon
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| | [[1560edo|1560]]
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| | 2<sup>3</sup> × 3 × 5 × 13
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| | {{Citation needed}}
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| |-
| |
| | śata
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| | [[1600edo|1600]]
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| | 2<sup>6</sup> × 5<sup>2</sup>
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| | From Sanskrit ''śatam'': hundred; [[Relative cent]] of Armodue 16edo Theory{{Citation needed}}
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| |-
| |
| | Tile
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| | [[1632edo|1632]]
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| | 2<sup>5</sup> × 3 × 17
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| | {{Citation needed}}
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| |-
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| | [[Iota]]
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| | [[1700edo|1700]]
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| | 2<sup>2</sup> × 5<sup>2</sup> × 17
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| | [[Relative cent]] of [[17edo]]; proposed by [[Margo Schulter]] (2002) and [[George Secor]]<ref name="measure"/>.
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| |-
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| | [[Harmos]]
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| | [[1728edo|1728]]
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| | 2<sup>6</sup> × 3<sup>3</sup>
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| | 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>.
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| |-
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| | Hind śat / Indian cent
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| | 2200
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| | 2<sup>3</sup> × 11 × 5<sup>2</sup>
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| | {{Citation needed}}
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| |-
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| | [[Mina]]
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| | [[2460edo|2460]]
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| | 2<sup>2</sup> × 3 × 5 × 41
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| | 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>.
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| |-
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| | Centidiesis
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| | 3100
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| | 2<sup>2</sup> × 5<sup>2</sup> x 31
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| | {{Citation needed}}
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| |-
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| | Centiméride
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| | 4300
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| | 2<sup>2</sup> × 5<sup>2</sup> x 43
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| | {{Citation needed}}
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| |-
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| | [[Major tina]]
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| | [[8269edo|8269]]
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| | 8269 (prime)
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| | 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>.
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| |-
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| | [[Tina]]
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| | [[8539edo|8539]]
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| | 8539 (prime)
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| | 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>.
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| |-
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| | [[Purdal]]
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| | [[9900edo|9900]]
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| | 2<sup>2</sup> × 3<sup>2</sup> × 5<sup>2</sup> × 11
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| | [[Relative cent]] of [[99edo]]; Suggested by [[Osmiorisbendi]], advocated by [[Tútim Dennsuul Wafiil]]. See the dedicated page.
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| |-
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| | [[Türk sent]] / [[Turkish cent]]
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| | [[10600edo|10600]]
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| | 2<sup>3</sup> × 5<sup>2</sup> × 53
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| | [[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>.
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| |-
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| | [[Prima]]
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| | [[12276edo|12276]]
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| | 2<sup>2</sup> × 3<sup>2</sup> × 11 × 31
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| | Proposed by [[Erv Wilson]], [[Gene Ward Smith]] and [[Gavin Putland]]<ref name="measure"/>.
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| |-
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| | [[Jinn]]
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| | [[16808edo|16808]]
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| | 2<sup>3</sup> × 11 × 191
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| | See the dedicated page.
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| |-
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| | [[Jot]]
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| | [[30103edo|30103]]
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| | 30103 (prime)
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| | 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"/>.
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| |-
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| | [[Imp]]
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| | [[31920edo|31920]]
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| | 2<sup>4</sup> × 3 × 5 × 7 × 19
| |
| | <ref name="measure"/>
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| |-
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| | [[Flu]]
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| | [[46032edo|46032]]
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| | 2<sup>4</sup> × 3 × 7 × 137
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| | Proposed by Gene Ward Smith (2005)<ref name="measure"/><ref>[http://tonalsoft.com/enc/f/flu.aspx Tonalsoft | ''Flu'']</ref>.
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| |-
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| | [[Normal atom]]
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| | [[78005edo|78005]]
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| | 5 × 15601
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| | 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)
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| | [[196608edo|196608]]
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| | 2<sup>16</sup> × 3
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| | Fourteenth MIDI-resolution unit, 1/16384 (1/(2<sup>14</sup>)) of [[12edo]] semitone<ref name="measure"/>.
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| |}
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