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Interval size measure: Difference between revisions

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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<ref>[http://www.armodue.com/risorse.htm Armodue: le risorse di un nuovo sistema musicale]</ref>.  
| 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 shruti]]
| [[Normal shruti]]
| [[22edo|22]]
| [[22edo|22]]
| 2 × 11
| 2 × 11
| Proposed by [[User:Tristanbay|Tristan Bay]] in reference to the Indian tradition of dividing the octave into 22 unequal parts.
| Proposed by [[User:Tristanbay|Tristan Bay]] (2025) in reference to the Indian tradition of dividing the octave into 22 unequal parts.
|-
|-
| [[Normal diesis]]
| [[Normal diesis]]
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| 31 (prime)
| 31 (prime)
| See the dedicated page.  
| See the dedicated page.  
|-
| [[Dea]]
| [[41edo|41]]
| 41 (prime)
| Proposed by [[User:Tristanbay|Tristan Bay]] (2025) to reflect that a mina is a "minute" (1/60 the width) of a 1\41 "degree".
|-
|-
| [[Méride]]
| [[Méride]]
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| See the dedicated page.
| See the dedicated page.
|-
|-
| [[Holdrian comma|Mercator’s old comma]]
| [[Holdrian comma|Mercator's old comma]]
| [[55edo|55]]
| [[55edo|55]]
| 5 × 11
| 5 × 11
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| [[60edo|60]]
| [[60edo|60]]
| 2<sup>2</sup> × 3 × 5
| 2<sup>2</sup> × 3 × 5
|
| Standard SI prefix + 12edo tone
|-
|-
| [[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 name="measure"/><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]]
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| [[494edo|494]]
| [[494edo|494]]
| 2 × 13 × 19
| 2 × 13 × 19
| {{Citation needed}}
| Named after [[729/728]], the squbema, due to its similar size.
|-
|-
| Great [[iring]] / [[centitone]]
| [[Great iring]] / [[great centitone|centitone]]
| [[500edo|500]]
| [[500edo|500]]
| 2<sup>2</sup> × 5<sup>3</sup>
| 2<sup>2</sup> × 5<sup>3</sup>
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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 name="measure"/><ref>[http://www.tonalsoft.com/enc/c/centitone.aspx Tonalsoft | ''Centitone, iring'']</ref>.
| [[Relative cent]] of [[6edo]]; proposed by [[Widogast Iring]] (1898), later by [[Joseph Yasser]] as a "centitone", a standard SI prefix + 12edo tone (1932)<ref name="measure"/><ref>[http://www.tonalsoft.com/enc/c/centitone.aspx Tonalsoft | ''Centitone, iring'']</ref>.  
|-
|-
| [[Skisma]] (Sk)
| [[Nil]] / [[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 name="measure"/><ref>[http://tonalsoft.com/enc/s/sk.aspx Tonalsoft | ''Sk, 612-edo'']</ref>.  
| Proposed by [[James Paul White]] (1894) as ''nil'', and by Gene Ward Smith (2007) as ''skisma''<ref name="measure"/><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".  
|-
|-
| [[Delfi]]
| [[Delfi]]
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| <ref name="measure"/>
| <ref name="measure"/>
|-
|-
| Small [[iring]] / [[centitone]]
| [[Small iring]] / [[small centitone|centitone]]
| [[700edo|700]]
| [[700edo|700]]
| 2<sup>2</sup> × 5<sup>2</sup> x 7
| 2<sup>2</sup> × 5<sup>2</sup> x 7
| {{Citation needed}}
| {{Citation needed}}
|-
|-
| [[Woolhouse]]
| [[Woolhouse unit]]
| [[730edo|730]]
| [[730edo|730]]
| 2 × 5 × 73
| 2 × 5 × 73
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| See the dedicated page.  
| See the dedicated page.  
|-
|-
| Greater muon
| Dingle
| [[1224edo|1224]]
| [[1395edo|1395]]
| 2<sup>3</sup> × 3<sup>2</sup> × 17
| 3<sup>2</sup> × 5 × 31
| {{Citation needed}}
| Proposed by [[User:Tristanbay|Tristan Bay]] (2026) as a 31edo-friendly fine-grain measure, shortened from "'''di'''esis a'''ngle'''".
|-
| Triangular cent
| [[1260edo|1260]]
| 2<sup>2</sup> × 3<sup>2</sup> × 5 × 7
| {{Citation needed}}
|-
| Pion
| [[1272edo|1272]]
| 2<sup>3</sup> × 3 × 53
| {{Citation needed}}
|-
| Pound
| [[1344edo|1344]]
| 2<sup>6</sup> × 3 × 7
| {{Citation needed}}
|-
| Neutron
| [[1392edo|1392]]
| 2<sup>4</sup> × 3 × 29
| {{Citation needed}}
|-
| Lesser muon
| [[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
| 2<sup>5</sup> × 3<sup>2</sup> × 5
| 1/10 of [[Farab]] unit<ref name="measure"/>.  
| Standard SI prefix + [[farab]]<ref name="measure"/>.  
|-
| Quadratic cent
| [[1452edo|1452]]
| 2<sup>2</sup> × 3 × 11<sup>2</sup>
| {{Citation needed}}
|-
| Ksion
| [[1476edo|1476]]
| 2<sup>2</sup> × 3<sup>2</sup> × 41
| {{Citation needed}}
|-
| Cubic cent
| [[1500edo|1500]]
| 2<sup>2</sup> × 3 × 5<sup>3</sup>
| {{Citation needed}}
|-
|-
| Heptamu (7mu)
| Heptamu (7mu)
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| 2<sup>9</sup> × 3
| 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>
| 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
| [[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>  
| 2<sup>6</sup> × 5<sup>2</sup>  
| From Sanskrit ''śatam'': hundred; [[Relative cent]] of Armodue 16edo Theory{{Citation needed}}
| From Sanskrit ''śatam'': hundred; [[relative cent]] of Armodue 16edo theory{{Citation needed}}
|-
| Tile
| [[1632edo|1632]]
| 2<sup>5</sup> × 3 × 17
| {{Citation needed}}
|-
|-
| [[Iota]]
| [[Iota]]
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| 2<sup>2</sup> × 5<sup>2</sup> x 43
| 2<sup>2</sup> × 5<sup>2</sup> x 43
| {{Citation needed}}
| {{Citation needed}}
|-
| [[4320edo|Click]]
| [[4320edo|4320]]
| 2<sup>5</sup> × 3<sup>3</sup> × 5
| Proposed by [[User:Eliora|Eliora]]. See the dedicated page.
|-
|-
| [[Major tina]]
| [[Major tina]]
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| [[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]]. See the dedicated page.  
| [[Relative cent]] of [[99edo]]; suggested by [[Osmiorisbendi]], advocated by [[Tútim Dennsuul Wafiil]]. See the dedicated page.  
|-
|-
| [[Türk sent]] / [[Turkish cent]]
| [[Türk sent]] / [[Turkish cent]]
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| [[30103edo|30103]]
| [[30103edo|30103]]
| 30103 (prime)
| 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"/>.  
| 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]]
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| [[78005edo|78005]]
| [[78005edo|78005]]
| 5 × 15601
| 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}}
| Proposed by Tristan Bay (2023); 78005edo consistently maps Kirnberger's atom to 1 edostep and is a very strong 5-limit system.
|-
|-
| [[MIDI Tuning Standard unit]] (14mu)
| [[MIDI Tuning Standard unit]] (14mu)
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| Euhekt
| Euhekt
| 3/1 (twelfth)
| 3/1 (twelfth)
| 1900
| 3900
| 1/100 of 19edt (OnlyPure) scale step
| 1/100 of 39edt (Triboh) scale step
|-
|-
| Grad
| Grad
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=== Relative measures ===
=== Relative measures ===
Within a given [[Equal-step tuning|equal-stepped]] tonal system, the [[relative cent]] (rct, r¢) can be used to describe properties of pitches (for instance the approximation of [[Just intonation|JI]] intervals). It is defined as on 100th (or 1 percent) of the interval between two neighbouring pitches in the used equal tuning.
Within a given [[equal-step tuning|equal-stepped tuning system]], the [[relative cent]] (rct, r¢) can be used to describe properties of pitches (for instance the approximation of [[Just intonation|JI]] intervals). It is defined as on 100th (or 1 percent) of the interval between two neighbouring pitches in the used equal tuning.


== Ratio ==
== Ratio ==
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