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Interval size measure: Difference between revisions

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Dw0391 (talk | contribs)
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m Sorry, this time I actually did remember to change "List of Non-Octave Fine Measures (Logarithmic)" table as indicated in the previous edit summary - mea culpa
Dw0391 (talk | contribs)
26 edits
Added "Prime Factors" column to table "List of Octave-Based Fine Measures (Logarithmic)"; populated column
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!Unit name (symbol):
!Unit name (symbol):
!Divisions of Octave
!Divisions of Octave
!Prime Factors
!Origin / Significance
!Origin / Significance
|-
|-
|[[Armodue_theory|Eka]]
|[[Armodue_theory|Eka]]
|[[16edo|16]]
|[[16edo|16]]
|2<sup>4</sup>
|From Sanskrit ''eka'': one, unit; chromatic unit of Armodue 16ED2 Theory
|From Sanskrit ''eka'': one, unit; chromatic unit of Armodue 16ED2 Theory
|-
|-
|[[Normal_diesis|Normal diesis]]
|[[Normal_diesis|Normal diesis]]
|[[31edo|31]]
|[[31edo|31]]
|PRIME
|
|
|-
|-
|[[Méride]]
|[[Méride]]
|[[43edo|43]]
|[[43edo|43]]
|PRIME
|Proposed by Joseph Sauveur as 7 heptaméride units
|Proposed by Joseph Sauveur as 7 heptaméride units
|-
|-
|[[Holdrian_comma|Holdrian comma]]
|[[Holdrian_comma|Holdrian comma]]
|[[53edo|53]]
|[[53edo|53]]
|PRIME
|
|
|-
|-
|[[Morion]]
|[[Morion]]
|[[72edo|72]]
|[[72edo|72]]
|2<sup>3</sup> × 3<sup>2</sup>
|
|
|-
|-
|[[Farab]]
|[[Farab]]
|[[144edo|144]]
|[[144edo|144]]
|2<sup>4</sup> × 3<sup>2</sup>
|Proposed by al-Farabi in 10th century; 1/12 of [[12edo|12ED2]] semitone
|Proposed by al-Farabi in 10th century; 1/12 of [[12edo|12ED2]] semitone
|-
|-
|[[Mem]]
|[[Mem]]
|[[205edo|205]]
|[[205edo|205]]
|5 × 41
|Unit used by [http://musictheory.zentral.zone/huntsystem1.html H-Pi Instruments]
|Unit used by [http://musictheory.zentral.zone/huntsystem1.html H-Pi Instruments]
|-
|-
|[[Tredek]]
|[[Tredek]]
|[[270edo|270]]
|[[270edo|270]]
|2 × 3<sup>3</sup> × 5
|
|
|-
|-
|[[Eptaméride|Heptaméride/Eptaméride]] or [[Savart]]
|[[Eptaméride|Heptaméride/Eptaméride]] or [[Savart]]
|[[301edo|301]]
|[[301edo|301]]
|7 × 43
|Proposed by Joseph Sauveur, advocated by Félix Savart; 301 ≃ 1,000 * log<sub>10</sub>2; 1/7 of Méride unit
|Proposed by Joseph Sauveur, advocated by Félix Savart; 301 ≃ 1,000 * log<sub>10</sub>2; 1/7 of Méride unit
|-
|-
|[[Gene]]
|[[Gene]]
|[[311edo|311]]
|[[311edo|311]]
|PRIME
|
|
|-
|-
|[[Dröbisch_Angle|Dröbisch Angle]]
|[[Dröbisch_Angle|Dröbisch Angle]]
|[[360edo|360]]
|[[360edo|360]]
|2<sup>3</sup> × 3<sup>2</sup> × 5
|
|
|-
|-
|[[Squb]]
|[[Squb]]
|[[494edo|494]]
|[[494edo|494]]
|2 × 13 × 19
|
|
|-
|-
|[[Iring]]
|[[Iring]]
|[[600edo|600]]
|[[600edo|600]]
|2<sup>3</sup> × 3 × 5<sup>2</sup>
|
|
|-
|-
|[[Skisma]]
|[[Skisma]]
|[[612edo|612]]
|[[612edo|612]]
|2<sup>2</sup> × 3<sup>2</sup> × 17
|
|
|-
|-
|[[Delfi]]
|[[Delfi]]
|[[665edo|665]]
|[[665edo|665]]
|5 × 7 × 19
|
|
|-
|-
|[[Woolhouse]]
|[[Woolhouse]]
|[[730edo|730]]
|[[730edo|730]]
|2 × 5 × 73
|Proposed by Wesley S.B. Woolhouse in ''Essay on musical intervals'' (1835)
|Proposed by Wesley S.B. Woolhouse in ''Essay on musical intervals'' (1835)
|-
|-
|[[millioctave]] (mO)
|[[millioctave]] (mO)
|[[1000edo|1000]]
|[[1000edo|1000]]
|2<sup>3</sup> × 5<sup>3</sup>
|[https://en.wikipedia.org/wiki/Metric_prefix SI-prefix] division of octave
|[https://en.wikipedia.org/wiki/Metric_prefix SI-prefix] division of octave
|-
|-
|[[cent]] (¢)
|[[cent]] (¢)
|1200
|1200
|2<sup>4</sup> × 3 × 5<sup>2</sup>
|1/100 of [[12edo|12ED2]] semitone
|1/100 of [[12edo|12ED2]] semitone
|-
|-
|greater muon
|greater muon
|[[1224edo|1224]]
|[[1224edo|1224]]
|2<sup>3</sup> × 3<sup>2</sup> × 17
|
|
|-
|-
|triangular cent
|triangular cent
|[[1260edo|1260]]
|[[1260edo|1260]]
|2<sup>2</sup> × 3<sup>2</sup> × 5 × 7
|
|
|-
|-
|pion
|pion
|[[1272edo|1272]]
|[[1272edo|1272]]
|2<sup>3</sup> × 3 × 53
|
|
|-
|-
|pound
|pound
|[[1344edo|1344]]
|[[1344edo|1344]]
|2<sup>6</sup> × 3 × 7
|
|
|-
|-
|neutron
|neutron
|[[1392edo|1392]]
|[[1392edo|1392]]
|2<sup>4</sup> × 3 × 29
|
|
|-
|-
|lesser muon
|lesser muon
|[[1428edo|1428]]
|[[1428edo|1428]]
|2<sup>2</sup> × 3 × 7 × 17
|
|
|-
|-
|deciFarab
|deciFarab
|[[1440edo|1440]]
|[[1440edo|1440]]
|2<sup>5</sup> × 3<sup>2</sup> × 5
|1/10 of Farab unit
|1/10 of Farab unit
|-
|-
|quadratic cent
|quadratic cent
|[[1452edo|1452]]
|[[1452edo|1452]]
|2<sup>2</sup> × 3 × 11<sup>2</sup>
|
|
|-
|-
|ksion
|ksion
|[[1476edo|1476]]
|[[1476edo|1476]]
|2<sup>2</sup> × 3<sup>2</sup> × 41
|
|
|-
|-
|cubic cent
|cubic cent
|[[1500edo|1500]]
|[[1500edo|1500]]
|2<sup>2</sup> × 3 × 5<sup>3</sup>
|
|
|-
|-
|7mu
|7mu
|[[1536edo|1536]]
|[[1536edo|1536]]
|2<sup>9</sup> × 3
|(7th MIDI unit), seventh MIDI-resolution unit, 1/128 (1/(2<sup>7</sup>)) of [[12edo|12ED2]] semitone
|(7th MIDI unit), seventh MIDI-resolution unit, 1/128 (1/(2<sup>7</sup>)) of [[12edo|12ED2]] semitone
|-
|-
|rhoon
|rhoon
|[[1560edo|1560]]
|[[1560edo|1560]]
|2<sup>3</sup> × 3 × 5 × 13
|
|
|-
|-
|tile
|tile
|[[1632edo|1632]]
|[[1632edo|1632]]
|2<sup>5</sup> × 3 × 17
|
|
|-
|-
|[[Iota]]
|[[Iota]]
|[[1\1700_octave|1700]]
|[[1\1700_octave|1700]]
|2<sup>2</sup> × 5<sup>2</sup> × 17
|
|
|-
|-
|[[Harmos]]
|[[Harmos]]
|[[1728edo|1728]]
|[[1728edo|1728]]
|2<sup>6</sup> × 3<sup>3</sup>
|Proposed by Paul Beaver; 1728 = 12<sup>3</sup>; 1/144 of [[12edo|12ED2]] semitone
|Proposed by Paul Beaver; 1728 = 12<sup>3</sup>; 1/144 of [[12edo|12ED2]] semitone
|-
|-
|[[Mina]]
|[[Mina]]
|[[2460edo|2460]]
|[[2460edo|2460]]
|2<sup>2</sup> × 3 × 5 × 41
|Abbreviation of "schismina", ED2 representation of the "Olympian Level" of [[Sagittal_notation|Sagittal notation system]]
|Abbreviation of "schismina", ED2 representation of the "Olympian Level" of [[Sagittal_notation|Sagittal notation system]]
|-
|-
|[[Tina]]
|[[Tina]]
|[[8539edo|8539]]
|[[8539edo|8539]]
|Prime; provides good approximations for 41-limit primes except 37; named by [[Dave_Keenan|Keenan]] and [[George_Secor|Secor]]
|PRIME
|Provides good approximations for 41-limit primes except 37; named by [[Dave_Keenan|Keenan]] and [[George_Secor|Secor]]
|-
|-
|[[Purdal]]
|[[Purdal]]
|[[9900edo|9900]]
|[[9900edo|9900]]
|2<sup>2</sup> × 3<sup>2</sup> × 5<sup>2</sup> × 11
|
|
|-
|-
|[[Türk_sent|Türk sent]]
|[[Türk_sent|Türk sent]]
|[[10600edo|10600]]
|[[10600edo|10600]]
|2<sup>3</sup> × 5<sup>2</sup> × 53
|
|
|-
|-
|[[Prima]]
|[[Prima]]
|[[12276edo|12276]]
|[[12276edo|12276]]
|2<sup>2</sup> × 3<sup>2</sup> × 11 × 31
|
|
|-
|-
|[[Jinn]]
|[[Jinn]]
|[[16808edo|16808]]
|[[16808edo|16808]]
|2<sup>3</sup> × 11 × 191
|
|
|-
|-
|[[Jot]]
|[[Jot]]
|[[30103edo|30103]]
|[[30103edo|30103]]
|PRIME
|
|
|-
|-
|[[Imp]]
|[[Imp]]
|[[31920edo|31920]]
|[[31920edo|31920]]
|2<sup>4</sup> × 3 × 5 × 7 × 19
|
|
|-
|-
|[[Flu]]
|[[Flu]]
|[[46032edo|46032]]
|[[46032edo|46032]]
|2<sup>4</sup> × 3 × 7 × 137
|
|
|-
|-
|[[MIDI_Tuning_Standard_unit|MIDI Tuning Standard unit]]
|[[MIDI_Tuning_Standard_unit|MIDI Tuning Standard unit]]
|[[196608edo|196608]]
|[[196608edo|196608]]
|2<sup>16</sup> × 3
|14mu (14th MIDI unit), fourteenth MIDI-resolution unit, 1/16384 (1/(2<sup>14</sup>)) of [[12edo|12ED2]] semitone
|14mu (14th MIDI unit), fourteenth MIDI-resolution unit, 1/16384 (1/(2<sup>14</sup>)) of [[12edo|12ED2]] semitone
|}
|}
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