Interval size measure: Difference between revisions
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The [[cent|cent]] (¢), [[1200edo|1\1200 octave]], is the classic measure for intervals when more precision than 12edo is required. Some people object to it on the grounds that it is too (obviously) closely related to 12 equal. | The [[cent|cent]] (¢), [[1200edo|1\1200 octave]], is the classic measure for intervals when more precision than 12edo is required. Some people object to it on the grounds that it is too (obviously) closely related to 12 equal. | ||
Other measures include the [[Armodue_theory|Eka]], [[16edo|1\16 octave]], the [[Normal_diesis|Normal diesis]]: [[31edo|1\31 octave]]; the [[Méride|Méride]]: [[43edo|1\43 octave]]; the [[Holdrian_comma|Holdrian comma]]: [[53edo|1\53 octave]]; the [[Morion|Morion]]: [[72edo|1\72 octave]]; the [[Farab|Farab]]: [[144edo|1\144 octave]]; the [[Mem|Mem]]: [[205edo|1\205 octave]] (used by [http://www.h-pi.com/theory/measurement3.html H-pi Instruments]); the [[Tredek|Tredek]]: [[270edo|1\270 octave]]; the [[Eptaméride|Eptaméride]] or [[Savart|Savart]]: [[301edo|1\301 of an octave]]; the [[Gene|Gene]]: [[31edo|1\311 octave]]; the [[Dröbisch_Angle|Dröbisch Angle]]: [[360edo|1\360 octave]]; the [[Squb|Squb]]: [[494edo|1\494 octave]]; the [[Iring|Iring]]: [[600edo|1\600 octave]]; the [[Skisma|Skisma]]: [[612edo|1\612 octave]]; the [[Delfi|Delfi]]: [[665edo|1\665 octave]]; the [[Woolhouse|Woolhouse]]: [[730edo|1\730 octave]]; the [[millioctave|millioctave]] (mO), [[1000edo|1\1000 octave]]; the [[fine_cent|fine cent]]<nowiki/>s and fine cent-like units from [[1201edo|1\1201 octave]] down to [[1728edo|1\1728 octave]] (including the greater and lesser muons: [[1224edo|1\1224 octave]] and [[1428edo|1\1428 octave]]; the triangular, quadratic and cubic cents: [[1260edo|1\1260 octave]], [[1452edo|1\1452 octave]] and [[1500edo|1\1500 octave]]; the pion: [[1272edo|1\1272 octave]]; the pound: [[1344edo|1\1344 octave]]; the neutron: [[1392edo|1\1392 octave]]; the deciFarab: [[1440edo|1\1440 octave]]; the ksion: [[1476edo|1\1476 octave]]; the 7mu: [[1536edo|1\1536 octave]]; the rhoon: [[1560edo|1\1560 octave]]; the tile: [[1632edo|1\1632 octave]]; the [[Iota|Iota]]: [[1\1700_octave|1\1700 octave]] and finally the [[Harmos|Harmos]]: [[1728edo|1\1728 octave]]; the [[mina|Mina]]: [[2460edo|1\2460 octave]]; the [[Tina|Tina]]: [[8539edo|1\8539 octave]]; the [[Purdal|Purdal]]: [[9900edo|1\9900 octave]]; the [[Türk_sent|Türk sent]]: [[10600edo|1\10600 octave]]; the [[Prima|Prima]]: [[12276edo|1\12276 octave]], the [[jinn|Jinn]]: [[16808edo|1\16808 octave]], the [[Jot|Jot]]: [[30103edo|1\30103 octave]]; the [[Imp|Imp]]: [[31920edo|1\31920 octave]]; the [[Flu|Flu]]: [[46032edo|1\46032 octave]]; and the [[MIDI_Tuning_Standard_unit|MIDI Tuning Standard unit]]: [[196608edo|1\196608 octave]]. Not based on the octave are the [[Grad|Grad]]: 1/12 of a Pythagorean comma and the [[Hekt|Hekt]]: 1/1300 part of 3, ie 3^(1/1300). | Other measures include the [[Armodue_theory|Eka]], [[16edo|1\16 octave]], the [[Normal_diesis|Normal diesis]]: [[31edo|1\31 octave]]; the [[Méride|Méride]]: [[43edo|1\43 octave]]; the [[Holdrian_comma|Holdrian comma]]: [[53edo|1\53 octave]]; the [[Morion|Morion]]: [[72edo|1\72 octave]]; the [[Farab|Farab]]: [[144edo|1\144 octave]]; the [[Mem|Mem]]: [[205edo|1\205 octave]] (used by [http://www.h-pi.com/theory/measurement3.html H-pi Instruments]); the [[Tredek|Tredek]]: [[270edo|1\270 octave]]; the [[Eptaméride|Eptaméride]] or [[Savart|Savart]]: [[301edo|1\301 of an octave]]; the [[Gene|Gene]]: [[31edo|1\311 octave]]; the [[Dröbisch_Angle|Dröbisch Angle]]: [[360edo|1\360 octave]]; the [[Squb|Squb]]: [[494edo|1\494 octave]]; the [[Iring|Iring]]: [[600edo|1\600 octave]]; the [[Skisma|Skisma]]: [[612edo|1\612 octave]]; the [[Delfi|Delfi]]: [[665edo|1\665 octave]]; the [[Woolhouse|Woolhouse]]: [[730edo|1\730 octave]]; the [[millioctave|millioctave]] (mO), [[1000edo|1\1000 octave]]; the [[fine_cent|fine cent]]<nowiki/>s and fine cent-like units from [[1201edo|1\1201 octave]] down to [[1728edo|1\1728 octave]] (including the greater and lesser muons: [[1224edo|1\1224 octave]] and [[1428edo|1\1428 octave]]; the triangular, quadratic and cubic cents: [[1260edo|1\1260 octave]], [[1452edo|1\1452 octave]] and [[1500edo|1\1500 octave]]; the pion: [[1272edo|1\1272 octave]]; the pound: [[1344edo|1\1344 octave]]; the neutron: [[1392edo|1\1392 octave]]; the deciFarab: [[1440edo|1\1440 octave]]; the ksion: [[1476edo|1\1476 octave]]; the 7mu: [[1536edo|1\1536 octave]]; the rhoon: [[1560edo|1\1560 octave]]; the tile: [[1632edo|1\1632 octave]]; the [[Iota|Iota]]: [[1\1700_octave|1\1700 octave]] and finally the [[Harmos|Harmos]]: [[1728edo|1\1728 octave]]); the [[mina|Mina]]: [[2460edo|1\2460 octave]]; the [[Tina|Tina]]: [[8539edo|1\8539 octave]]; the [[Purdal|Purdal]]: [[9900edo|1\9900 octave]]; the [[Türk_sent|Türk sent]]: [[10600edo|1\10600 octave]]; the [[Prima|Prima]]: [[12276edo|1\12276 octave]], the [[jinn|Jinn]]: [[16808edo|1\16808 octave]], the [[Jot|Jot]]: [[30103edo|1\30103 octave]]; the [[Imp|Imp]]: [[31920edo|1\31920 octave]]; the [[Flu|Flu]]: [[46032edo|1\46032 octave]]; and the [[MIDI_Tuning_Standard_unit|MIDI Tuning Standard unit]]: [[196608edo|1\196608 octave]]. Not based on the octave are the [[Grad|Grad]]: 1/12 of a Pythagorean comma and the [[Hekt|Hekt]]: 1/1300 part of 3, ie 3^(1/1300). | ||
See [http://www.huygens-fokker.org/docs/measures.html Logarithmic Interval Measures] | See [http://www.huygens-fokker.org/docs/measures.html Logarithmic Interval Measures] | ||