Interval size measure: Difference between revisions

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For "atonal" music it was replaced by the number of 12edo-semitones.

Proposal: The '''relative interval measure''' is the number of steps between two pitches of an [[Equal|equal]] tuning, sometimes called [[Degree|degree]]s (of an edo). For generators, the backslash notation is used d\edo, but it is also a ratio (of a logarithmic measure).

Proposal: The '''relative interval measure''' is the number of steps between two pitches of an [[Equal temperament|equal]] tuning, sometimes called [[Degree|degree]]s (of an edo). For generators, the backslash notation is used d\edo, but it is also a ratio (of a logarithmic measure).

===Fine===

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]] (¢), [[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]]: [[43edo|1\43 octave]]; the [[Holdrian_comma|Holdrian comma]]: [[53edo|1\53 octave]]; the [[Morion]]: [[72edo|1\72 octave]]; the [[Farab]]: [[144edo|1\144 octave]]; the [[Mem]]: [[205edo|1\205 octave]] (used by [http://www.h-pi.com/theory/measurement3.html H-pi Instruments]); the [[Tredek]]: [[270edo|1\270 octave]]; the [[Eptaméride]] or [[Savart]]: [[301edo|1\301 of an octave]]; the [[Gene]]: [[311edo|1\311 octave]]; the [[Dröbisch_Angle|Dröbisch Angle]]: [[360edo|1\360 octave]]; the [[Squb]]: [[494edo|1\494 octave]]; the [[Iring]]: [[600edo|1\600 octave]]; the [[Skisma]]: [[612edo|1\612 octave]]; the [[Delfi]]: [[665edo|1\665 octave]]; the [[Woolhouse]]: [[730edo|1\730 octave]]; the [[millioctave]] (mO), [[1000edo|1\1000 octave]]; the [[fine_cent|fine cent]]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]]: [[1\1700_octave|1\1700 octave]] and finally the [[Harmos]]: [[1728edo|1\1728 octave]]); the [[Mina]]: [[2460edo|1\2460 octave]]; the [[Tina]]: [[8539edo|1\8539 octave]]; the [[Purdal]]: [[9900edo|1\9900 octave]]; the [[Türk_sent|Türk sent]]: [[10600edo|1\10600 octave]]; the [[Prima]]: [[12276edo|1\12276 octave]], the [[Jinn]]: [[16808edo|1\16808 octave]], the [[Jot]]: [[30103edo|1\30103 octave]]; the [[Imp]]: [[31920edo|1\31920 octave]]; the [[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]]: 1/12 of a Pythagorean comma, the [[Tuning unit]]: 1/720 of a Pythagorean comma and the [[Hekt]]: 1/1300 part of 3, ie 3^(1/1300).

See [http://www.huygens-fokker.org/docs/measures.html Logarithmic Interval Measures]

Within a given [[Equal|equal]]-stepped tonal system, the [[Relative_cent|relative cent]] (rct, r¢) can be used to describe properties of pitches (for instance the approximation of [[JI|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 temperament|equal]]-stepped tonal system, the [[Relative_cent|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.

see also: Kirnberger Atom http://arxiv.org/abs/0907.5249

@@ Line 9: / Line 9: @@
 For "atonal" music it was replaced by the number of 12edo-semitones.
-Proposal: The '''relative interval measure''' is the number of steps between two pitches of an [[Equal|equal]] tuning, sometimes called [[Degree|degree]]s (of an edo). For generators, the backslash notation is used d\edo, but it is also a ratio (of a logarithmic measure).
+Proposal: The '''relative interval measure''' is the number of steps between two pitches of an [[Equal temperament|equal]] tuning, sometimes called [[Degree|degree]]s (of an edo). For generators, the backslash notation is used d\edo, but it is also a ratio (of a logarithmic measure).
 ===Fine===
-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]] (¢), [[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]]: [[43edo|1\43 octave]]; the [[Holdrian_comma|Holdrian comma]]: [[53edo|1\53 octave]]; the [[Morion]]: [[72edo|1\72 octave]]; the [[Farab]]: [[144edo|1\144 octave]]; the [[Mem]]: [[205edo|1\205 octave]] (used by [http://www.h-pi.com/theory/measurement3.html H-pi Instruments]); the [[Tredek]]: [[270edo|1\270 octave]]; the [[Eptaméride]] or [[Savart]]: [[301edo|1\301 of an octave]]; the [[Gene]]: [[311edo|1\311 octave]]; the [[Dröbisch_Angle|Dröbisch Angle]]: [[360edo|1\360 octave]]; the [[Squb]]: [[494edo|1\494 octave]]; the [[Iring]]: [[600edo|1\600 octave]]; the [[Skisma]]: [[612edo|1\612 octave]]; the [[Delfi]]: [[665edo|1\665 octave]]; the [[Woolhouse]]: [[730edo|1\730 octave]]; the [[millioctave]] (mO), [[1000edo|1\1000 octave]]; the [[fine_cent|fine cent]]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]]: [[1\1700_octave|1\1700 octave]] and finally the [[Harmos]]: [[1728edo|1\1728 octave]]); the [[Mina]]: [[2460edo|1\2460 octave]]; the [[Tina]]: [[8539edo|1\8539 octave]]; the [[Purdal]]: [[9900edo|1\9900 octave]]; the [[Türk_sent|Türk sent]]: [[10600edo|1\10600 octave]]; the [[Prima]]: [[12276edo|1\12276 octave]], the [[Jinn]]: [[16808edo|1\16808 octave]], the [[Jot]]: [[30103edo|1\30103 octave]]; the [[Imp]]: [[31920edo|1\31920 octave]]; the [[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]]: 1/12 of a Pythagorean comma, the [[Tuning unit]]: 1/720 of a Pythagorean comma and the [[Hekt]]: 1/1300 part of 3, ie 3^(1/1300).
 See [http://www.huygens-fokker.org/docs/measures.html Logarithmic Interval Measures]
-Within a given [[Equal|equal]]-stepped tonal system, the [[Relative_cent|relative cent]] (rct, r¢) can be used to describe properties of pitches (for instance the approximation of [[JI|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 temperament|equal]]-stepped tonal system, the [[Relative_cent|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.
 see also: Kirnberger Atom http://arxiv.org/abs/0907.5249