Interval size measure: Difference between revisions

'''Interval size measure''' means the ''distance'' between pitches. Intervals can be measured logarithmically or by frequency ratios.

==Logarithmic==

===Gross===

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).

===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 closely related to 12 equal.

Other measures include the [[Armodue_theory|Eka]], [[16edo|1\16 octave]], [[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 Hi-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]] or deciFarab: [[1440edo|1\1440 octave]]; the [[Iota|Iota]]: [[1\1700_octave|1\1700 octave]]; the [[Harmos|Harmos]]: [[1728edo|1\1728octave]]; 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]

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.

 

 

Another notation for ratios is a vector of prime factor exponents, often called a [[monzo|monzo]], such as |-4 4 -1> (for the syntonic comma, 81/80 = 2^(-4) * 3^4 * 5^(-1)), which builds a bridge back to the logarithmic measure: intervals can be combined by component-wise addition or subtraction of their vectors.

[[Category:interval]]

[[Category:interval_size]]

[[Category:interval_size_measure]]

[[Category:measure]]

[[Category:proposal]]

[[Category:size]]

[[Category:theory]]

[[Category:todo:review]]