Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: The OMRAS2 Temperament Ontology Chris@0: Chris@0: Chris@0: Draft Revision: 1.0 Chris@0: Chris@0: Chris@0: Chris@0: This ontology can be used to give a detailed description Chris@0: of the tuning of an instrument. Chris@0: Chris@0: Chris@0: Chris@0: $Date: 2009/11/18 13:54:19 $ Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Temperament Chris@0: Chris@0: Chris@0: A temperament specifies a system of Chris@0: instrument tuning. Chris@0: Tempering is a way of altering the size of intervals, Chris@0: such that they no longer based on pure rational intervals. Chris@0: Chris@0: Chris@0: stable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Regular Temperament Chris@0: Chris@0: Chris@0: Regular temperament is a class of temperaments Chris@0: where each interval is altered by the same amount. Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Well Temperament Chris@0: Chris@0: Chris@0: Well temperament represents a system of tuning Chris@0: where 5ths are tempered by irregular amounts, such that some 5ths Chris@0: are tempered by an equal amount, while others remain pure. Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Meantone Temperament Chris@0: Chris@0: Chris@0: In a meantone temperament, each fifth is narrowed Chris@0: by the same amount relative to its width in Just Intonation. Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Restricted Temperament Chris@0: Chris@0: Chris@0: In restricted temperaments Chris@0: playing some keys results in poor intonation. Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Temperament Description Chris@0: Chris@0: Chris@0: Chris@0: A super class of temperament descriptions using, Chris@0: for example, deviation from equal temperament, Chris@0: or the circle of fifths. Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: temperament description Chris@0: Chris@0: Chris@0: Associates a temperament with its detailed description. Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: mathematical constraint Chris@0: Chris@0: Chris@0: A mathematical constrain on the temperament (This can be described in a named graph or and N3 graph literal). Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Comma Chris@0: Chris@0: Chris@0: A comma is a very small interval between Chris@0: two enharmonic notes tuned in different ways. (Source: Wikipedia) Chris@0: Chris@0: Chris@0: stable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Pitch Class Chris@0: Chris@0: Chris@0: The set of all pitches that are a Chris@0: whole number of octaves apart. Chris@0: Chris@0: Chris@0: stable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Interval Chris@0: Chris@0: Chris@0: Describes the relationship between the Chris@0: pitches of two notes or pitch classes. Chris@0: Chris@0: Chris@0: stable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Pitch Class Interval Chris@0: Chris@0: Chris@0: Describes the relationship between two pitch classes. Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Fifth Interval Chris@0: Chris@0: Chris@0: A fifth interval between notes, either Chris@0: pure or altered. In the case of a pure fifth it is a Chris@0: frequecy ratio of 3:2. We may use it to represent a Chris@0: specific interval on the circle of fifths, with a specific Chris@0: deviation from a pure fifth. Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Wolf Interval Chris@0: Chris@0: Chris@0: An interval which is regarded as howling may be Chris@0: called a wolf interval. It is typically a wolf fifth in Chris@0: meantone temperament. Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Deviations From Equal Chris@0: Chris@0: Chris@0: A type of temperament description which describes Chris@0: a tuning in terms of the deviation of each note (in cents) Chris@0: from the equal temperament. Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Circle Of Fifths Chris@0: Chris@0: Chris@0: We use the circle of fifth to describe a temperament. Chris@0: Each alteration of a fifth can be expressed in a number of ways, Chris@0: for example, we may express interval deviations in a particular Chris@0: comma. Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Interval Deviation (from pure interval) Chris@0: Chris@0: Chris@0: Represents any type of alteration of a pure interval. Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Pitch Class Deviation Chris@0: Chris@0: Chris@0: Deviation in cents of a pitch class from its value in equal temperament. Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Deviation from Fifth Chris@0: Chris@0: Chris@0: Represent the deviation from a pure fifth interval. Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: interval Chris@0: Chris@0: Chris@0: Associates a specific interval on the circle of fifths. Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: interval deviation Chris@0: Chris@0: Chris@0: Links an interval with a particular deviation Chris@0: from pure that characterises the interval. Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: pitch class deviation Chris@0: Chris@0: Chris@0: The deviation of a particular pitch class in the described Chris@0: temperament from its equivalent in equal temperament. Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: comma Chris@0: Chris@0: Chris@0: Links an interval deviation with a type of comma. Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: deviation value Chris@0: Chris@0: Chris@0: Links an interval deviation to its float value (in cents). Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: lower pitch class Chris@0: Chris@0: Chris@0: Links an interval a pitch calss which is lower on a scale. Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: upper pitch class Chris@0: Chris@0: Chris@0: Links an interval with a pitch class which is higher on a scale compared to the other pitch class of this interval. Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: pitch class Chris@0: Chris@0: Chris@0: The pitch class of a particular pitch class deviation. Chris@0: This can be used to express deviations from equal temperament. Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: frequency ratio Chris@0: Chris@0: Chris@0: The frequency ratio of the two pitch classes in the interval. Chris@0: This may be a single value or an expression (given for example in an N3 graph literal). Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: unstable Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Valotti Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Neidhardt Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Bendeler Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Stanhope Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: KirnbergerIII Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: YoungII Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: WerckmeisterIII Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: QuarterCommaMeantone Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: FifthCommaMeantone Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: SixthCommaMeantone Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Pythagorean Comma Chris@0: Chris@0: Chris@0: One Pythagorean Comma, the difference between Chris@0: 7 octaves and 12 pure fifths, is 23.5 cents. It is equivalent to the Ditonic comma. Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Ditonic Comma Chris@0: Chris@0: Chris@0: The Ditonic comma is equivalent to the Pythagorean comma. Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Syntonic Comma Chris@0: Chris@0: Chris@0: One Syntonic Comma is 21.51 cents. Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Didymus Comma Chris@0: Chris@0: Chris@0: The Didymus is equivalent to the Syntonic comma (21.51 cents). Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Diaschisma Chris@0: Chris@0: Chris@0: One Diaschisma is 19.55 cents. Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Schisma Chris@0: Chris@0: Chris@0: One Schisma is 1.95 cents. Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: A Chris@0: Chris@0: Chris@0: pitch class A Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: B Chris@0: Chris@0: Chris@0: pitch class B Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: C Chris@0: Chris@0: Chris@0: pitch class C Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: D Chris@0: Chris@0: Chris@0: pitch class D Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: E Chris@0: Chris@0: Chris@0: pitch class E Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: F Chris@0: Chris@0: Chris@0: pitch class F Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: G Chris@0: Chris@0: Chris@0: pitch class G Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Ab Chris@0: Chris@0: Chris@0: pitch class Ab Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Bb Chris@0: Chris@0: Chris@0: pitch class Bb Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Cb Chris@0: Chris@0: Chris@0: pitch class Cb Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Db Chris@0: Chris@0: Chris@0: pitch class Db Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Eb Chris@0: Chris@0: Chris@0: pitch class Eb Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Fb Chris@0: Chris@0: Chris@0: pitch class Fb Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Gb Chris@0: Chris@0: Chris@0: pitch class Gb Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: As Chris@0: Chris@0: Chris@0: pitch class As Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Bs Chris@0: Chris@0: Chris@0: pitch class Bs Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Cs Chris@0: Chris@0: Chris@0: pitch class Cs Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Ds Chris@0: Chris@0: Chris@0: pitch class Ds Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Es Chris@0: Chris@0: Chris@0: pitch class Es Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Fs Chris@0: Chris@0: Chris@0: pitch class Fs Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Gs Chris@0: Chris@0: Chris@0: pitch class Gs Chris@0: Chris@0: