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The temperament ontology can be used to give a detailed description of the tuning of an instrument. It is developed in the OMRAS2 project, and intended to be used in conjunction with the Music Ontology, for example, when describing the tuning that was used in a particular harpsichord recording.
This is a work in progress! This document is changing on a daily if not hourly basis. Comments are very welcome, please send them to gyorgy.fazekas@elec.qmul.ac.uk. Thank you.
The temperament ontology aims to describe instrument tuning systems and their particularities.
It may also be used to characterise a (potentially unknown) temperament that was used when tuning an
instrument for a particular performance or recording.
At this stage the ontology is far from exhaustive. We primarily deal with
temperaments in western tonal music with an emphasis on tuning keyboard instruments.
One important objective is to be able to describe arbitrary temperaments,
or express the results of automatic temperament extraction from audio recordings.
Tuning an instrument consists of choosing the frequency values and spacing (or ratio) of pitches that are used. Pure (just) intervals of pitches correspond to whole number ratios of their frequencies, however these ratios are not compatible with each other as they arranged in scales (the way octaves are divided into discrete pitch classes) in western music. For example, it is not possible to fit twelve pure fifths (3:2)^12 into seven octaves (2:1)^7. The difference is called the Pythagorean or Ditonic comma (23.5 cents). This difference has to be tempered out ---that is, some (or all) fifths has to be mistuned slightly in order to fit them. There are many tuning systems. Most commonly, they differ in the way they compromise pure intervals to solve this problem.
There is no mutual agreement in the literature on the description or classification of temperaments. Therefore, in this ontology we do not impose a hierarchy between types of temperaments. We define an opaque top-level temperament concept. Subclasses of this concept can be used in describing individual temperaments, if necessary, using multiple class memberships. Since there is more than one way to associate tuning systems with their properties, we treat temperament descriptions as concepts as well, and use reification to keep the model open and extensible.
Temperaments can be characterised in lots of different ways. The most common methods are using either the circle of fifths or give the pitch deviations from equal temperament. We define these descriptions as concepts in the ontology, however, other descriptions may be used and defined in the future. (For example, one might find it convenient to express the same information using the circle of fourths.)
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In equal temperament an octave is divided into twelve equal intervals. As a result only octaves are pure. All other intervals are impure, and the deviation from pure is different in case of each interval. Since equal temperament has become very common, other temperaments are often described by the frequency deviations (in cents) of each pitch class from the corresponding pitch class in equal temperament.
An alphabetical index of Temperament terms, by class (concepts) and by property (relationships, attributes), are given below. All the terms are hyperlinked to their detailed description for quick reference.
Classes: CircleOfFifths, Comma, DeviationFromFifth, DeviationsFromEqual, Interval, IntervalDeviation, MeantoneTemperament, PitchClass, PitchClassDeviation, PitchClassInterval, RegularTemperament, RestrictedTemperament, Temperament, TemperamentDescription, WellTemperament,
Properties: comma, constraint, description, deviation, frequency_ratio, interval, lower, pitch_class, pitch_class_deviation, upper, value,
Instances: A, Ab, As, B, Bb, Bendeler, Bs, C, Cb, Cs, D, Db, Diaschisma, DidymusComma, DitonicComma, Ds, E, Eb, Es, F, Fb, FifthCommaMeantone, Fs, G, Gb, Gs, KirnbergerIII, Neidhardt, PythagoreanComma, QuarterCommaMeantone, Schisma, SixthCommaMeantone, Stanhope, SyntonicComma, Valotti, WerckmeisterIII, YoungII,
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Here is a very basic example describing a pitch class interval in the Valotti temperament using the circle of fifths.
@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>. @prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#>. @prefix xsd: <http://www.w3.org/2001/XMLSchema#> . @prefix tm: <http://purl.org/ontology/temperament/> . @prefix pc: <http://purl.org/ontology/temperament/pitchclass/> . :ValottiTemperament a tm:WellTemperament; tm:description :ValottiDescription1 . :ValottiDescription1 a tm:CircleOfFifths; tm:interval [ a tm:FifthInterval ; tm:deviation [ a tm:IntervalDeviation ; tm:comma tm:PythagoreanComma ; tm:value "-0.16667"^^xsd:float ; rdfs:label "-1/6" ] ; tm:lower pc:C ; tm:upper pc:G ] ; tm:interval [ # the rest of the intervals on the circle of fifths ] .
A graphical representation of a similar description is shown in figure 2. We explicitly name the pitch classes involved in each interval on the circle of fifths. The IntervalDeviation concept describes the amount of deviation from a pure interval in terms of a specific type of comma and a corresponding value (a fraction of that comma). We can safely assume that a fifth is pure, unless the deviation is given.
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URI: http://purl.org/ontology/temperament/CircleOfFifths
Circle Of Fifths - We use the circle of fifth to describe a temperament. Each alteration of a fifth can be expressed in a number of ways, for example, we may express interval deviations in a particular comma.
URI: http://purl.org/ontology/temperament/Comma
Comma - A comma is a very small interval between two enharmonic notes tuned in different ways. (Source: Wikipedia)
URI: http://purl.org/ontology/temperament/DeviationFromFifth
Deviation from Fifth - Represent the deviation from a pure fifth interval.
URI: http://purl.org/ontology/temperament/DeviationsFromEqual
Deviations From Equal - A type of temperament description which describes a tuning in terms of the deviation of each note (in cents) from the equal temperament.
URI: http://purl.org/ontology/temperament/Interval
Interval - Describes the relationship between the pitches of two notes or pitch classes.
URI: http://purl.org/ontology/temperament/IntervalDeviation
Interval Deviation (from pure interval) - Represents any type of alteration of a pure interval.
URI: http://purl.org/ontology/temperament/MeantoneTemperament
Meantone Temperament - In a meantone temperament, each fifth is narrowed by the same amount relative to its width in Just Intonation.
URI: http://purl.org/ontology/temperament/PitchClass
Pitch Class - The set of all pitches that are a whole number of octaves apart.
URI: http://purl.org/ontology/temperament/PitchClassDeviation
Pitch Class Deviation - Deviation in cents of a pitch class from its value in equal temperament.
URI: http://purl.org/ontology/temperament/PitchClassInterval
Pitch Class Interval - Describes the relationship between two pitch classes.
URI: http://purl.org/ontology/temperament/RegularTemperament
Regular Temperament - Regular temperament is a class of temperaments where each interval is altered by the same amount.
URI: http://purl.org/ontology/temperament/RestrictedTemperament
Restricted Temperament - In restricted temperaments playing some keys results in poor intonation.
URI: http://purl.org/ontology/temperament/Temperament
Temperament - A temperament specifies a system of instrument tuning. Tempering is a way of altering the size of intervals, such that they no longer based on pure rational intervals.
URI: http://purl.org/ontology/temperament/TemperamentDescription
Temperament Description - A super class of temperament descriptions using, for example, deviation from equal temperament, or the circle of fifths.
URI: http://purl.org/ontology/temperament/WellTemperament
Well Temperament - Well temperament represents a system of tuning where 5ths are tempered by irregular amounts, such that some 5ths are tempered by an equal amount, while others remain pure.
URI: http://purl.org/ontology/temperament/comma
comma - Links an interval deviation with a type of comma.
URI: http://purl.org/ontology/temperament/constraint
mathematical constraint - A mathematical constrain on the temperament (This can be described in a named graph or and N3 graph literal).
URI: http://purl.org/ontology/temperament/description
temperament description - Associates a temperament with its detailed description.
URI: http://purl.org/ontology/temperament/deviation
interval deviation - Links an interval with a particular deviation from pure that characterises the interval.
URI: http://purl.org/ontology/temperament/frequency_ratio
frequency ratio - The frequency ratio of the two pitch classes in the interval. This may be a single value or an expression (given for example in an N3 graph literal).
URI: http://purl.org/ontology/temperament/interval
interval - Associates a specific interval on the circle of fifths.
URI: http://purl.org/ontology/temperament/lower
lower pitch class - Links an interval a pitch calss which is lower on a scale.
URI: http://purl.org/ontology/temperament/pitch_class
pitch class - The pitch class of a particular pitch class deviation. This can be used to express deviations from equal temperament.
URI: http://purl.org/ontology/temperament/pitch_class_deviation
pitch class deviation - The deviation of a particular pitch class in the described temperament from its equivalent in equal temperament.
URI: http://purl.org/ontology/temperament/upper
upper pitch class - Links an interval with a pitch class which is higher on a scale compared to the other pitch class of this interval.
URI: http://purl.org/ontology/temperament/value
deviation value - Links an interval deviation to its float value (in cents).
URI: http://purl.org/ontology/temperament/pitchclass/A
A - pitch class A
URI: http://purl.org/ontology/temperament/pitchclass/Ab
Ab - pitch class Ab
URI: http://purl.org/ontology/temperament/pitchclass/As
As - pitch class As
URI: http://purl.org/ontology/temperament/pitchclass/B
B - pitch class B
URI: http://purl.org/ontology/temperament/pitchclass/Bb
Bb - pitch class Bb
URI: http://purl.org/ontology/temperament/Bendeler
Bendeler -
URI: http://purl.org/ontology/temperament/pitchclass/Bs
Bs - pitch class Bs
URI: http://purl.org/ontology/temperament/pitchclass/C
C - pitch class C
URI: http://purl.org/ontology/temperament/pitchclass/Cb
Cb - pitch class Cb
URI: http://purl.org/ontology/temperament/pitchclass/Cs
Cs - pitch class Cs
URI: http://purl.org/ontology/temperament/pitchclass/D
D - pitch class D
URI: http://purl.org/ontology/temperament/pitchclass/Db
Db - pitch class Db
URI: http://purl.org/ontology/temperament/Diaschisma
Diaschisma - One Diaschisma is 19.55 cents.
URI: http://purl.org/ontology/temperament/DidymusComma
Didymus Comma - The Didymus is equivalent to the Syntonic comma (21.51 cents).
URI: http://purl.org/ontology/temperament/DitonicComma
Ditonic Comma - The Ditonic comma is equivalent to the Pythagorean comma.
URI: http://purl.org/ontology/temperament/pitchclass/Ds
Ds - pitch class Ds
URI: http://purl.org/ontology/temperament/pitchclass/E
E - pitch class E
URI: http://purl.org/ontology/temperament/pitchclass/Eb
Eb - pitch class Eb
URI: http://purl.org/ontology/temperament/pitchclass/Es
Es - pitch class Es
URI: http://purl.org/ontology/temperament/pitchclass/F
F - pitch class F
URI: http://purl.org/ontology/temperament/pitchclass/Fb
Fb - pitch class Fb
URI: http://purl.org/ontology/temperament/FifthCommaMeantone
FifthCommaMeantone -
URI: http://purl.org/ontology/temperament/pitchclass/Fs
Fs - pitch class Fs
URI: http://purl.org/ontology/temperament/pitchclass/G
G - pitch class G
URI: http://purl.org/ontology/temperament/pitchclass/Gb
Gb - pitch class Gb
URI: http://purl.org/ontology/temperament/pitchclass/Gs
Gs - pitch class Gs
URI: http://purl.org/ontology/temperament/KirnbergerIII
KirnbergerIII -
URI: http://purl.org/ontology/temperament/Neidhardt
Neidhardt -
URI: http://purl.org/ontology/temperament/PythagoreanComma
Pythagorean Comma - One Pythagorean Comma, the difference between 7 octaves and 12 pure fifths, is 23.5 cents. It is equivalent to the Ditonic comma.
URI: http://purl.org/ontology/temperament/QuarterCommaMeantone
QuarterCommaMeantone -
URI: http://purl.org/ontology/temperament/Schisma
Schisma - One Schisma is 1.95 cents.
URI: http://purl.org/ontology/temperament/SixthCommaMeantone
SixthCommaMeantone -
URI: http://purl.org/ontology/temperament/Stanhope
Stanhope -
URI: http://purl.org/ontology/temperament/SyntonicComma
Syntonic Comma - One Syntonic Comma is 21.51 cents.
URI: http://purl.org/ontology/temperament/Valotti
Valotti -
URI: http://purl.org/ontology/temperament/WerckmeisterIII
WerckmeisterIII -
URI: http://purl.org/ontology/temperament/YoungII
YoungII -
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first published draft 18-12-2009
Some modelling concepts in this ontology were borrowed form the Chord Ontology and the Music Similarity Ontology.