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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.
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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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first published draft 18-12-2009
Some modelling concepts in this ontology were borrowed form the Chord Ontology and the Music Similarity Ontology.