Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Temperament Ontology: Temperament Ontology Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0: Chris@0:

The Temperament Ontology

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Working Draft — 18 Dec 2009

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This version:
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http://purl.org/ontology/temperament/draft1-20091218/
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Latest version:
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http://purl.org/ontology/temperament/
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Last Update: 18. Dec. 2009.
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Date: 18. Dec. 2009.
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Editors:
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Gyorgy Fazekas, Centre for Digital Music Queen Mary University of London
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Authors:
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Gyorgy Fazekas, Dan Tidhar, Centre for Digital Music Queen Mary University of London
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Contributors:
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See acknowledgements
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You are granted a license to use, reproduce and create derivative works of this document under Creative Commons.

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Abstract

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Chris@0: The temperament ontology can be used to give a detailed description of the tuning of an instrument. Chris@0: It is developed in the OMRAS2 project, and intended to be used in conjunction Chris@0: with the Music Ontology, Chris@0: for example, when describing the tuning that was used in a particular harpsichord recording. Chris@0:

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Status of this Document

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Chris@0: This is a work in progress! This document is changing Chris@0: on a daily if not hourly basis. Comments are very welcome, please send Chris@0: them to gyorgy.fazekas@elec.qmul.ac.uk. Thank you. Chris@0:

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Table of Contents

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  1. Introduction Chris@0:
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    1. About instrument tuning
      2. Chris@0:
    2. An open-ended temperament description model
      3. Chris@0:
    3. Chris@0: The many ways of describing temperaments Chris@0:
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      1. The Circle of Fifths
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      2. Deviation from Equal Temperament
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      4. Chris@0:
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    2. Chris@0:
  2. Temperament ontology at a glance
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  3. Chris@0: Temperament ontology overview Chris@0:
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    1. Example
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    4. Chris@0:
  4. Cross-reference for Temperament classes and properties
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Appendixes

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  1. Normative References
    2. Chris@0:
  2. Changes in this version (Non-Normative)
    3. Chris@0:
  3. Acknowledgements (Non-Normative)
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1 Introduction

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The temperament ontology aims to describe instrument tuning systems and their particularities. Chris@0: It may also be used to characterise a (potentially unknown) temperament that was used when tuning an Chris@0: instrument for a particular performance or recording.

Chris@0: At this stage the ontology is far from exhaustive. We primarily deal with Chris@0: temperaments in western tonal music with an emphasis on tuning keyboard instruments. Chris@0: One important objective is to be able to describe arbitrary temperaments, Chris@0: or express the results of automatic temperament extraction from audio recordings. Chris@0:

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1.1 About instrument tuning

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Tuning an instrument consists of choosing the frequency values and spacing (or ratio) of pitches that are used. Chris@0: Pure (just) intervals of pitches correspond to whole number ratios of their frequencies, however Chris@0: 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. Chris@0: For example, it is not possible to fit twelve pure fifths (3:2)^12 into seven octaves (2:1)^7. The difference Chris@0: is called the Pythagorean or Ditonic comma (23.5 cents). This difference has to be Chris@0: tempered out ---that is, some (or all) fifths has to be mistuned slightly in order to Chris@0: fit them. There are many tuning systems. Most commonly, they differ in the way they compromise Chris@0: pure intervals to solve this problem.

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1.2 An open-ended temperament description model

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There is no mutual agreement in the literature on the description or classification Chris@0: of temperaments. Therefore, in this ontology we do not impose a Chris@0: hierarchy between types of temperaments. We define an opaque Chris@0: top-level temperament concept. Subclasses of this concept can be used Chris@0: in describing individual temperaments, if necessary, using multiple class memberships. Chris@0: Since there is more than one way to associate tuning systems with their properties, Chris@0: we treat temperament descriptions as concepts as well, Chris@0: and use reification to keep the model open and extensible.

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Using the Circle of Fifths to describe a temperament. Chris@0:

Figure 1. Overview of the temperament ontology.

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1.3 The many ways of describing temperaments

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Temperaments can be characterised in lots of different ways. Chris@0: The most common methods are using either the circle of fifths or Chris@0: give the pitch deviations from equal temperament. We define these Chris@0: descriptions as concepts in the ontology, however, other descriptions Chris@0: may be used and defined in the future. Chris@0: (For example, one might find it convenient to express the same information using the circle of fourths.)

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1.3.1 The Circle of Fifths

Chris@0: The circle of fifths has several uses in music theory. Chris@0: It shows the harmonic relationships of the twelve major and minor keys. Chris@0: It can also be seen as a circle of the corresponding pitch class intervals, Chris@0: such as (C-G), (G-D), (D-A) etc... If we go around the circle using pure fifth Chris@0: intervals, it wouldn't close. What remains is the Pythagorean comma. Chris@0: Hence, it is often used to describe temperaments by showing how Chris@0: the comma is distributed among the intervals to close the circle. Chris@0: (Note that there are several types of commas related to different Chris@0: tuning problems. These are defined in the ontology.) Chris@0: Chris@0: Chris@0: Chris@0:

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1.3.2 Deviations from Equal Temperament

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In equal temperament an octave is divided into twelve equal intervals. Chris@0: As a result only octaves are pure. All other intervals are impure, and the Chris@0: deviation from pure is different in case of each interval. Since equal temperament Chris@0: has become very common, other temperaments are often described by Chris@0: the frequency deviations (in cents) of each pitch class from the Chris@0: corresponding pitch class in equal temperament.

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2. Temperament ontology at a glance

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Chris@0: An alphabetical index of Temperament terms, by class (concepts) and by property Chris@0: (relationships, attributes), are given below. All the terms are hyperlinked Chris@0: to their detailed description for quick reference. Chris@0:

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3. Temperament ontology overview

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3.1. Example

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Here is a very basic example describing a pitch class interval in the Valotti temperament using the circle of fifths.

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Chris@0: 		@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>.
Chris@0: 		@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#>.
Chris@0: 		@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
Chris@0: 		@prefix tm: <http://purl.org/ontology/temperament/> .
Chris@0: 		@prefix pc: <http://purl.org/ontology/temperament/pitchclass/> .
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Chris@0: 		:ValottiTemperament a tm:WellTemperament;
Chris@0: 			tm:description :ValottiDescription1 .
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Chris@0: 		:ValottiDescription1 a tm:CircleOfFifths;
Chris@0: 			tm:interval [
Chris@0: 				a tm:FifthInterval ;
Chris@0: 				tm:deviation [
Chris@0: 					a tm:IntervalDeviation ;
Chris@0: 					tm:comma tm:PythagoreanComma ; 
Chris@0: 					tm:value "-0.16667"^^xsd:float ;
Chris@0: 					rdfs:label "-1/6"
Chris@0: 					] ;
Chris@0: 				tm:lower pc:C ;
Chris@0: 				tm:upper pc:G ] ;
Chris@0: 			tm:interval [ # the rest of the intervals on the circle of fifths 
Chris@0: 				] .
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A graphical representation of a similar description is shown in figure 2. Chris@0: We explicitly name the pitch classes involved in each interval on the circle of fifths. Chris@0: The IntervalDeviation concept describes the amount of deviation from a pure interval Chris@0: in terms of a specific type of comma and a corresponding value (a fraction of that comma). Chris@0: We can safely assume that a fifth is pure, unless the deviation is given.

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Using the Circle of Fifths to describe a temperament. Chris@0:

Figure 2. Describing temperaments using the circle of fifths.

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4. Cross-reference for Temperament classes and properties

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A References

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Music Ontology
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The Music Ontology is a thorough and mature ontology for describing Chris@0: music-related data, including musicological information. This ontology is intended to be Chris@0: used in conjunction with the Music Ontology.
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B Changes in this version (Non-Normative)

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C Acknowledgements (Non-Normative)

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Some modelling concepts in this ontology were borrowed form the Chris@0: Chord Ontology Chris@0: and the Chris@0: Music Similarity Ontology. Chris@0:

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