Temperament Ontology: Temperament Ontology

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Abstract

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:

Status of this Document

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:

Appendixes

1 Introduction

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:

1.1 About instrument tuning

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.

1.2 An open-ended temperament description model

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.

1.3 The many ways of describing temperaments

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.)

1.3.1 The Circle of Fifths

1.3.2 Deviations from Equal Temperament

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.

2. Temperament ontology at a glance

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:

3. Temperament ontology overview

3.1. Example

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

Chris@0:

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/> .
Chris@0: 
Chris@0: 		:ValottiTemperament a tm:WellTemperament;
Chris@0: 			tm:description :ValottiDescription1 .
Chris@0: 
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: 				] .
Chris@0:

Chris@0:

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.

4. Cross-reference for Temperament classes and properties

Chris@0:

Class: tm:CircleOfFifths

Chris@0:

URI: http://purl.org/ontology/temperament/CircleOfFifths

Circle Of Fifths - 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:

sub-class-of:: tm:TemperamentDescription

Chris@0:

The Temperament Ontology

Working Draft — 18 Dec 2009

Abstract

Status of this Document

Table of Contents

Appendixes

1 Introduction

1.1 About instrument tuning

1.2 An open-ended temperament description model

1.3 The many ways of describing temperaments

1.3.1 The Circle of Fifths

1.3.2 Deviations from Equal Temperament

2. Temperament ontology at a glance

3. Temperament ontology overview

3.1. Example

4. Cross-reference for Temperament classes and properties

Class: tm:CircleOfFifths

Class: tm:Comma

Class: tm:DeviationFromFifth

Class: tm:DeviationsFromEqual

Class: tm:Interval

Class: tm:IntervalDeviation

Class: tm:MeantoneTemperament

Class: tm:PitchClass

Class: tm:PitchClassDeviation

Class: tm:PitchClassInterval

Class: tm:RegularTemperament

Class: tm:RestrictedTemperament

Class: tm:Temperament

Class: tm:TemperamentDescription

Class: tm:WellTemperament

Property: tm:comma

Property: tm:constraint

Property: tm:description

Property: tm:deviation

Property: tm:frequency_ratio

Property: tm:interval

Property: tm:lower

Property: tm:pitch_class

Property: tm:pitch_class_deviation

Property: tm:upper

Property: tm:value

Instance: A

Instance: Ab

Instance: As

Instance: B

Instance: Bb

Instance: Bendeler

Instance: Bs

Instance: C

Instance: Cb

Instance: Cs

Instance: D

Instance: Db

Instance: Diaschisma

Instance: DidymusComma

Instance: DitonicComma

Instance: Ds

Instance: E

Instance: Eb

Instance: Es

Instance: F

Instance: Fb

Instance: FifthCommaMeantone

Instance: Fs

Instance: G

Instance: Gb

Instance: Gs

Instance: KirnbergerIII

Instance: Neidhardt

Instance: PythagoreanComma

Instance: QuarterCommaMeantone

Instance: Schisma

Instance: SixthCommaMeantone

Instance: Stanhope

Instance: SyntonicComma

Instance: Valotti

Instance: WerckmeisterIII

Instance: YoungII

A References