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Chris@0 1 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML+RDFa 1.0//EN" "http://www.w3.org/MarkUp/DTD/xhtml-rdfa-1.dtd">
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Chris@0 4 xmlns:mvcb="http://webns.net/mvcb/"
Chris@0 5 xml:lang="en"
Chris@0 6 >
Chris@0 7
Chris@0 8 <head>
Chris@0 9 <title>Temperament Ontology: Temperament Ontology</title>
Chris@0 10 <meta http-equiv="content-type" content="text/xhtml+xml; charset=utf-8" />
Chris@0 11 <link rel="mvvb:generatorAgent" type="application/rdf+xml" title="DOAP" href="http://rdfohloh.wikier.org/project/specgen" />
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Chris@0 14 </head>
Chris@0 15
Chris@0 16 <body>
Chris@0 17
Chris@0 18 <h1 id="title">The Temperament Ontology</h1>
Chris@0 19
Chris@0 20 <!--<h2 id="subtitle">LONG Temperament </h2>-->
Chris@0 21
Chris@0 22 <h3 id="mymw-doctype">Working Draft &mdash; 18 Dec 2009</h3>
Chris@0 23
Chris@0 24 <dl>
Chris@0 25
Chris@0 26 <dt>This version:</dt>
Chris@0 27 <dd><a href="http://purl.org/ontology/temperament/draft1-20091218/">http://purl.org/ontology/temperament/draft1-20091218/</a></dd>
Chris@0 28
Chris@0 29 <dt>Latest version:</dt>
Chris@0 30 <dd><a href="http://purl.org/ontology/temperament/">http://purl.org/ontology/temperament/</a></dd>
Chris@0 31
Chris@0 32 <dt>Last Update: 18. Dec. 2009.</dt>
Chris@0 33 <dd>Date: 18. Dec. 2009.</dd>
Chris@0 34
Chris@0 35 <dt>Editors:</dt>
Chris@0 36 <dd>Gyorgy Fazekas, Centre for Digital Music Queen Mary University of London</dd>
Chris@0 37
Chris@0 38 <dt>Authors:</dt>
Chris@0 39 <dd>Gyorgy Fazekas, Dan Tidhar, Centre for Digital Music Queen Mary University of London</dd>
Chris@0 40
Chris@0 41 <dt>Contributors:</dt>
Chris@0 42 <dd>See <a href="#acknowledgements">acknowledgements</a></dd>
Chris@0 43
Chris@0 44 </dl>
Chris@0 45
Chris@0 46 <p class="copyright">You are granted a license to use, reproduce and create derivative works of this document under <a rel="license" href="http://creativecommons.org/licenses/by/3.0/">Creative Commons</a>.</p>
Chris@0 47
Chris@0 48 <!-- ===================================================================== -->
Chris@0 49
Chris@0 50 <hr />
Chris@0 51
Chris@0 52 <h2 id="abstract">Abstract</h2>
Chris@0 53 <p>
Chris@0 54 The temperament ontology can be used to give a detailed description of the tuning of an instrument.
Chris@0 55 It is developed in the OMRAS2 project, and intended to be used in conjunction
Chris@0 56 with the <em><a href="http://purl.org/ontology/mo/">Music Ontology</a></em>,
Chris@0 57 for example, when describing the tuning that was used in a particular harpsichord recording.
Chris@0 58 </p>
Chris@0 59
Chris@0 60 <h2 id="status">Status of this Document</h2>
Chris@0 61 <p>
Chris@0 62 <strong>This is a work in progress!</strong> This document is changing
Chris@0 63 on a daily if not hourly basis. Comments are very welcome, please send
Chris@0 64 them to <a href="mailto:gyorgy.fazekas@elec.qmul.ac.uk">gyorgy.fazekas@elec.qmul.ac.uk</a>. Thank you.
Chris@0 65 </p>
Chris@0 66
Chris@0 67 <h2 id="contents">Table of Contents</h2>
Chris@0 68 <ol id="toc">
Chris@0 69 <li><a href="#intro">Introduction</a>
Chris@0 70 <ol>
Chris@0 71 <li><a href="#s11">About instrument tuning</a></li>
Chris@0 72 <li><a href="#s12">An open-ended temperament description model</a></li>
Chris@0 73 <li>
Chris@0 74 <a href="#s13">The many ways of describing temperaments</a>
Chris@0 75 <ol>
Chris@0 76 <li><a href="#s131">The Circle of Fifths</a></li>
Chris@0 77 <li><a href="#s132">Deviation from Equal Temperament</a></li>
Chris@0 78 </ol>
Chris@0 79 </li>
Chris@0 80 </ol>
Chris@0 81 </li>
Chris@0 82 <li><a href="#sec-glance">Temperament ontology at a glance</a></li>
Chris@0 83 <li>
Chris@0 84 <a href="#overview">Temperament ontology overview</a>
Chris@0 85 <ol>
Chris@0 86 <li><a href="#s31">Example</a></li>
Chris@0 87 </ol>
Chris@0 88 </li>
Chris@0 89 <li><a href="#reference">Cross-reference for Temperament classes and properties</a></li>
Chris@0 90 </ol>
Chris@0 91
Chris@0 92 <h3>Appendixes</h3>
Chris@0 93 <ol id="appendix">
Chris@0 94 <li><a href="#references">Normative References</a></li>
Chris@0 95 <li><a href="#changes">Changes in this version</a> (Non-Normative)</li>
Chris@0 96 <li><a href="#acknowledgements">Acknowledgements</a> (Non-Normative)</li>
Chris@0 97 </ol>
Chris@0 98
Chris@0 99 <hr />
Chris@0 100
Chris@0 101 <!-- ===================================================================== -->
Chris@0 102
Chris@0 103 <h2 id="intro">1 Introduction</h2>
Chris@0 104
Chris@0 105 <p>The temperament ontology aims to describe instrument tuning systems and their particularities.
Chris@0 106 It may also be used to characterise a (potentially unknown) temperament that was used when tuning an
Chris@0 107 instrument for a particular performance or recording. <br><br>
Chris@0 108 At this stage the ontology is far from exhaustive. We primarily deal with
Chris@0 109 temperaments in western tonal music with an emphasis on tuning keyboard instruments.
Chris@0 110 One important objective is to be able to describe arbitrary temperaments,
Chris@0 111 or express the results of automatic temperament extraction from audio recordings.
Chris@0 112 </p>
Chris@0 113
Chris@0 114 <h3 id="s11">1.1 About instrument tuning</h3>
Chris@0 115
Chris@0 116 <p>Tuning an instrument consists of choosing the frequency values and spacing (or ratio) of pitches that are used.
Chris@0 117 Pure (just) intervals of pitches correspond to whole number ratios of their frequencies, however
Chris@0 118 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@0 119 For example, it is not possible to fit twelve pure fifths (3:2)^12 into seven octaves (2:1)^7. The difference
Chris@0 120 is called the Pythagorean or Ditonic comma (23.5 cents). This difference has to be
Chris@0 121 tempered out ---that is, some (or all) fifths has to be mistuned slightly in order to
Chris@0 122 fit them. There are many tuning systems. Most commonly, they differ in the way they compromise
Chris@0 123 pure intervals to solve this problem. </p>
Chris@0 124
Chris@0 125
Chris@0 126 <h3 id="s12">1.2 An open-ended temperament description model</h3>
Chris@0 127 <p>There is no mutual agreement in the literature on the description or classification
Chris@0 128 of temperaments. Therefore, in this ontology we do not impose a
Chris@0 129 hierarchy between types of temperaments. We define an opaque
Chris@0 130 top-level temperament concept. Subclasses of this concept can be used
Chris@0 131 in describing individual temperaments, if necessary, using multiple class memberships.
Chris@0 132 Since there is more than one way to associate tuning systems with their properties,
Chris@0 133 we treat temperament descriptions as concepts as well,
Chris@0 134 and use reification to keep the model open and extensible.</p>
Chris@0 135
Chris@0 136 <p><center><img src="TemperamentDescription.png" alt="Using the Circle of Fifths to describe a temperament." width="850">
Chris@0 137 <br><br>Figure 1. Overview of the temperament ontology.</center></p>
Chris@0 138
Chris@0 139
Chris@0 140 <h3 id="s13">1.3 The many ways of describing temperaments</h3>
Chris@0 141
Chris@0 142 <p>Temperaments can be characterised in lots of different ways.
Chris@0 143 The most common methods are using either the circle of fifths or
Chris@0 144 give the pitch deviations from equal temperament. We define these
Chris@0 145 descriptions as concepts in the ontology, however, other descriptions
Chris@0 146 may be used and defined in the future.
Chris@0 147 (For example, one might find it convenient to express the same information using the circle of fourths.)</p>
Chris@0 148
Chris@0 149 <h4 id="s131">1.3.1 The Circle of Fifths</h4>
Chris@0 150 The circle of fifths has several uses in music theory.
Chris@0 151 It shows the harmonic relationships of the twelve major and minor keys.
Chris@0 152 It can also be seen as a circle of the corresponding pitch class intervals,
Chris@0 153 such as (C-G), (G-D), (D-A) etc... If we go around the circle using pure fifth
Chris@0 154 intervals, it wouldn't close. What remains is the Pythagorean comma.
Chris@0 155 Hence, it is often used to describe temperaments by showing how
Chris@0 156 the comma is distributed among the intervals to close the circle.
Chris@0 157 (Note that there are several types of commas related to different
Chris@0 158 tuning problems. These are defined in the ontology.)
Chris@0 159
Chris@0 160 <!--<p><center><img src="CircleOfFifths.png" alt="Using the Circle of Fifths to describe a temperament." width="350"></center></p>-->
Chris@0 161
Chris@0 162 <p>...</p>
Chris@0 163
Chris@0 164 <h4 id="s132">1.3.2 Deviations from Equal Temperament</h4>
Chris@0 165
Chris@0 166 <p>In equal temperament an octave is divided into twelve equal intervals.
Chris@0 167 As a result only octaves are pure. All other intervals are impure, and the
Chris@0 168 deviation from pure is different in case of each interval. Since equal temperament
Chris@0 169 has become very common, other temperaments are often described by
Chris@0 170 the frequency deviations (in cents) of each pitch class from the
Chris@0 171 corresponding pitch class in equal temperament.</p>
Chris@0 172
Chris@0 173 <!-- ===================================================================== -->
Chris@0 174
Chris@0 175 <h2 id="sec-glance">2. Temperament ontology at a glance</h2>
Chris@0 176
Chris@0 177 <p>
Chris@0 178 An alphabetical index of Temperament terms, by class (concepts) and by property
Chris@0 179 (relationships, attributes), are given below. All the terms are hyperlinked
Chris@0 180 to their detailed description for quick reference.
Chris@0 181 </p>
Chris@0 182
Chris@0 183 <!-- The list of classes and properties goes here -->
Chris@0 184 %s
Chris@0 185 <!-- End of the terms list -->
Chris@0 186
Chris@0 187 <p>...</p>
Chris@0 188
Chris@0 189 <!-- ===================================================================== -->
Chris@0 190
Chris@0 191 <h2 id="overview">3. Temperament ontology overview</h2>
Chris@0 192
Chris@0 193 <!--<p>The Temperament definitions presented here are ...</p>-->
Chris@0 194
Chris@0 195 <h3 id="s31">3.1. Example</h3>
Chris@0 196
Chris@0 197 <p>Here is a very basic example describing a pitch class interval in the Valotti temperament using the circle of fifths.</p>
Chris@0 198
Chris@0 199 <div class="example" style="white-space: pre-wrap;">
Chris@0 200 <pre>
Chris@0 201 @prefix rdf: &lt;http://www.w3.org/1999/02/22-rdf-syntax-ns#&gt;.
Chris@0 202 @prefix rdfs: &lt;http://www.w3.org/2000/01/rdf-schema#&gt;.
Chris@0 203 @prefix xsd: &lt;http://www.w3.org/2001/XMLSchema#&gt; .
Chris@0 204 @prefix tm: &lt;http://purl.org/ontology/temperament/&gt; .
Chris@0 205 @prefix pc: &lt;http://purl.org/ontology/temperament/pitchclass/&gt; .
Chris@0 206
Chris@0 207 :ValottiTemperament a tm:WellTemperament;
Chris@0 208 tm:description :ValottiDescription1 .
Chris@0 209
Chris@0 210 :ValottiDescription1 a tm:CircleOfFifths;
Chris@0 211 tm:interval [
Chris@0 212 a tm:FifthInterval ;
Chris@0 213 tm:deviation [
Chris@0 214 a tm:IntervalDeviation ;
Chris@0 215 tm:comma tm:PythagoreanComma ;
Chris@0 216 tm:value "-0.16667"^^xsd:float ;
Chris@0 217 rdfs:label "-1/6"
Chris@0 218 ] ;
Chris@0 219 tm:lower pc:C ;
Chris@0 220 tm:upper pc:G ] ;
Chris@0 221 tm:interval [ # the rest of the intervals on the circle of fifths
Chris@0 222 ] .
Chris@0 223 </pre>
Chris@0 224 </div>
Chris@0 225
Chris@0 226 <p>A graphical representation of a similar description is shown in figure 2.
Chris@0 227 We explicitly name the pitch classes involved in each interval on the circle of fifths.
Chris@0 228 The IntervalDeviation concept describes the amount of deviation from a pure interval
Chris@0 229 in terms of a specific type of comma and a corresponding value (a fraction of that comma).
Chris@0 230 We can safely assume that a fifth is pure, unless the deviation is given.</p>
Chris@0 231
Chris@0 232 <p><center><img src="CircleOfFifths.png" alt="Using the Circle of Fifths to describe a temperament." width="350">
Chris@0 233 <br><br>Figure 2. Describing temperaments using the circle of fifths.</center></p>
Chris@0 234
Chris@0 235
Chris@0 236 <!-- ===================================================================== -->
Chris@0 237
Chris@0 238 <h2 id="reference">4. Cross-reference for Temperament classes and properties</h2>
Chris@0 239
Chris@0 240 <p>...</p>
Chris@0 241
Chris@0 242 <!-- The following is the script-generated list of classes and properties -->
Chris@0 243 %s
Chris@0 244 <!-- End of the terms list -->
Chris@0 245
Chris@0 246 <p>...</p>
Chris@0 247
Chris@0 248 <!-- ===================================================================== -->
Chris@0 249
Chris@0 250 <h2 id="references">A References</h2>
Chris@0 251
Chris@0 252 <dl>
Chris@0 253 <dt class="label" id="ref-some">Music Ontology</dt>
Chris@0 254 <dd><em>The <a href="http://purl.org/ontology/mo/">Music Ontology</a></em> is a thorough and mature ontology for describing
Chris@0 255 music-related data, including musicological information. This ontology is intended to be
Chris@0 256 used in conjunction with the Music Ontology.</dd>
Chris@0 257 </dl>
Chris@0 258
Chris@0 259 <!--
Chris@0 260 <h3 id="references-other">A.2 Other references</h3>
Chris@0 261
Chris@0 262 <dl>
Chris@0 263 <dt class="label" id="ref-rfc2119">IETF RFC 2119</dt>
Chris@0 264 <dd>
Chris@0 265 <em><a href="http://www.ietf.org/rfc/rfc2119.txt">RFC 2119: Key words
Chris@0 266 for use in RFCs to Indicate Requirement Levels</a></em>. Internet
Chris@0 267 Engineering Task Force, 1997 (see http://www.ietf.org/rfc/rfc2119.txt).
Chris@0 268 </dd>
Chris@0 269 </dl>
Chris@0 270 -->
Chris@0 271
Chris@0 272 <!-- ===================================================================== -->
Chris@0 273
Chris@0 274 <h2 id="changes">B Changes in this version (Non-Normative)</h2>
Chris@0 275
Chris@0 276 <ul>
Chris@0 277 <li><p>first published draft 18-12-2009</p></li>
Chris@0 278 </ul>
Chris@0 279
Chris@0 280 <h2><a id="acknowledgements"></a>C Acknowledgements (Non-Normative)</h2>
Chris@0 281
Chris@0 282 <p>Some modelling concepts in this ontology were borrowed form the
Chris@0 283 <a href="http://purl.org/ontology/chord/">Chord Ontology</a></em>
Chris@0 284 and the
Chris@0 285 <a href="http://purl.org/ontology/similarity/">Music Similarity Ontology</a></em>.
Chris@0 286 </p>
Chris@0 287
Chris@0 288 </body>
Chris@0 289
Chris@0 290 </html>
Chris@0 291