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