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<title>Time point</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Time point</span></span>

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</style><div role="note" class="hatnote navigation-not-searchable">For other uses, see <a href="Timepoint_(disambiguation)" class="mw-redirect mw-disambig" title="Timepoint (disambiguation)">Timepoint</a>.</div>

<p>In <a href="Music" title="Music">music</a> a <b>time point</b> or <i>timepoint</i> (<a href="Point_(geometry)" title="Point (geometry)">point</a> in <a href="Time" title="Time">time</a>) is "an instant, analogous to a geometrical point in space".<sup id="cite_ref-FOOTNOTEKramer1988454_1-0" class="reference"><a href="#cite_note-FOOTNOTEKramer1988454-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Because it has no <a href="Duration_(music)" title="Duration (music)">duration</a>, it literally cannot be heard,<sup id="cite_ref-FOOTNOTEKramer198897_2-0" class="reference"><a href="#cite_note-FOOTNOTEKramer198897-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> but it may be used to represent "the point of initiation of a single pitch, the repetition of a pitch, or a <a href="Simultaneity_(music)" title="Simultaneity (music)">pitch simultaneity</a>",<sup id="cite_ref-FOOTNOTEBabbitt196272_3-0" class="reference"><a href="#cite_note-FOOTNOTEBabbitt196272-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> therefore the beginning of a <a href="Sound" title="Sound">sound</a>, rather than its duration. It may also designate the release of a <a href="Musical_note" title="Musical note">note</a> or the point within a note at which something changes (such as dynamic level).<sup id="cite_ref-FOOTNOTEWuorinen1979131_4-0" class="reference"><a href="#cite_note-FOOTNOTEWuorinen1979131-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Other terms often used in music theory and analysis are <i><a href="Attack_(music)" class="mw-redirect" title="Attack (music)">attack point</a></i><sup id="cite_ref-HillerFuller_5-0" class="reference"><a href="#cite_note-HillerFuller-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> and <i>starting point</i>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> <a href="Milton_Babbitt" title="Milton Babbitt">Milton Babbitt</a> calls the distance from one time point, attack, or starting point to the next a <i>time-point interval</i>,<sup id="cite_ref-FOOTNOTEBabbitt196267_7-0" class="reference"><a href="#cite_note-FOOTNOTEBabbitt196267-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> independent of the durations of the sounding notes which may be either shorter than the time-point interval (resulting in a silence before the next time point), or longer (resulting in overlapping notes). <a href="Charles_Wuorinen" title="Charles Wuorinen">Charles Wuorinen</a> shortens this expression to just <i>time interval</i>.<sup id="cite_ref-FOOTNOTEWuorinen1979130_8-0" class="reference"><a href="#cite_note-FOOTNOTEWuorinen1979130-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Other writers use the terms <i>attack interval</i>,<sup id="cite_ref-HillerFuller_5-1" class="reference"><a href="#cite_note-HillerFuller-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> or (translating the German <i>Einsatzabstand</i>), <i>interval of entry</i>,<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> <i>interval of entrance</i>,<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> or <i>starting interval</i>.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Interonset_interval">Interonset interval</h2></div>

<div class="mw-ext-score noresize" data-midi="//upload.wikimedia.org/score/o/r/orl7tbe6ewd825m1znk9g9isi56oa6z/orl7tbe6.midi"><div style="margin-top: 3px;"></div></div></div><div class="thumbcaption"><a href="Half-time_(music)" title="Half-time (music)">Half-time</a> <a href="Drum_pattern" class="mw-redirect" title="Drum pattern">drum pattern</a>: the first and second <a href="Bar_(music)" title="Bar (music)">measures</a> have identical time-point, attack, or interonset intervals and will sound identical given certain <a href="Instrumentation_(music)" title="Instrumentation (music)">instrumentation</a> and <a href="Performance_practice" class="mw-redirect" title="Performance practice">performance practices</a>.</div></div></div><p>Half time: the snare moves to beats 3 of measure one and two (beats 3 & 7) while the hi-hat plays only on the quarter notes. Also, the quarter notes 'sound like' eighth notes in one giant measure.

</p><p>The corresponding term used in acoustics and audio engineering to describe the initiation of a sound is <a href="Onset_(audio)" title="Onset (audio)">onset</a>, and the <i>interonset interval</i> or IOI is the <a href="Time" title="Time">time</a> between the beginnings or attack points of successive events or <a href="Musical_note" title="Musical note">notes</a>, the interval between onsets, not including the <a href="Duration_(music)" title="Duration (music)">duration</a> of the events.<sup id="cite_ref-London_12-0" class="reference"><a href="#cite_note-London-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> A variant of this term is <i>interval of onset</i>.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>

</p><p>For example, two <a href="Sixteenth_note" title="Sixteenth note">sixteenth notes</a> separated by dotted eighth <a href="Rest_(music)" title="Rest (music)">rest</a>, would have the same interonset interval as between a <a href="Quarter_note" title="Quarter note">quarter note</a> and a sixteenth note:

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<p>The concept is often useful for considering <a href="Rhythm" title="Rhythm">rhythms</a> and <a href="Metre_(music)" title="Metre (music)">meters</a>.<sup id="cite_ref-London_12-1" class="reference"><a href="#cite_note-London-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Time-point_sets">Time-point sets</h2></div>

<p>In <a href="Serial_music" class="mw-redirect" title="Serial music">serial music</a> a <i>time-point set</i>, proposed in 1962 by Milton Babbitt,<sup id="cite_ref-Babbitt_14-0" class="reference"><a href="#cite_note-Babbitt-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> is a temporal order of <a href="Pitch_class" title="Pitch class">pitches</a> in a <a href="Tone_row" title="Tone row">tone row</a> which indicates the instants at which the <a href="Note_(music)" class="mw-redirect" title="Note (music)">notes</a> start. This has certain advantages over a <a href="Duration_series" title="Duration series">duration scale</a> or row built from multiples of a unit,<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> derived from <a href="Olivier_Messiaen" title="Olivier Messiaen">Olivier Messiaen</a>.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup>

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</style><blockquote class="templatequote"><p>since duration is a measure of distance between time points, as <a href="Interval_(music)" title="Interval (music)">interval</a> is a measure of distance between pitch points, we begin by interpreting interval as duration. Then, pitch number is interpretable as the point of initiation of a temporal event, that is, as a time-point number.</p></blockquote><div class="templatequotecite"><p style="display: inline; padding-left: 2.3em;">— Milton Babbitt<sup id="cite_ref-Babbitt_14-1" class="reference"><a href="#cite_note-Babbitt-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Oxford_17-0" class="reference"><a href="#cite_note-Oxford-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup></p></div>

<p>For example, a <a href="Bar_(music)" title="Bar (music)">measure</a> may be divided into twelve <a href="Meter_(music)" class="mw-redirect" title="Meter (music)">metrical</a> positions. In <span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="serif-fonts" style="font-family: 'Georgia Pro', Georgia, 'DejaVu Serif', Times, 'Times New Roman', FreeSerif, 'DejaVu Math TeX', 'URW Bookman L', serif;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:0.85em;font-size:80%;text-align:center"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"><b>3</b></sup><br><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"><b>4</b></sub></span></span></span></span> this equals sixteenth notes. The start of each position, or time point, may then be labeled, in order, 0–11. Pitches may then be assigned locations within measures according to their pitch set number, now their pitch/time-set number. In Babbitt's first example he shows subsequent numbers which ascend (0–11) as within the same measure (if four follows three it may sound immediately), and subsequent numbers which descend as in the following measure (if three follows four it must necessarily wait for the next appearance of time-point three).<sup id="cite_ref-Oxford_17-1" class="reference"><a href="#cite_note-Oxford-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup>

</p><p>Babbitt uses time points in <i>Partitions</i> (1957), <i><a href="All_Set_(Babbitt)" title="All Set (Babbitt)">All Set</a></i> (1957), and <i>Post-Partitions</i> (1966),<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> as well as in <i>Phonemena</i> (1969–70), <a href="String_Quartet_No._3_(Babbitt)" title="String Quartet No. 3 (Babbitt)">String Quartets No. 3</a> (1969–70) and <a href="String_Quartet_No._4_(Babbitt)" title="String Quartet No. 4 (Babbitt)">No. 4</a> (1970), <i>Arie da capo</i> (1974), <i>My Ends Are My Beginnings</i> (1978), and <i>Paraphrases</i> (1979).<sup id="cite_ref-A.Mead_19-0" class="reference"><a href="#cite_note-A.Mead-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup>

</p><p><a href="Charles_Wuorinen" title="Charles Wuorinen">Charles Wuorinen</a> has also developed an approach to the time-point system, which differs greatly from Babbitt's.<sup id="cite_ref-A.Mead_19-1" class="reference"><a href="#cite_note-A.Mead-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Sources">Sources</h2></div>

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<li id="cite_note-FOOTNOTEKramer1988454-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEKramer1988454_1-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKramer1988">Kramer 1988</a>, p. 454.</span>

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<li id="cite_note-FOOTNOTEKramer198897-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEKramer198897_2-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKramer1988">Kramer 1988</a>, p. 97.</span>

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<li id="cite_note-FOOTNOTEBabbitt196272-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBabbitt196272_3-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBabbitt1962">Babbitt 1962</a>, p. 72.</span>

</li>

<li id="cite_note-FOOTNOTEWuorinen1979131-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEWuorinen1979131_4-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFWuorinen1979">Wuorinen 1979</a>, p. 131.</span>

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<li id="cite_note-HillerFuller-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-HillerFuller_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-HillerFuller_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Lejaren Hiller and Ramon Fuller, "Structure and Information in Webern's Symphonie, Op. 21", <i><a href="Journal_of_Music_Theory" title="Journal of Music Theory">Journal of Music Theory</a></i> 11, no. 1 (Spring 1967): 60–115. Citation on p. 94.</span>

</li>

<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">Hubert S. Howe, Jr., <i>Electronic Music Synthesis: Concepts, Facilities, Techniques</i> (New York: W. W. Norton, 1975): p. 28</span>

</li>

<li id="cite_note-FOOTNOTEBabbitt196267-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBabbitt196267_7-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBabbitt1962">Babbitt 1962</a>, p. 67.</span>

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<li id="cite_note-FOOTNOTEWuorinen1979130-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEWuorinen1979130_8-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFWuorinen1979">Wuorinen 1979</a>, p. 130.</span>

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<li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">Armin Klammer, "Webern's Piano Variations, Op. 27, 3rd Movement", translated by Leo Black, <i><a href="Die_Reihe" title="Die Reihe">Die Reihe</a></i> 2: "Anton Webern" (English edition, 1958): 81–92, citations on pp. 81, 82, 86; <a href="Karlheinz_Stockhausen" title="Karlheinz Stockhausen">Karlheinz Stockhausen</a>, "Structure and Experiential Time", translated by Leo Black, <i><a href="Die_Reihe" title="Die Reihe">Die Reihe</a></i> 2: "Anton Webern" (English edition, 1958): 64–74, citation on p. 64; <a href="Richard_Toop" title="Richard Toop">Richard Toop</a>, <i>Six Lectures from the Stockhausen Courses Kürten 2002</i> (Kürten: Stockhausen-Verlag, for the Stockhausen Foundation for Music, 2005): 30, <style data-mw-deduplicate="TemplateStyles:r1238218222">

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</style><a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>3-00-016185-6</bdi>.</span>

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<li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">Pascal Decroupet, "Rhythms—Durations—Rhythmic Cells—Groups, Concepts of Microlevel Time-Organisation in Serial Music and Their Consequences on Shaping Time on Higher Structural Levels", in <i>Unfolding Time: Studies in Temporality in Twentieth-century Music</i>, Geschriften van het Orpheus Instituut 8, edited by Marc Delaere and <a href="Darla_Crispin" title="Darla Crispin">Darla Crispin</a>, 69–94 (Louvain: Leuven University Press, 2009): p. 85. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9789058677358</bdi>.</span>

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<li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><a href="Dieter_Schnebel" title="Dieter Schnebel">Dieter Schnebel</a>, "Epilogue", translated by Sharmila Bose, in <i>Stockhausen in Calcutta</i>, selected by Hans-Jürgen Nagel, pp. 1–5 (Calcutta: Seagull Books, 1984): 2.</span>

</li>

<li id="cite_note-London-12"><span class="mw-cite-backlink">^ <a href="#cite_ref-London_12-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-London_12-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">London, Justin (2004). <i>Hearing in Time: Psychological Aspects of Musical Meter</i>, p. 4. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-19-974437-4</bdi>.</span>

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<li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text">John MacKay, "On the Perception of Density and Stratification in Granular Sonic Textures: An Exploratory Study", <i>Interface</i> 13 (1984): 171–186. Citation on p. 185.</span>

</li>

<li id="cite_note-Babbitt-14"><span class="mw-cite-backlink">^ <a href="#cite_ref-Babbitt_14-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Babbitt_14-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFBabbitt1962">Babbitt 1962</a>, p. 63</span>

</li>

<li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><a href="Curtis_Roads" title="Curtis Roads">Roads, Curtis</a> (2001). <i>Microsound</i>, pp. 74–78. Cambridge: MIT Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-262-18215-7</bdi>.</span>

</li>

<li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><a href="Ton_de_Leeuw" title="Ton de Leeuw">Leeuw, Ton de</a> (2006). <i>Music of the Twentieth Century</i>, p. 171. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9789053567654</bdi>.</span>

</li>

<li id="cite_note-Oxford-17"><span class="mw-cite-backlink">^ <a href="#cite_ref-Oxford_17-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Oxford_17-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="Richard_Taruskin" title="Richard Taruskin">Taruskin, Richard</a> (2009). <i>The Oxford History of Western Music: Music in the Late Twentieth Century</i>, pp. 166–167. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-19-538485-7</bdi>.</span>

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<li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><a href="Paul_Griffiths_(writer)" title="Paul Griffiths (writer)">Griffiths, Paul</a> (1996). <i>Modern Music and After</i>, p. 64. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-19-816511-8</bdi>.</span>

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<li id="cite_note-A.Mead-19"><span class="mw-cite-backlink">^ <a href="#cite_ref-A.Mead_19-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-A.Mead_19-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Mead, Andrew (1987) "About <i>About Time</i><span class="nowrap" style="padding-left:0.1em;">'s</span> Time: A Survey of Milton Babbitt's Recent Rhythmic Practice", <i><a href="Perspectives_of_New_Music" title="Perspectives of New Music">Perspectives of New Music</a></i> 25, nos. 1–2 (Winter/Summer 1987): 182–235. Citations on pp. 187–189, 192–193, 195–197, 200–205, 215, and 225–230.</span>

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<p><b>Sources</b>

</p>

<ul><li><cite id="CITEREFBabbitt1962" class="citation journal cs1"><a href="Milton_Babbitt" title="Milton Babbitt">Babbitt, Milton</a> (Fall 1962). "Twelve-Tone Rhythmic Structure and the Electronic Medium". <i><a href="Perspectives_of_New_Music" title="Perspectives of New Music">Perspectives of New Music</a></i>. <b>1</b> (1): <span class="nowrap">49–</span>79. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F832179">10.2307/832179</a>. <a href="JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/832179">832179</a>.</cite></li>

<li><cite id="CITEREFKramer1988" class="citation book cs1"><a href="Jonathan_Kramer" title="Jonathan Kramer">Kramer, Jonathan D.</a> (1988). <i>The Time of Music: New Meanings, New Temporalities, New Listening Strategies</i>. New York; London: Schirmer; Collier Macmillan. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-02-872590-5</bdi>.</cite></li>

<li><cite id="CITEREFWuorinen1979" class="citation book cs1"><a href="Charles_Wuorinen" title="Charles Wuorinen">Wuorinen, Charles</a> (1979). <i>Simple Composition</i>. Longman Music Series. New York: Longman. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9780582280595</bdi>.</cite></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

<ul><li>Johnson, William Marvin (1984). "Timepoint Sets and Meter". <i><a href="Perspectives_of_New_Music" title="Perspectives of New Music">Perspectives of New Music</a></i> 23, no. 1 (Fall–Winter): 278–297.</li>

<li>Oxford, Parncutt and Mc Pherson (eds.) (2002). <i> The Science and Psychology of Music Performance</i>, p. 200–202. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-19-513810-4</bdi></li>

<li>Scotto, Ciro (1988). "Preparing a Performance of Babbitt's <i>Arie da Capo</i>". <i>Perspectives of New Music</i> 26, no. 2 (Summer): 6–24.</li></ul>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="http://www.music.indiana.edu/som/courses/rhythm/illustrations/interonset_interval_(ioi).html">"interonset interval (IOI)"</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20121017233924/http://www.music.indiana.edu/som/courses/rhythm/illustrations/interonset_interval_(ioi).html">Archived</a> 2012-10-17 at the <a href="Wayback_Machine" title="Wayback Machine">Wayback Machine</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20131231052926/http://courses.music.indiana.edu/rhythm/illustrations/interonset_interval_(ioi).html">archived on 31 Dec 2013</a>, Rhythm and Meter Bibliography and Glossary at the <a href="Jacobs_School_of_Music" title="Jacobs School of Music">School of Music at Indiana University</a></li></ul>

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</style><div id="Rhythm_and_meter38" style="font-size:114%;margin:0 4em"><a href="Rhythm" title="Rhythm">Rhythm</a> and <a href="Metre_(music)" title="Metre (music)">meter</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Additive_rhythm_and_divisive_rhythm" title="Additive rhythm and divisive rhythm">Additive and divisive</a></li>

<li><a href="Anacrusis" title="Anacrusis">Anacrusis</a></li>

<li><a href="Canter_rhythm" title="Canter rhythm">Canter rhythm</a></li>

<li><a href="Colotomy" title="Colotomy">Colotomy</a></li>

<li><a href="Counting_(music)" title="Counting (music)">Counting</a>

<ul><li><a href="Count_off" title="Count off">Count off</a></li></ul></li>

<li><a href="Cross-beat" title="Cross-beat">Cross-beat</a></li>

<li><a href="Duration_(music)" title="Duration (music)">Duration</a>

<ul><li><a href="Note_value" title="Note value">Note value</a></li></ul></li>

<li><i><a href="Gatra_(music)" title="Gatra (music)">Gatra</a></i></li>

<li><a href="Groove_(music)" title="Groove (music)">Groove</a></li>

<li><a href="Harmonic_rhythm" title="Harmonic rhythm">Harmonic rhythm</a></li>

<li><a href="Hemiola" title="Hemiola">Hemiola</a></li>

<li><a href="Homorhythm" title="Homorhythm">Homorhythm</a></li>

<li><a href="Isorhythm" title="Isorhythm">Isorhythm</a></li>

<li><a href="Metric_modulation" title="Metric modulation">Metric modulation</a></li>

<li><a href="Retrograde_(music)" title="Retrograde (music)">Non-retrogradable rhythm</a></li>

<li><a href="Notes_in%C3%A9gales" title="Notes inégales">Notes inégales</a></li>

<li><a href="Note_value" title="Note value">Note value</a></li>

<li><a href="Polyrhythm" title="Polyrhythm">Polyrhythm</a></li>

<li><a href="Prolation" title="Prolation">Prolation</a></li>

<li><a href="Prosody_(music)" title="Prosody (music)">Prosody</a></li>

<li><a href="Pulse_(music)" title="Pulse (music)">Pulse</a></li>

<li><a href="Rhythmic_mode" title="Rhythmic mode">Rhythmic mode</a></li>

<li><a href="Swing_(jazz_performance_style)" class="mw-redirect" title="Swing (jazz performance style)">Swing</a></li>

<li><a href="Syncopation" title="Syncopation">Syncopation</a></li>

<li><a href="Tempo" title="Tempo">Tempo</a></li>

<li><a href="Time_signature" title="Time signature">Time signature</a></li>

<li><a href="Tuplet" title="Tuplet">Tuplet</a></li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Twelve-tone_technique_and_serialism296" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3" style="background:#dbc3a3;"><div id="Twelve-tone_technique_and_serialism296" style="font-size:114%;margin:0 4em"><a href="Twelve-tone_technique" title="Twelve-tone technique">Twelve-tone technique</a> and <a href="Serialism" title="Serialism">serialism</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;">Fundamentals</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Combinatoriality" title="Combinatoriality">Combinatoriality</a></li>

<li><a href="Complement_(music)" title="Complement (music)">Complementation</a></li>

<li><a href="Derived_row" title="Derived row">Derivation</a></li>

<li><a href="Hexachord" title="Hexachord">Hexachord</a></li>

<li><a href="Interval_class" title="Interval class">Interval class</a></li>

<li><a href="Twelve-tone_technique#Invariance" title="Twelve-tone technique">Invariance</a></li>

<li><a href="Derived_row" title="Derived row">Partition</a>

<ul><li><a href="Cross_partition" class="mw-redirect" title="Cross partition">Cross partition</a></li></ul></li>

<ul><li><a href="Tone_row#total_chromatic" title="Tone row">Aggregate</a></li>

</div></td><td class="noviewer navbox-image" rowspan="4" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;"><a href="Permutation_(music)" title="Permutation (music)">Permutations</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Twelve-tone_technique#Transformations" title="Twelve-tone technique">Prime row</a></li>

<li><a href="Retrograde_(music)" title="Retrograde (music)">Retrograde</a></li>

<li><a href="Melodic_inversion" class="mw-redirect" title="Melodic inversion">Inversion</a></li>

<li><a href="Retrograde_inversion" title="Retrograde inversion">Retrograde inversion</a></li>

<li><a href="Multiplication_(music)" title="Multiplication (music)">Multiplication</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;">Notable<br> composers</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Milton_Babbitt" title="Milton Babbitt">Milton Babbitt</a></li>

<li><a href="Pierre_Boulez" title="Pierre Boulez">Pierre Boulez</a></li>

<li><a href="Josef_Matthias_Hauer" title="Josef Matthias Hauer">Josef Matthias Hauer</a></li>

<li><a href="Second_Viennese_School" title="Second Viennese School">Second Viennese School</a>

<ul><li><a href="Alban_Berg" title="Alban Berg">Alban Berg</a></li>

<li><a href="Arnold_Schoenberg" title="Arnold Schoenberg">Arnold Schoenberg</a></li>

<li><a href="Anton_Webern" title="Anton Webern">Anton Webern</a></li></ul></li>

<li><a href="Charles_Wuorinen" title="Charles Wuorinen">Charles Wuorinen</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;">Related articles</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="All-interval_twelve-tone_row" title="All-interval twelve-tone row">All-interval twelve-tone row</a></li>

<li><a href="All-trichord_hexachord" title="All-trichord hexachord">All-trichord hexachord</a></li>

<li><a href="Atonality" title="Atonality">Atonality</a></li>

<li><a href="Chromatic_scale" title="Chromatic scale">Chromatic scale</a></li>

<li><a href="Duration_series" title="Duration series">Duration series</a></li>

<li><a href="Equivalence_class_(music)" title="Equivalence class (music)">Equivalence</a></li>

<li><a href="Formula_composition" title="Formula composition">Formula composition</a></li>

<li><a href="Modernism_(music)" title="Modernism (music)">Modernism (music)</a></li>

<li><a href="Punctualism" title="Punctualism">Punctualism</a></li>

<li><a href="Semitone" title="Semitone">Semitone</a></li>

<li><a href="Set_theory_(music)" title="Set theory (music)">Set theory</a></li>

<li><a href="Trope_(music)" title="Trope (music)">Trope</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><div><span class="noviewer" typeof="mw:File"><span title="List-Class article"></span></span> <a href="List_of_dodecaphonic_and_serial_compositions" title="List of dodecaphonic and serial compositions">List of dodecaphonic and serial compositions</a></div></td></tr></tbody></table></div></div><div><div class="zim-footer">

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