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{{other uses|Timepoint (disambiguation){{!}}Timepoint}}

In [[music]] a '''time point''' or ''timepoint'' ([[point (geometry)|point]] in [[time]]) is "an instant, analogous to a geometrical point in space".{{sfn|Kramer|1988|p=454}} Because it has no [[duration (music)|duration]], it literally cannot be heard,{{sfn|Kramer|1988|p=97}} but it may be used to represent "the point of initiation of a single pitch, the repetition of a pitch, or a [[simultaneity (music)|pitch simultaneity]]",{{sfn|Babbitt|1962|p=72}} therefore the beginning of a [[sound]], rather than its duration. It may also designate the release of a [[Musical note|note]] or the point within a note at which something changes (such as dynamic level).{{sfn|Wuorinen|1979|p=131}} Other terms often used in music theory and analysis are ''[[Attack (music)|attack point]]''<ref name="HillerFuller">Lejaren Hiller and Ramon Fuller, "Structure and Information in Webern's Symphonie, Op. 21", ''[[Journal of Music Theory]]'' 11, no. 1 (Spring 1967): 60–115. Citation on p.&nbsp;94.</ref> and ''starting point''.<ref>Hubert S. Howe, Jr., ''Electronic Music Synthesis: Concepts, Facilities, Techniques'' (New York: W. W. Norton, 1975): p.&nbsp;28</ref> [[Milton Babbitt]] calls the distance from one time point, attack, or starting point to the next a ''time-point interval'',{{sfn|Babbitt|1962|p=67}} 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). [[Charles Wuorinen]] shortens this expression to just ''time interval''.{{sfn|Wuorinen|1979|p=130}} Other writers use the terms ''attack interval'',<ref name="HillerFuller"/> or (translating the German ''Einsatzabstand''), ''interval of entry'',<ref>Armin Klammer, "Webern's Piano Variations, Op. 27, 3rd Movement", translated by Leo Black, ''[[Die Reihe]]'' 2: "Anton Webern" (English edition, 1958): 81–92, citations on pp.&nbsp;81, 82, 86; [[Karlheinz Stockhausen]], "Structure and Experiential Time", translated by Leo Black, ''[[Die Reihe]]'' 2: "Anton Webern" (English edition, 1958): 64–74, citation on p.&nbsp;64; [[Richard Toop]], ''Six Lectures from the Stockhausen Courses Kürten 2002'' (Kürten: Stockhausen-Verlag, for the Stockhausen Foundation for Music, 2005): 30, {{ISBN|3-00-016185-6}}.</ref> ''interval of entrance'',<ref>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 ''Unfolding Time: Studies in Temporality in Twentieth-century Music'', Geschriften van het Orpheus Instituut 8, edited by Marc Delaere and [[Darla Crispin]], 69–94 (Louvain: Leuven University Press, 2009): p.&nbsp;85. {{ISBN|9789058677358}}.</ref> or ''starting interval''.<ref>[[Dieter Schnebel]], "Epilogue", translated by Sharmila Bose, in ''Stockhausen in Calcutta'', selected by Hans-Jürgen Nagel, pp.&nbsp;1–5 (Calcutta: Seagull Books, 1984): 2.</ref>

==Interonset interval<!--[[Interonset interval]] redirects directly here.-->==
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\header { tagline = ##f}
\score {
  <<
    \drums \with {midiInstrument = "drums"} \with { \numericTimeSignature } {
      \repeat volta 1 {
     <<{cymra4 cymra cymra cymra}\\{bd2 sne2}>>
      <<{cymra8 r cymra r cymra r cymra r}\\{bd4 r sne4 r}>>\break
 

    }}
>>
\layout {indent=0}

\midi { \tempo 4 = 100 }


}</score>|width=320|align=right|caption=[[Half-time (music)|Half-time]] [[drum pattern]]: the first and second [[bar (music)|measures]] have identical time-point, attack, or interonset intervals and will sound identical given certain [[instrumentation (music)|instrumentation]] and [[performance practice]]s.|max-width=400}}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.

The corresponding term used in acoustics and audio engineering to describe the initiation of a sound is [[Onset (audio)|onset]], and the ''interonset interval'' or IOI is the [[time]] between the beginnings or attack points of successive events or [[Musical note|note]]s, the interval between onsets, not including the [[Duration (music)|duration]] of the events.<ref name="London">London, Justin (2004). ''Hearing in Time: Psychological Aspects of Musical Meter'', p. 4. {{ISBN|978-0-19-974437-4}}.</ref> A variant of this term is ''interval of onset''.<ref>John MacKay, "On the Perception of Density and Stratification in Granular Sonic Textures: An Exploratory Study", ''Interface'' 13 (1984): 171–186. Citation on p. 185.</ref>

For example, two [[sixteenth note]]s separated by dotted eighth [[rest (music)|rest]], would have the same interonset interval as between a [[quarter note]] and a sixteenth note:
{|
|colspan=3|{{center|[[File:Interonset interval - sixteenth versus quarter.png|220px]]}}
|-
|[[File:Interonset interval - sixteenth versus quarter.mid|thumb|70px|Snare]]
|[[File:Interonset interval - sixteenth versus quarter piano.mid|thumb|70px|Piano]]
|[[File:Interonset interval - sixteenth versus quarter clarinet.mid|thumb|70px|Clarinet]]
|}{{clear}}

The concept is often useful for considering [[rhythm]]s and [[metre (music)|meters]].<ref name="London"/>

==Time-point sets==
[[File:Time-point series.png|thumb|Division of the measure/{{Zero width space}}chromatic scale, followed by pitch/time-point series[[File:Time-point series.mid]]]]

In [[serial music]] a ''time-point set'', proposed in 1962 by Milton Babbitt,<ref name="Babbitt">{{harvnb|Babbitt|1962|p=63}}</ref> is a temporal order of [[pitch class|pitches]] in a [[tone row]] which indicates the instants at which the [[note (music)|notes]] start. This has certain advantages over a [[duration series|duration scale]] or row built from multiples of a unit,<ref>[[Curtis Roads|Roads, Curtis]] (2001). ''Microsound'', pp. 74–78. Cambridge: MIT Press. {{ISBN|0-262-18215-7}}.</ref> derived from [[Olivier Messiaen]].<ref>[[Ton de Leeuw|Leeuw, Ton de]] (2006). ''Music of the Twentieth Century'', p. 171. {{ISBN|9789053567654}}.</ref>

{{quote|since duration is a measure of distance between time points, as [[interval (music)|interval]] 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.|Milton Babbitt<ref name="Babbitt"/><ref name="Oxford">[[Richard Taruskin|Taruskin, Richard]] (2009). ''The Oxford History of Western Music: Music in the Late Twentieth Century'', pp. 166–167. {{ISBN|978-0-19-538485-7}}.</ref>}}

For example, a [[bar (music)|measure]] may be divided into twelve [[meter (music)|metrical]] positions. In {{music|time|3|4}} 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).<ref name="Oxford"/>

Babbitt uses time points in ''Partitions'' (1957), ''[[All Set (Babbitt)|All Set]]'' (1957), and ''Post-Partitions'' (1966),<ref>[[Paul Griffiths (writer)|Griffiths, Paul]] (1996). ''Modern Music and After'', p. 64. {{ISBN|978-0-19-816511-8}}.</ref> as well as in ''Phonemena'' (1969–70), [[String Quartet No. 3 (Babbitt)|String Quartets No. 3]] (1969–70) and [[String Quartet No. 4 (Babbitt)|No. 4]] (1970), ''Arie da capo'' (1974), ''My Ends Are My Beginnings'' (1978), and ''Paraphrases'' (1979).<ref name=A.Mead>Mead, Andrew (1987) "About ''About Time''{{'s}} Time: A Survey of Milton Babbitt's Recent Rhythmic Practice", ''[[Perspectives of New Music]]'' 25, nos. 1–2 (Winter/Summer 1987): 182–235. Citations on pp. 187–189, 192–193, 195–197, 200–205, 215, and 225–230.</ref>

[[Charles Wuorinen]] has also developed an approach to the time-point system, which differs greatly from Babbitt's.<ref name=A.Mead/>{{clarify|date=January 2014}}<!--How?-->

==Sources==
{{reflist}}
'''Sources'''
* {{cite journal|last=Babbitt|first=Milton|author-link=Milton Babbitt|title=Twelve-Tone Rhythmic Structure and the Electronic Medium|journal=[[Perspectives of New Music]]|volume=1|number=1|date=Fall 1962|pages=49–79|doi=10.2307/832179 |jstor=832179 }}
* {{cite book|last=Kramer|first=Jonathan D.|author-link=Jonathan Kramer|title=The Time of Music: New Meanings, New Temporalities, New Listening Strategies|location=New York; London|publisher=Schirmer; Collier Macmillan|year=1988|isbn=0-02-872590-5}}
* {{cite book|last=Wuorinen|first=Charles|author-link=Charles Wuorinen|title=Simple Composition|series=Longman Music Series|location=New York|publisher=Longman|year=1979|isbn=9780582280595}}

==Further reading==
* Johnson, William Marvin (1984). "Timepoint Sets and Meter". ''[[Perspectives of New Music]]'' 23, no. 1 (Fall–Winter): 278–297.
* Oxford, Parncutt and Mc Pherson (eds.) (2002). '' The Science and Psychology of Music Performance'', p.&nbsp;200–202. {{ISBN|0-19-513810-4}}
* Scotto, Ciro (1988). "Preparing a Performance of Babbitt's ''Arie da Capo''". ''Perspectives of New Music'' 26, no. 2 (Summer): 6–24.

==External links==
*[http://www.music.indiana.edu/som/courses/rhythm/illustrations/interonset_interval_(ioi).html "interonset interval (IOI)"] {{Webarchive|url=https://web.archive.org/web/20121017233924/http://www.music.indiana.edu/som/courses/rhythm/illustrations/interonset_interval_(ioi).html |date=2012-10-17 }} [https://web.archive.org/web/20131231052926/http://courses.music.indiana.edu/rhythm/illustrations/interonset_interval_(ioi).html archived on 31 Dec 2013], Rhythm and Meter Bibliography and Glossary at the [[Jacobs School of Music|School of Music at Indiana University]]

{{Rhythm and meter}}
{{Twelve-tone technique}}

[[Category:Rhythm and meter]]
[[Category:Serialism]]