# Time point

In music a time point or timepoint (point in time) is "an instant, analogous to a geometrical point in space". Because it has no duration, it literally cannot be heard, but it may be used to represent "the point of initiation of a single pitch, the repetition of a pitch, or a pitch simultaneity", therefore the beginning of a sound, rather than its duration. It may also designate the release of a note or the point within a note at which something changes (such as dynamic level). Other terms often used in music theory and analysis are attack point and starting point. Milton Babbitt calls the distance from one time point, attack, or starting point to the next a time-point interval, 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. Other writers use the terms attack interval, or (translating the German Einsatzabstand), interval of entry, interval of entrance, or starting interval.

## Interonset interval

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, and the interonset interval or IOI is the time between the beginnings or attack points of successive events or notes, the interval between onsets, not including the duration of the events. A variant of this term is interval of onset.
For example, two sixteenth notes separated by dotted eighth rest, would have the same interonset interval as between a quarter note and a sixteenth note:
The concept is often useful for considering rhythms and meters.

## Time-point sets

In serial music a time-point set, proposed in 1962 by Milton Babbitt, is a temporal order of pitches in a tone row which indicates the instants at which the notes start. This has certain advantages over a duration scale or row built from multiples of a unit, derived from Olivier Messiaen.
   since duration is a measure of distance between time points, as 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.
For example, a measure may be divided into twelve metrical positions. In $^3$ $_4$ 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).
Babbitt uses time points in Partitions (1957), All Set (1957), and Post-Partitions (1966), as well as in Phonemena (1969–70), String Quartets No. 3 (1969–70) and No. 4 (1970), Arie da capo (1974), My Ends Are My Beginnings (1978), and Paraphrases (1979).
Charles Wuorinen has also developed an approach to the time-point system, which differs greatly from Babbitt's.

## Sources

* ↑ Kramer 1988, p. 454.
* ↑ Kramer 1988, p. 97.
* ↑ Babbitt 1962, p. 72.
* ↑ Wuorinen 1979, p. 131.
* 1 2 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. 94.
* ↑ Hubert S. Howe, Jr., Electronic Music Synthesis: Concepts, Facilities, Techniques (New York: W. W. Norton, 1975): p. 28
* ↑ Babbitt 1962, p. 67.
* ↑ Wuorinen 1979, p. 130.
* ↑ 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. 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. 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.
* ↑ 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. 85. ISBN 9789058677358.
* ↑ Dieter Schnebel, "Epilogue", translated by Sharmila Bose, in Stockhausen in Calcutta, selected by Hans-Jürgen Nagel, pp. 1–5 (Calcutta: Seagull Books, 1984): 2.
* 1 2 London, Justin (2004). Hearing in Time: Psychological Aspects of Musical Meter, p. 4. ISBN 978-0-19-974437-4.
* ↑ 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.
* 1 2 Babbitt 1962, p. 63
* ↑ Roads, Curtis (2001). Microsound, pp. 74–78. Cambridge: MIT Press. ISBN 0-262-18215-7.
* ↑ Leeuw, Ton de (2006). Music of the Twentieth Century, p. 171. ISBN 9789053567654.
* 1 2 Taruskin, Richard (2009). The Oxford History of Western Music: Music in the Late Twentieth Century, pp. 166–167. ISBN 978-0-19-538485-7.
* ↑ Griffiths, Paul (1996). Modern Music and After, p. 64. ISBN 978-0-19-816511-8.
* 1 2 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.
Sources
* Babbitt, Milton (Fall 1962). "Twelve-Tone Rhythmic Structure and the Electronic Medium". Perspectives of New Music. 1 (1): 49–79. doi:10.2307/832179. JSTOR 832179.
* Kramer, Jonathan D. (1988). The Time of Music: New Meanings, New Temporalities, New Listening Strategies. New York; London: Schirmer; Collier Macmillan. ISBN 0-02-872590-5.
* Wuorinen, Charles (1979). Simple Composition. Longman Music Series. New York: Longman. ISBN 9780582280595.