Editing Interval (music) (section)

== Generalizations and non-pitch uses ==
[[File:Time-point series.png|thumb|upright=1.2|Division of the measure/chromatic scale, followed by pitch/time-point series[[File:Time-point series.mid]]]]

The term "interval" can also be generalized to other music elements besides pitch. [[David Lewin]]'s ''Generalized Musical Intervals and Transformations'' uses interval as a generic measure of distance between [[time-point|time point]]s, [[timbre]]s, or more abstract musical phenomena.<ref>[[David Lewin|Lewin, David]] (1987). ''Generalized Musical Intervals and Transformations'', for example sections 3.3.1 and 5.4.2. New Haven: Yale University Press. Reprinted Oxford University Press, 2007. {{ISBN|978-0-19-531713-8}}</ref><ref>Ockelford, Adam (2005). ''Repetition in Music: Theoretical and Metatheoretical Perspectives'', p.&nbsp;7. {{ISBN|0-7546-3573-2}}. "Lewin posits the notion of musical 'spaces' made up of elements between which we can intuit 'intervals'....Lewin gives a number of examples of musical spaces, including the diatonic gamut of pitches arranged in scalar order; the 12 pitch classes under equal temperament; a succession of time-points pulsing at regular temporal distances one time unit apart; and a family of durations, each measuring a temporal span in time units....transformations of timbre are proposed that derive from changes in the spectrum of partials..."</ref>

For example, an interval between two bell-like sounds, which have no pitch salience, is still perceptible. When two tones have similar acoustic spectra (sets of partials), the interval is just the distance of the shift of a tone spectrum along the frequency axis, so linking to pitches as reference points is not necessary. The same principle naturally applies to pitched tones (with similar harmonic spectra), which means that intervals can be perceived "directly" without pitch recognition. This explains in particular the predominance of [[Interval recognition|interval hearing]] over [[absolute pitch]] hearing.<ref name="Tanguiane1993">{{Cite book|last=Tanguiane (Tangian) |first=Andranick|author-link=Andranik Tangian|date=1993|title= Artificial Perception and Music Recognition|series= Lecture Notes in Artificial Intelligence|volume=746|publisher=Springer |location=Berlin-Heidelberg|isbn=978-3-540-57394-4}}</ref><ref name="Tangian1994">{{Cite journal |last=Tanguiane (Tangian)|first=Andranick|author-link=Andranik Tangian|year=1994|title= A principle of correlativity of perception and its application to music recognition|journal=[[Music Perception]]|volume=11 |issue=4 |pages=465–502|doi= 10.2307/40285634 |jstor=40285634 }}</ref>