Editing Polyrhythm (section)

== Cross-rhythm ==
[[Cross-rhythm]] refers to systemic polyrhythm. The ''Concise Oxford Dictionary of Music'' defines it as “The Regular shift of some beats in a metric pattern to points ahead of or behind their normal positions.” <ref>Kennedy, M. and Bourne, J. (eds) (2007) ''The Concise Oxford Dictionary of Music'', Oxford University Press.</ref> The finale of [[Brahms]] [[Symphony No. 2 (Brahms)|Symphony No. 2]] features a powerful passage where the prevailing metre of four beats to the bar becomes disrupted.  Here is the passage as notated in the score:[[File:Brahms Symphony No. 2, finale, bars 126-142.png|thumb|center|500px|Brahms Symphony No. 2, finale, bars 126-142]] Here is the same passage re-barred to clarify how the ear may actually experience the changing metres:[[File:Brahms Symphony No. 2, finale, bars 126-142.wav|thumb|Brahms Symphony No. 2, finale, bars 126-142]][[File:Brahms Symphony No. 2, finale, bars 126-142, re-barred.png|thumb|center|500px|Brahms Symphony No. 2, finale, bars 126-142, re-barred]] “Polyrhythms run through Brahms’s music like an obsessive-compulsive streak...For Brahms, subdividing a measure of time into different units and layering different patterns on top of one another seemed to be almost a compulsion — as well as a compositional device and an engine of expression. ”<ref>Da Fonseca-Wollheim, C. (2018), "Does Brahms’s Obsession With Rhythmic Instability Explain His Music’s Magic?" ''New York Times'', 19 October.</ref>

Another straightforward example of a cross-rhythm is 3 evenly spaced notes against 2 (3:2), also known as a [[hemiola]]. Two simple and common ways to express this pattern in standard western musical notation would be 3 quarter notes over 2 dotted quarter notes within one bar of {{music|time|6|8}} time, quarter note triplets over 2 quarter notes within one bar of {{music|time|2|4}} time. Other cross-rhythms are 4:3 (with 4 dotted eighth notes over 3 quarter notes within a bar of {{music|time|3|4}} time as an example in standard western musical notation), 5:2, 5:3, 5:4, etc.

[[File:Polyrhythm 4 ll 5.svg|thumb|350px|Representation of 4 beats parallel to 5 beats]]

In auditory processing, rhythms are perceived as pitches once they have been sufficiently sped up. Furthermore, intervals of rhythms are perceived as intervals of pitch once sufficiently sped up. As such{{Citation needed|reason=This does not logically follow and needs evidence to prove it|date=February 2025}}, there is a parallel between cross-rhythms and [[interval (music)|musical intervals]]: in an audible frequency range, the 2:3 ratio produces the musical interval of a [[perfect fifth]], the 3:4 ratio produces a [[perfect fourth]], and the 4:5 ratio produces a [[major third]]. All these [[interval ratio]]s are found in the [[harmonic series (music)|harmonic series]]. These are called harmonic polyrhythms.

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