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In music, a polyrhythm is any simultaneous use of two or more rhythms which do not subdivide in such a way that they are aligned on all whole-number beats. Another way to phrase this is, two (or more) time signatures happen at the same time, which do not reduce to the same whole number, e.g. 3/4 and 4/4 played in either hand by a pianist is a polyrhythm, while 2/2 and 4/4 played together is not a polyrhythm, as both time signatures in the second example reduce to the whole number "1."

The classic rock band Queen used simultaneous 12/8 and 8/8 time signatures in their 1974 song "The March of the Black Queen."

3/4 and 6/8 together is also not a polyrhythm: while they individually behave as a triple meter and a duple meter respectively, both still reduce to the fraction "3/4." It should be noted that beats and pulses are not the same thing, in music, and while 6/8 time signature has a duple pulse, its beats still subdivide identically to 3/4 time signature, which has a triple pulse. The uneven alignment between pulses can create the illusion of polyrhythm, to the listener, where no polyrhythm exists.

The opposite circumstance can happen as well, as in the son clave of Afro-Cuban music: the clave uses a uniform pulse that is preserved across multiple simultaneous time signatures, with multiple instruments potentially performing in 4/4 against other instruments in 12/8, or 2/2 against 6/8. These are true polyrhythms, mathematically, but the pulses of all instruments align with each other. The resulting sound can be mistaken easily for having no polyrhythm, just a "swinging" quality inherent to the presence of 12/8 or 6/8 time signatures.

Polyrhythm is also achieved without changing or mixing time signatures, through the use of tuplets, which are note denominations divided by a prime number other than 2, such as triplets, which is a beat subdivided by 3, or quintuplets, a beat subdivided by 5. Setting any duple note division (the standard note denominations, e.g. breve, minim, crotchet, quaver) against a tuplet, or setting two different tuplets against each other, is polyrhythm.

Claude Debussy uses 3-against-2 and 4-against-3 polyrhythms in his "Deux Arabesques," setting triplets against eighth notes and quarter notes.

Polyrhythm is a staple defining feature of many genres of music, such as jazz, as well as having nearly universal presence in entire cultures of music, such as Carnatic music. Despite its sheer abundance and familiarity worldwide, polyrhythm presents one of the steeper learning curves for students of western classical music theory, which is prevailingly oriented around 4/4 time signature with 4/4 pulse landing precisely on the whole number beats. Several mnemonic devices are used to verbally encode the most common polyrhythms, as a workaround for this difficulty. The 3-against-2 polyrhythm aligns exactly to the syllables of the phrase "cold cup of tea," when the phrase is repeated over and over in the cadence most typically used by native English speakers. The 3-against-4 polyrythm aligns with the phrase "what atrocious weather!" as well as "pass the goddamn butter."

The substantially rarer and more difficult 5-against-4 polyrhythm can be accomplished by looping the phrase, "Christ! Okay, just tell me about-" but this is not a widely used mnemonic: as far as I can tell, this was coined by my own high school music instructor, as a way to get a disorderly bunch of teenagers to cope with the Mission Impossible theme.

Iron Noder 2019, 11/30