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I've recently watched a BBC documentary about the history of music and recall an episode where they talk about music that has two distinct tempos (and possibly time signatures) at the same time for different sets of instruments.

Still, I can't remember how this is called and who are the famous composers that composed that way (Stravinsky?).

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    @Mark: Polyrhythm and polymeter share either the same beat/pulse, or the same measure division. If it's truly different tempos, it sounds like neither. Steve Reich has used this technique, having similar or the same melodic figures, but with slightly different tempo playing against each other. These effects are not easily described by a ratio, which polyrhythms usually use. – Meaningful Username Mar 4 '15 at 21:07
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    "The Unanswered Question" is the only thing I can think of that uses the technique and it's not really a technique in this piece. It's more of a statement that the three different ideas are not synced up kind of like walking into a room and hearing different conversations about the same topic: youtube.com/watch?v=kkaOz48cq2g – Dom Mar 4 '15 at 22:10
  • Do you mean different sets of instruments are each being played at different tempos? In other words, the woodwinds are perhaps playing at 100 Bpm and the brass is playing at 200 Bpm or something like that? – Rockin Cowboy Mar 4 '15 at 22:48
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    @RockinCowboy I think your example could fall under the 'Polyrhythm' category; From what I understood, Op is looking for something like woodwinds at 100 and brass at 135 – Shevliaskovic Mar 4 '15 at 22:50
  • @Shevliaskovic most likely you are right. But more clarification from OP might prevent others from going off track with future answers. – Rockin Cowboy Mar 4 '15 at 23:11
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The answer here is deceptively simple: Polytempo. There are other names, such as multi-tempo, polytemporal, and others, but they all describe the same phenomena.

Here is a link for further reading on Wikipedia.

For a list of composers that have used this technique, as well as the pieces in which this technique was used, check out this page and look under "Compositions".


I want to clarify for everyone that Polyrhythm and Polymetric are both incorrect here. Polyrhythms are multiple, independent rhythmic lines (typically ostinatos) that can form a hemiola or hemiola-like effect in music. Polymeters are ways of organizing the beat. Tempo is the speed of the beat, not how it is organized, or the rhythms that it defines.

Here is a wonderful Q/A from this very website that addresses the difference: Polymeter vs Polyrhythm

  • multitempo has a more consistent derivation (Italian), while poly- is a greek prefix. Polychronic? – luser droog Mar 6 '15 at 7:31
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    @luserdroog Pick your poison, they all get you to the same place. English is wonderful for butchering other languages and cultures. :) – jjmusicnotes Mar 6 '15 at 13:17
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This sort of thing has been explored pretty deeply by, among other people, Conlon Nancarrow. He used player pianos to perform pieces which would most likely have been too complex for anyone to perform organically. One way in which he complicated things was that he used what he called a tempo canon. As discussed here, one such piece was his Study for Player Piano 41a. It used multiple voices, each with its own tempo and the ratios were on a strict, but irrational ratio. If the ratio between tempos was rational, it would line up, or converge, so that two notes could fall at the same time. However, if the ratio was irrational, they would never converge and dance around each other until the piece ended.

This basic concept, although the effect can be jarring, is really not very different from polyrhythms and polymeters. It's just obfuscated by using complicated ratios. For example, if you have a bar and a main voice hit four evenly spaced beats, you have the standard quarter note pulse in 4/4. You can fit 3 notes evenly into that same bar in a second voice and the second voice will be playing half-note triplets. For every four notes in the main voice and every three notes in the second voice, the voices will play together. That's your bar. And that's a polyrhythm. That would be a 4:3 ratio. I'm not sure that's how it's typically notated, but the idea translates. You can imagine how this can be seen as two voices at different tempos. Say maybe one voice in 4/4 at 120 and another voice in 3/4 at 90. They would line up the same way.

Here's another example. If your main voice plays 8 eighth notes before repeating and your second voice plays 7 eighth notes before repeating, they will line up every 56 (7×8) eighth notes. In other words, after your main voice repeats seven times and your second voice repeats eight times. That's a polymeter. Now you can see how these concepts can get mixed up. As the ratios get more complicated (ie 128:73) or less rational (ie √2:φ), the tempos line up less and less and the individual tempos will get closer and/or less distinguishable. That is where you cross the line into tempo canon territory.

Note: I understand that 'irrational ratio' is a terrible oxymoron, but I can't think of better terminology. Also, this is just the one conceptualization of the multiple tempo idea. There is world music where this is done organically and many people have already mentioned other composers who have worked with the idea. But hopefully this helps.

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    It's not an oxymoron. sqrt(2) : sqrt(3), for example, is irrational and also a ratio. – Soham Chowdhury Mar 5 '15 at 6:05
  • I understand. I'm just referring to how the root word of rational is ratio. So etymologically, an irrational ratio might be a ratio which is not a ratio. At least that's how I see it. The ideas are still there regardless. – Dan D Mar 5 '15 at 15:35
  • "Rational" refers to a ratio between two integers, so the concepts of being rational and being a ratio are sort of different. I see your point, though :) – Soham Chowdhury Mar 8 '15 at 8:07
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There is both polymeter and polyrhythm.

Polymeter is sometimes referred to as "tactus-preserving polymeter." The measure size differs, the beat is the same. Since the beat is the same, the various meters eventually agree.

https://en.wikipedia.org/wiki/Meter_%28music%29#Polymeter

A good example of polymeter is the Tala which is an extream form of complex time.

Polyrhythm is the simultaneous use of two or more conflicting rhythms, that are not readily perceived as deriving from one another, or as simple manifestations of the same meter. The rhythmic conflict may be the basis of an entire piece of music (cross-rhythm), or a momentary disruption. Polyrhythms can be distinguished from irrational rhythms, which can occur within the context of a single part; polyrhythms require at least two rhythms to be played concurrently, one of which is typically an irrational rhythm.

https://en.wikipedia.org/wiki/Polyrhythm

Commonly used in modren Jazz. See: Mongo Santamaria and Elvin Jones.

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    Polyrhythm is wrong as an answer here; the quote you provided states exactly what it is, which is not what OP asked. Polyrhythm is different rhythms, but same tempo – Shevliaskovic Mar 4 '15 at 21:16
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Neilsen's 5th symphony was an early example (1922). Towards the end of the first movement, the side drum part is in a different tempo and time signature from the rest of the orchestra. The first edition of the score instructed the drummer to "improvise as if at all costs he wants to stop the progress of the orchestra".

In a later edition that instruction was replaced by a written part which breaks off with the direction "cadenza ad lib".

Skip to about 14:45 here:

(There is also an important side drum part in a more "conventional" rhythm earlier in the piece.

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