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I'm not extremely versed with music theory so forgive me if this is trivial.

I was having a casual conversation with a teacher regarding the idea of "quintuplets" and other "k-tuplets" as a natural generalization to triplets, where one has k evenly spaced sub beats per whole beat.

The individual said this is inpossible. Which I assumed meant, "very difficult, or unusual" but they clarified by saying it is physically impossible to have anything outside of triplets, and powers of two.

I found this hard to believe but they were very rigid in their thinking and insisted I was being ridiculous for thinking this was possible.

Would someone be able to explain why it is formally impossible to have quintuplets etc in music. I must be silly but I can't see why one can't just arbitrarily subdivide a beat as they please.

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    What that "teacher" said is nonsense. Why should it be impossible? Of course, to most people quintuplets etc. don't come very naturally, but everybody can practice and learn to use them. – Matt L. Aug 31 '16 at 20:03
  • I suggest learning a 5-tuplet and doing it in front of the teacher and watch their head implode. – shaunxer Aug 31 '16 at 20:39
  • Your teacher may have been considering any k-tuplet as a combination of duplets and triplets (I haven't tested whether this is possible, hence not an answer - but I believe it should be). – alex_d Aug 31 '16 at 21:05
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It's easy to have k-tuplets. There are many examples in the literature. The piece, "Andalucia" from Ernesto Lecuona's "Andalucian Suite" has 5-tuplets in the left hand. The rhythm is "quarter, 5-tuplet sixteenths, quarter" in 3/4 measures. Notation using k-tuplets is common in piano stuff to represent quick but measured grace notes.

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You are not limited to simply having one sort of k-tuplet. Here's a clip from a 20th century piece (for pipe organ) where the solo player is expected to play 3 against 2 with his/her right hand, 7 against 4 with the left, and 5 against 4 with his/her feet - all at the same time.

Sorabji Organ symphony No 2, from page 2 of score

There is nothing new about quintuplets and more "exotic" groupings with 17, 22, or pretty much any number of notes. Chopin wrote plenty of them 150 years ago, and there are hundreds of videos on YouTube of people successfully playing them.

Download a random selection of the Nocturnes from http://imslp.org/wiki/Category:Chopin,_Fr%C3%A9d%C3%A9ric and see for yourself.

Finding a teacher who can distinguish his/her elbow from another part of his/her anatomy would be a good idea, as well.

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