# Is there music that recursively subdivides the beat in odd subdivisions?

For example: 3/4 has 3 quarter notes per beat, and each quarter note subdivides into 2 eighth notes, 4 sixteenth notes etc. which makes the total count an even number (6/8 or 12/16 etc.) Is there any example of music that subdivides the beat in three nth-notes, each of which are subdivided in 3 thirds or, 9 ninths or 27 twenty-sevenths? (like an hypothetical 3/3 subdivided in 9/9, 27/27 etc.). Or analogously a hypothetical 5/5 whole note subdivided in 25/25, 625/625 (I know this'd be unplayable unless the tempo was very slow)

Whether this exists or not (and I am curious as to how this would sound), how would one go about notating such an experiment? My first thought was taking my shortest note usage, lets say 27 sixteenth notes and group them by three, above them in the subdivision tree, I'd have 9 dotted eighth notes, and above them (if I'm correct) one half note tied to a sixteenth note, but I get the impression it would be kind of annoying to read (?)

• 9/8 is `SwwMwwMww` (where `S`=strong, `M`=medium, `w`=weak), is that what you mean? Jan 8 at 21:19
• I believe everything you’re asking about can be achieved by using the appropriate time signature and various types of tuplets. Also in your last paragraph, 27 16th notes divided into 3’s is actually 9 dotted 8th notes, not 9 dotted quarter notes. Jan 8 at 22:29
• it’s not what you’re looking for, but Nancarrow’s player piano pieces do some pretty crazy things with time. Jan 9 at 14:11
• @JohnBelzaguy Maybe a combination of tuplets and compound time if the recursion goes really deep. Jan 9 at 16:26
• (Oh, and yes: you're right that these experiments would be hard to read and/or play. By no means impossible for new-music performers, though, especially if you explain what's going on. You might also experiment, like Nancarrow, with using non-human playback, like MIDI.) Jan 9 at 18:11

9/8 comes close, like in the third motion of Bach's A minor violin concerto, BWV1041

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Use nested tuplets.

In Musescore you just select a note or rest and then hit or use the add tuplet menu...

To the "are there example" part of the question: Not that I'm aware of. There are plenty of examples of "triple compound meter": Three beats, each divided into three, aka 9/8, but I'm not aware of any "five beats, divided into quintuplets." (Speculation as to why might be found under this question; aside from "because of how we've always done it," I suspect it's because 2 and 3 are prime numbers, and larger numbers like 5 or 7 are often conceptualized as combinations of them—5/8 is often notated in a way that makes it clear whether it's "two plus three" or "three plus two".)

As to how you would notate it: "tuplets" can be given in any amount. Simply beam together as many notes as you wish and write that number outside of the beam.

For instance, using 5: You might declare your time signature to be 5/4. (It would also be intriguing to continue the conceit at larger levels: organize the music in 5-bar phrases, and sections of 5 phrases each. Maybe there are 5 movements!) Then, to subdivide your beat, write 5 notes connected by a single beam, as if they are eighth notes, and write "5" outside the beam. For the next subdivision, connect 25 notes with a double beam and write "25."

You'll note: your example, using groups of 3, worked from "small notes up to big notes" and wound up with dotted quarters. This is not unreasonable, as an extension of "compound triple," but the fact that you wound up with dotted quarters is a quirk of this one scenario.

• One only has to look at composers like Nancarrow or Adès to find examples of such time signatures. The error of your answer is that everything is still structured within the framework of bifurcated pulse, which is not what the OP is asking. Jan 9 at 17:37
• @jjmusicnotes Hm, one of us is not understanding the other. I don't mean to be discussing "bifurcation," i.e. divisive rhythm in multiples of two. Meanwhile, Nancarrow was the first name I thought of. I did a quick look over his work, but most of what I see is more about "x against y" relationships; I didn't see an example of "x subdivided into x parts, which are in turn subdivided into x parts." Jan 9 at 18:06
• @jjmusicnotes (Also, several have already mentioned that "time signature" doesn't tell a lot, and in fairness the OP only barely mentioned it.) Jan 9 at 18:08

The famous Spanish Romance for classical guitar is written in 3/4 where each 1/4 is played as a triplet.

This does actually not sound very interesting in terms of rhythmic feeling, it's more about the beautiful harmony.

On the other side there are very interesting rhythms which are technically 4/4 but use a lot of syncopation to give the listener an odd time feeling.

In my opinion the time signature of a piece does not tell you a lot about rhythmic complexity.

• This answer is only opinion and does not contain any factual information pertinent to the original question. A time signature absolutely gives information not only about rhythmic complexity, but about phrasing. A piece written 3+2/8 instead of 5/8 is quite literally telling you how the meter is divided. A piece written in 3/1 instead of 3/4 is quite literally telling you to feel the music "in one", which in turn shapes the phrasing. Jan 9 at 17:41
• I don't agree. The piece I given as example (that's what the OP asked for) is in 3/4 and it has a totally different feel and phrasing compared to e.g. a classical waltz which is also in 3/4. Jan 9 at 20:58