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Suppose I have a 4/4 bar for piano, and in the right hand I want to play a quintuplet over 1, 2 and 3, and I want to play a quadruplet over 2, 3 and 4.

What is the proper way to notate this?

The solution I came up with is quite unwieldy. In order for the start of the quadruplet to line up with the quintuplet, we need to retain the original division of the bar, which we can do by changing the quintuplet into a 15-tuplet, where the 15-tuplet contains 5 notes with a duration of 3 units. That way we retain the orginal division on note 1, 5 and 10 of the 15-tuplet.

In order for the quadruplet to line up with the notes of the 15-tuplet, we need to move to a 60-tuplet. The intended quintuplet then becomes a 60-tuplet with 5 notes of a duration of 12 units each. The quadruplet also becomes a 60-tuplet with 4 notes of duration of 15 units each, and that starts on the 20th note of the first 60-tuplet.

Now we can merge the two 60-tuplets into one 80-tuplet that covers the entire bar.

While this seems arithmatically correct to me, it leads to something quite unreadable, so I must assume there is another way to approach this.

2 Answers 2

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Divide the right hand part into two different voices, the top voice gets stems pointed up, and the bottom voice gets stems pointed down. Then put the tuplets in for each voice the usual way. This will make your intension clear and readable (even if it isn't easy to play).

A grand stave in 4/4 time.  The top staff has two voices: The highest voice has a quintuplet of quavers over the first three beats and then a crotchet, the second voice has a crotchet and then a quadruplet of crotchets over the next three beats. In the bottom staff has four crotchets.

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  • Thank you for the great response. Voices as an aspect of musical notation, I will dig deeper into. Commented Aug 28, 2023 at 12:07
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    Why is the quintuplet composed of "eighth" notes but the quadruplet of "quarter" notes? Commented Aug 29, 2023 at 13:27
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    @DanielWagner That was a somewhat arbitrary decision. I was using the logic that for the quintuplet: 5 "eighth" notes is closer to 6 eights notes, than 5 "quarter" notes would be to 3 quarter notes. And for the quadruplet that: 4 "quarter" notes is closer to 3 quarter notes, than 4 "eighth" notes would be to 6 eight notes. Though I wasn't particularly happy with the quintuplet being a stretching and the quadruplet being a squashing. As PipedPiper points out, these are non-standard tuplets, and really should be written more explicitly (with the ratio specified), and squashing both seems best. Commented Aug 29, 2023 at 14:36
  • Because both voices must fill the entire measure, this notation is unambiguous as-is. The presence of the two plain quarter notes makes it clear that each tuplet is three beats. I actually like having the two different value notes as additional clarification about which voice they belong to and which notes are shorter compared with the notation in the other answer with a bar full of mismatched quarter notes. Commented Aug 29, 2023 at 16:06
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For non-standard tuplets it's important to make it clear how much time they are taking up. This notation makes the tuplets more explicit:

enter image description here (the red notes should be black of course)

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