# Tuplets over the barline

I noticed in the video of the MOLA presentation that when a tuplet is split over a barline it is divided up into two constituent parts, each with their own tuplet marking. Will it be possible to do something like in the attached image?

Yes: by default, Dorico will split the tuplet into two shorter tuplets on either side of the barline, but if the tuplet is sufficiently complex that it can’t be split in that way, it will automatically show the kind of notation you show in your picture, which is generally not ideal, because you will often end up with a gap of some kind at the start of the bar. You can also choose to make a given tuplet draw as a single unit crossing a barline by way of selecting it and enabling that behaviour in the Properties panel.

There’s always a third way, which I’d prefer in every case to the example in the image, which is to split the middle note into two tied quavers over the barline, and keep the whole group under one triplet bracket. Then there’s no ambiguity about how big the gap at the start of the bar is before the third notehead kicks in.

You wouldn’t try the same trick outside tuplets - writing too much stuff into one bar and expecting people to just carry it over to the next bar. You’d always split the note that crosses the barline and tie them.

I don’t think your described third way is always mathematically possible, Neil, but I agree that it is preferable to show a tied note across the barline. In the situations where the note can be tied, Dorico will always default to showing separate brackets, but in that case you can specify it should show a single bracket by way of the Properties panel.

I may be about to drift off the point a bit, but I think tuplets can always be split at any point in the bar that’s expressible in powers of two and sums of powers of two, and by that I mean this:

Let’s say a crotchet is worth 256, so a 4/4 bar is 1024 long. Without resorting to tuplets you can express any integer point in that bar, so 1 is a tiny note with loads of tails on it, 128 is a quaver, 129 is a quaver tied to one of those tiny notes, 640 is a minim tied to a quaver etc. But you can’t express say a third of the way through the bar (because 1024/3 isn’t an integer) without using a tuplet.

There is a mathematical way of splitting any tuplet or nest of tuplets at any point in the bar that’s expressible in integers in that way. That’s the bold claim I’m making and I know the risk I’m running of someone proving me wrong and the egg that’ll be on my face as a result, and I know someone in the Steinberg team (James?) has had to go into this very very thoroughly for Dorico to do what it does, so I’ve already got some humble pie ready if it comes to that. But the tuplet-splitting stuff in the Draw Free Rhythm Barline plugin relies on it being true, and it works.

So if I’m right about that, then you can split any tuplet or nest of tuplets across the end of any power-of-two-based bar (i.e. where the denominator is a power of 2). And then, whether you then have two brackets or a single bracket spanning the barline doesn’t make much difference to the maths. I think. (In the example in the original post, for example, having two -3- brackets or having one, over the same span of notes, is the same. All the notes are still 3 in the time of 2.)

Simultaneously sure of my ground and expecting to be proved wrong within half an hour - odd feeling! Anyway, it doesn’t matter. If Dorico can split any splittable tuplets, you can’t ask for more than that.

Well, you’ve successfully blinded me with science, anyway, Neil. But I’m a typical singer – I can just about count to four, if I absolutely have to.

Seeing as Dorico can handle time signatures like 5/3 though, all bets are off in bars like that. If a bar is 5/3 of a semibreve long, there are some tuplets over barlines that won’t be splittable cleanly.

(Talking of singers and counting, there’s a copy of a piece in Chichester Cathedral marked up by one of their singers. He’s labelled the three beats of a 3/4 bar as 1, 2, 3 and 4.)

I think this is always possible, without the “powers of two” restriction.

• Any note that can be written using tuplets and/or time signatures like 5/3 has a duration that is a fraction of a whole note, written as the ratio of two integers.
• Any arithmetic operation of fractions (for example to split the duration of a note across a barline) can only produce another fraction.
• You can express any set of fractional note durations as a tuplet, by putting all the fractions over the same denominator.

But whether this splitting is easier to read in a situation like the attachment is a different question entirely.

Of course there is no rational reason why notes should not have the durations in the ratio of the square root of 2 : 1, or pi : 1 (bad pun intentional!) but that’s beyond conventional music notation.

Thanks Rob.

Draw Free Rhythm Barline within Sibelius calls both the divided tuplets 7:4, like in the attachment. I think just that makes them easier to read. In general I’d prefer to see them both under a single 7:4 bracket. Easier still I think.

If you don’t tie over the barline and have a note somewhere that’s too long for the first bar, it’s only easy to read if the tuplet is one of these easy ones we’ve concocted. But if you have something where there aren’t seven semiquavers in a row all obviously drawing attention to how equal they are, and especially if there are tuplets nested inside, it could be very hard to know what to play.

Incidentally, I couldn’t play your 7:5 example however you present it!

Can’t work out how to upload an image at the moment and time is short but you can imagine it.

Attachment 1 is the way Draw Free Rhythm Barline in Sibelius splits Rob’s 7:5 tuplet. Attachment 2 is the way I’d prefer it.

In my (Lilypond) version, the 14:8 and 21:12 are both equivalent to 7:4, of course. I’m not sure that “7:4 32nd notes” followed by “7:4 dotted 32nd notes” improves the notation over “14:8 64th notes, then 21:12 64th notes”.

And the split version has the curious property that the notation for five equal notes is represented by “something in the time of four”.

It’s not hard using one hand for each rhythm on a keyboard - to paraphrase the advice of somebody who plays this sort of stuff professionally, “concentrate on keeping the metronome inside your head ticking evenly, and [after sufficient practice!] your fingers will follow your internal click-track automatically”.

The practice of allowing tuplets to carry slightly into the next measure and leave a gap is common enough that I would certainly want to have it as an option (even though it does make the mathematically anal part of me shutter).

The same notational style, however, appears in a lot of modern transcriptions of medieval and Renaissance music (“Mensurstricht” transcription), whereby as much as is possible, the full value of the note is given where it first appears, and ties across barlines are not used (see “Contratenor” of mm 1-2 of the first example). When a system break needs to occur often, the residual value is given in small parentheses (see systems 2-3, again Contratenor part).

(The placement of barlines only between lines is the only aspect of Mensurstrict notation that one of your competitors supports.)

This style of notation can occasionally be found in 19th c. editions as well, such as the augmentation dot substituting for the tie in the Bach Gesellschaft edition of the Musical Offering (m. 5-6 below).

My friends who work on new complexity music whom I shared this thread with (and who work on Lilypond) hugely argue for making Staff 2 default or at least supported.