# Four dotted sixteenths in a triplet

The following excerpt is from a piece called Brincado by the Brazilian composer Alberto Nepomuceno from the collection 5 Little Pieces for the Left Hand (imslp)

How should I count this?

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That is indeed baffling and extremely unusual. –  Wheat Williams May 1 '12 at 12:37
Maybe it is the software tool that he is using that tries to be too smart? I guess the rhythm in another voice may have disturbed this one, say if another instrument does play a triplet. –  Gauthier May 2 '12 at 7:52
@Gauthier I doubt it's a software problem - Nepomuceno died in 1920. As for other parts interfering - the piece is written for left hand only! –  Widor May 2 '12 at 10:25
This is odd-looking, but I wonder if the composer was implying a finger-pedaling and to play the dotted-triplet-16ths as a legato and blended into each other without the use of any pedal? –  Retired_Admin Oct 9 '14 at 20:29
@Widor True, but this typesetting is from 2007. The best answer to "why?" would probably be to contact Jayme Mendonça Luna Filho who set this edition and ask him directly... –  NReilingh Oct 9 '14 at 20:57

As far as I can tell, the composer's either having a mathematical in-joke, is trying to be "too" clever, or he's just a little confused.

Either way, the short answer is that you should play/count that passage in exactly the same way as if the semiquavers (16ths) weren't dotted, and the triplet marking didn't exist.

Why? Well, let's look it it mathematically if not musically (I'll use British note names if that's ok - it's less confusing when talking about quantites and note lengths in the same sentence):

The piece is in 6/8 time and 4 of those 6 quavers are accounted for prior to the dotted semiquavers:

So, the 4 dotted semiquavers are representing the last 2 quavers' worth of time in the bar.

The triplet marking tells us that instead of just 2 quaver divisions, we need to squeeze 3 into the same amount of time - in other words, we'd expect to have to use 6 semiquavers (= 3 quavers).
The effect of squeezing three of anything into the space of two, is that all three get reduced by a third - or multiplied by 2/3 if we're being mathematical (and we are)!

However, we only see four semiquavers in the score - but all 4 of their lengths have been increased by half again (that's what the dots mean).
Increasing "by half again" is the equivalent of multiplying by 1.5 - and 4 semiquavers x 1.5 = 6 semiquavers!

To put it even simpler, all that's happened is that we've had to reduce our quaver lengths by a third (observing the triplet marking), then immediately increased them by 50% (as per the dotted notation).

2/3 x 1.5 = 1 - in other words, we end up with exactly what we started with. The fact that we're notating the 'squeezed-then-stretched' notes using dotted semiquavers is just a distraction in trying to understand what's going on here.

I can't work out whether I think this composer's a comedy genius or the musical equivalent of the nerdy kid at school who annoyed everyone by trying to be a little too clever.

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Nepomuceno does the same thing in measure 41 and basically the same thing again in measure 20. There is a dotted eighth and two dotted sixteenths all in one triplet which can be simplified to an eighth and two sixteenths. –  American Luke May 1 '12 at 18:04