# Does this dectuplet make sense?

I recently encountered this dectuplet as you can see in the picture attached. To me this doesn't make sense. This makes 10 16th notes instead of 4. This reduces the notes' lentgh 2.5 times.

Should one not write this as 10 32th notes instead of 8? That would make more sense to me. Then the notes' length would only be reduced 1.25 times. Or better even: two quintuplets of 32th notes.

Moreover, this notation makes it impossible to determine how long it should be if not for the base notes and the rest of the measure. Say for example you use this in an anacrusis, without the base ...

Theoretically, you're right, I think. Strictly, the example you show should be read as "play these 10 notes with the same duration that 8 normal 16th notes would have", i.e., the total duration of a half note, which does not fit the meter.

This may be a typesetting mistake, or a simplification for readability (a lot of beam lines in this case don't give a lot of useful information and clutter the score). I'm not saying it's right, but it's quite clear in this presentation what you're supposed to do.

BTW, looking at the pencil markings, it should be noted that the composer (if that's what the composer actually wrote) chose to write a dectuplet and not two qintuplets. That division may be useful when learning the piece, but care must be taken that the 10 notes sound as a continous fluid phrase, not as two separate phrases.

This isn't going to be played with mathematical precision. Along with the "smorzando", the choice of note value indicates a relaxed tempo related to the preceding 16th note, rather than something twice as fast. As you say, there is plenty of information in the rest of the notation.

• True. And probably in this style of music you will long have figured out how to play this before you perform it. But if it wasn't during a smorzando and someone wanted to play it on sight, it might confuse him enough for him to lose the correct tempo. – Lu Kas May 25 '16 at 14:45

In the fourth bar of the same Chopin prelude you also find something equally suspicious from the point of view of modern notation practice. There it's seven notes written with a single beam even though their duration is just a quarter note. You'd understand it from context there as well.

Septuples can be confusing, and many people mistakenly would write, say, a septuple over a half note with double beams because each note's duration is so close to a 16th note.

But the rule would be to have the number of beams that would make the tuple, if read as 8th, 16th, 32th (etc) notes longer than the timespan it fits into, but shorter than the double timespan. (Maybe this can be stated much more clearly by someone?)

• I didn't see that septuplet further in the prelude (it isn't my sheet music), so there it is actually the same "mistake"? I agree that a tuple is always about more notes than the normal notation. So in the example you describe it should indeed be eighth notes since it is 7 instead of 4 and should not be 7 instead of 8. – Lu Kas May 25 '16 at 15:00

What Chopin wrote: [from http://www.chopinonline.ac.uk/iip/iipsrv.fcgi?FIF=jp2/ocvejp2-proc/28/28-A_PLWNn_Mus93/32/32.jp2&cnt=1&QLT=100&RGN=0.338039215686,0.405726076864,0.23137254902,0.197317513541&CVT=JPG]

It's `9` underneath, but there are ten notes and editions after (apart from Fontana's copying) show ten
(see Online Chopin Variorum Edition at this bar, bar 79.

My suggestion is that it is in fact 9 and the end three notes are a tuplet nested inside the 9.

Separately, `9` as a division is extremely unique where it can be expressed with two beams and also with three beams. Elaine Gould, 2011, Behind Bars, p.203, shows this in the table below:

Here is how I suggest it should be written:

And this is the pedantic way to write it out (which I would really doubt it existing in a Chopin holograph or any edition):

On slow agogé it makes sense. But there is a big error in the score! the dectuplet must be formed by 10/32, NOT by 10/16 hehehe