LilyPond: tuplet bars don't seem to match time used

Question

Please take a look at these three snippets, from a piece in 4/4 time.
LilyPond 2.24.3 via Frescobaldi in MacOS.

1. e8 (b e4~ \tuplet 5/8{ e32 d cis d e} d8\noBeam) r8
   \acciaccatura{fis8} fis'2~ fis16 fis(g fis e[ d) cis-- d--]
   

   

2. e8 (b e~ \tuplet 5/4{ e32 d cis d e} d4) r8. fis16
   \acciaccatura{fis8} fis'2~ fis16 fis(g fis e[ d) cis-- d--]
   

   

3. e8 (b e~ \tuplet 5/8{ e32 d cis d e} d8\noBeam) fis16 fis16 fis16 fis16 fis16 fis16 
   

   

The top and bottom ones are the ones I don't understand. The middle one is how I expect beams to be presented, i.e. five notes where four 32nd notes are "normal", beamed as 32nds.

The top & bottom samples are also beamed as 32nds, but as shown by where the measure break occurs, are "calculated" internally as five 16th notes.

EDIT I would expect them to be beamed as 16ths in this case. Is LilyPond fouling up or have I failed to take notice of some other note-length command?

Answer 1

Maybe I'm not understanding the question correctly. Is your problem contained in the fact that the quintuplet of 32nd notes (that should take up a length of a 8th note in total) is taking twice as much in the top & bottom examples?

If so, then your problem is in the fraction supplied to the \tuplet command. Observe it is 5/4 in the middle snippet and 5/8 in the top and bottom ones. This makes the tuplet twice as long as it should have been.

There is an older command called \times that does just what it says: \times 4/5 { a b c d e } will make the things inside the brackets last 4/5 of the time it would have lasted normally. Similarly, \times 8/5 { a b c d e } will make them last 8/5 of the time they would have lasted normally.

The \tuplet command does just the same thing but uses a reciprocal fraction, so \tuplet X is equivalent to \times 1/X. That's why using 5/8 in the top & bottom examples will make the tuplet last twice as long.

Lilypond will happily let you use any fraction you want, and there is an option (I can't remember how to do it though) that will put ratios above your tuplets instead of just one of the numbers. However, as long as you use the "traditional" tuplet notation, the cases with the same numerator cannot be told apart in the score.

In order to make sure your tuplets are the "traditional ones", you should make sure the fraction you supply to \tuplet is greater than 1 and less than 2 (or, if you use \times, it should be between 1/2 and 1).

EDIT: If you want Lilypond to engrave sixteenths, you must enter sixteenths. There's no other way about it. The \times and \tuplet commands are more akin to the * "operator" — that too will make things take up more time but it won't make them look any different. Just as a32*2 means "draw a 32nd note but make it last twice as long", \tuplet 5/8 {a32 ...} means "draw 32nd notes, make them last 8/5 times as long and put a bracket with a number on top of them".

Answer 2

So this is a somewhat music philosophical thing. What is a tuplet? Essentially a tuplet is section which is rhythmically divided in a different manner than the general mode of the piece. And the Lilypond syntax can be read as exactly that: \tuplet 5/4 can be read as take 5 notes and put them into the space that would else be occupied by 4 notes. Except in Lilypond it is even more generic. In Lilypond \tuplet 5/4 is more or less a verbose way of \scaleDurations 4/5. This means that in Lilypond we can have partial Tuplets such as this

{
  \time 2/4
  8 8 8 8
  \tuplet 3/2 4 {
    8 8 8 8 8 8
  }
  \time 2/6
  \tuplet 3/2 4*2/3 {
    8 8 8 8
    8 8 8 8
  }
  \time 2/4
  8 8 8 8
}

But most of the time we’d read a m/n tuplet as divide the space of n units into m units.

So what is the difference between a 5/4 tuplet and a 5/8 tuplet? Well the first one speeds up notes slightly, while the latter slows down significantly. So clearly if we have a quintuplet there needs to be a "conventional" reading (else it is also common to specify the tuplet ratio instead of just a number).

Take for example duplets, which are commonly found in 6/8. Traditionally such duplets would be notated like this:

{
  \time 6/8
  8 8 8 8 8 8
  \tuplet 2/3 4. { 8 8 8 8 }
}

Now, there are some people who like to promote the convention that tuplets only speed up, so m/n with m > n. Then this would need to be notated as

{
  \time 6/8
  8 8 8 8 8 8
  \tuplet 2/3 4. \scaleDurations 1/2 { 4 4 4 4 }
}

Which in my opinion looks totally weird (also is means things like 7-tuplets are really weird).

I suppose a more conservative convention would be to try to keep the ratio close (5/4 rather than 5/8), and in case there are multiple acceptable ways try to preserve the overall beat/subbeat structure. E.g. in 6/8 it makes sense to displace three 8ths by two 8ths, not to displace one dotted 4th by two undotted 4ths. But in 3/4 in totally makes sense to displace three 4ths by four 4ths rather than displacing three 4ths by four 8ths.

In fact if you use unconventional tuplets you can even do stuff like this:

<<
  \new Staff { 4 8 8 4 16 16 16 16 4 }
  \new Staff { 4 \tuplet 2/1 { 4 4 } 4 \tuplet 4/1 { 4 4 4 4 } 4 }
>>

So essentially: A tuplet does not change the beaming. The two cases you have are different tuplets, where one is canon (5/4) and one is a bit uncommon (5/8).