Re: different rhythmic units for tuplet's numerator and denominator

[Uri Sala]

It is a bit more convoluted than that. I will try to make myself clearer:
I want to write 3 against 5. In this case, since 3 is smaller than 5, it has to use a rhythmic unit twice longer than the unit associated with 5. Let's be over-explicit and call this "3 equally spaced attacks within the duration of 5 sixteenth-notes." Well, I will argue against most people and most notation manuals and most modern scores that the only correct way to notate this is 3 eight-notes against 5 sixteenth notes. Now, neither sibelius nor ENP nor finale allow me to do this, since they force upon the editor the assumed notion that nominator and denominator in a tuplet use the same rhythmic value. This axioma makes it impossible to correctly notate all possible complex tuplets (with non-binary denominators), and makes the construction of an algorithm that translates proportional notation (a la ENP) into lilypond code incredibly convoluted. I thought lilypond was different - in that I could stipulate different values for nom and denom - but I am not sure now. 

Many people would argue that you can use the same value for both, since 3 is so close to 5. But that makes your run into a contradiction. The only way one can stipulate a general and infallible rule for writing tuplets is that a tuplet is the insertion of a certain number of rhythmic values into a space that is smaller. Or, to put it another way, a tuplet - a correct one - is a compression of the duration of a rhythmic value. Very easy to prove: how would you write 6 against 5 sixteenths? Well, just like that. (times 5/6 {c16 c c c c c}. So, if we write 3 against 5, the value that those three notes take should be 8th notes, because all we would have to do is aggregate each 2 sixteenths of the 6:5 into eighth notes. But remember, I want still a total duration of 5 16ths!! So writing times 5/3 {c8 c c} will result in a tuplet twice as long in duration than what I want, since lily thinks that I want the duration to be 5 eighth notes. I have to be able to tell lilypond that I want 3 eighth notes in the space of 5 sixteenth notes (and that is just one of many examples. Trying to to 3 against 7 is even more complicated since the duration is more than twice the attack. In 3 against 7, the three should be notated with quarter notes!). Hope I made myself understood now.
I hope this does not turn into a discussion of the way to notate tuplets, since there is only one that is actually inequivocal and consistent. Unfortunately no editor allows one to produce it, which is a very disturbing fact. 
Could lilypond be the one?

cheers 
uri

On Mon, Jul 7, 2008 at 6:49 PM, Reinhold Kainhofer <address@hidden> wrote:

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Am Montag, 7. Juli 2008 schrieb Uri Sala:

> The only way one can write a tuplet such as "3 notes in the duration of 7
> 16ths " in a consistent and correct way with a general law of tuplet
> notation is to assign the rhythmic value of a quarter note to the 3 notes,
> so that the total value is of 12 16ths (the first rule of a correct
> treatment of tuplets is that the tuplet is of more value than what it
> substitutes.
> Is it possible to assign different rhythmic units to the numerator and the
> denominator of a tuplet?

I'm not sure I understand your question here... Do you mean something like
\times 12/16 {..} ?

> Is it possible to show those rhytmic figures next
> to each?

You mean you want 16:12 to be displayed instead of 16?

 \override TupletNumber #'text = #tuplet-number::calc-fraction-text

Cheers,
Reinhold

- --
- ------------------------------------------------------------------
Reinhold Kainhofer, Vienna University of Technology, Austria
email: address@hidden, http://reinhold.kainhofer.com/
 * Financial and Actuarial Mathematics, TU Wien, http://www.fam.tuwien.ac.at/
 * K Desktop Environment, http://www.kde.org, KOrganizer maintainer
 * Chorvereinigung "Jung-Wien", http://www.jung-wien.at/
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