[MEI-L] Example: [Tuplets and] non-integer divisions of the whole note

[Byrd, Donald A.]

Craig is absolutely right -- except he didn't put it strongly enough, 
for a couple of reasons. See comments below.


On Wed, 12 Aug 2009 16:40:37 -0700, Craig Sapp <craigsapp at gmail.com> wrote:

> Hi Perry,
>
> From a computational viewpoint, I cannot see how to extract the rhythmic
> information from the example encoding:
>
> <score>
> <scoredef key.sig="3s" meter.count="3" meter.unit="4">
>   <staffdef n="1"/>
> </scoredef>
> <section>
>   <measure>
>     <staff n="1">
>       <layer n="1">
>         <tuplet num.place="above" num.format="count" bracket.visible="false">
>           <note pname="a" oct="4" dur="8"/>
>           <note pname="c" oct="5"/>
>           <note pname="e"/>
>           <note pname="g"/>
>           <note pname="e"/>
>           <note pname="g"/>
>           <note pname="a"/>
>         </tuplet>
>       </layer>
>       <layer n="2">
>         <tuplet num.place="below" num.format="count" bracket.visible="false">
>           <note pname="e" oct="4" dur="16"/>
>           <note pname="d"/>
>           <note pname="c" dur="8"/>
>           <note pname="e"/>
>           <note pname="a"/>
>           <note pname="g"/>
>         </tuplet>
>       </layer>
>     </staff>
>   </measure>
> </section>
> </score>
>
> Either the logical duration of the <tuplet> or the <note> needs to be
> explicit,
> or the tuplet factor needs to be explicit.  For example: "7 in the
> time of 6" for
> the first layer. The "7" can be extracted (painfully) from the data, but the
> "6" cannot.  Relying on the logical duration of the <measure> will work in
> this particular case, but not in the general case. Suppose that you have:
>
> <measure in 3/4 meter>
>    <tuplet/>
>    <tuplet/>
> </measure>
>
> Who is to say that the first tuplet takes two beats and the second tuplet
> takes one beat, or vice-versa?

A great example, but even with one tuplet filling the measure, you 
can't always rely on the logical duration of the <measure>! There are 
many cases where it's very difficult for a program to know what the 
logical duration of a <measure> is. I just uploaded (after updating it 
to clarify this point) to my Examples folder a document, 
CheckMeasDurVsTimeSigNotEasyNEW.doc, that makes this point.

Also, I don't think "n in the time of d" (using n for numerator, d for 
denominator, like a fraction) is enough in the most general case! It's 
certainly not if they both have to be integers; consider a 5/8 measure 
with a duplet of two quarter notes, as in the Barber Piano Concerto. 
But there are also cases like a tuplet containing 7 dotted 16ths 
filling a bar of 3/4 and labeled "7 dotted 16ths = dotted half", as in 
the Carter Concerto for Orchestra. In other words, numerator 7 with 
duration unit of a dotted 16th, and denominator 1 with duration unit of 
a dotted half note. Does MEI have a way to handle that? The Byrd & 
Isaacson paper I've mentioned too many times :-) discusses these and 
other examples in detail, and says "In terms of the confusion they 
cause -- particularly with respect to terminology -- tuplets are in a 
class by themselves"; I still think that's true. (Full disclosure: 
"duration unit" isn't a standard term; I think Eric and I invented it.)


--Don

>
> [---- SNIP ----]
>
> -=+Craig
>
>


--
Donald Byrd
Senior Scientist
Adjunct Associate Professor of Informatics & Music
Indiana University, Bloomington