Rhythmic Possibilities

[ibanezmonster]

I've had this idea in mind recently- splitting tuplets. Can anyone find any examples of this? I know of Boulez and Ades' weird time signatures which are somewhat like this (still trying to figure them out), but I was thinking more of the possibilities of this idea in a straightforward overall meter, like 4/4.

So the most simple example I can think of is having the value of one triplet, playing 4 16th notes and then the value of two triplets. Together it adds up to 2/4 (3 triplets = one quarter note). Rhythmically, I don't think this is even possible to notate in music programs without some sort of workaround (I probably don't even wanna know what you'd have to do to get this).



2    [3]    (16ths)     [3]
    --o----o-o-o-o---o--o------|
4 

instead of

2         [3]             (16ths)     
    --o--o---o------o-o-o-o--|
4 




And of course, this idea could be expanded upon to create all sorts of musical stutterings. 

[Luke]

Just checking in to keep an eye on the board as I do every week or two at the moment, until time permits me to return properly, but I can't let this one pass, because it's the kind of topic I love!

I remember having this exact idea when I was about 14 or 15 - I know it was then because I recall showing my piano teacher at the time the little composition which resulted, though I don't know where the piece itself went. I recall that the left hand started with a single quaver/eighth note triplet, continued in straight quavers/eighths for a couple of beats, and then picked up the remaining two triplets at the end of the bar. Something like that.

As you say, there are examples in Boulez, Ades, and also e.g. the new complexity guys. Also irrational bars, of course, which are fun. Also, Carter-style metrical modulation gives us what is effectively this sort of thing all the time. But in straightforward 2/4 as you describe, I suppose, the easiest thing to do would be to convert things to 6/8. Then your example, which I guess is:

2/4    t qqqq tt (where t=triplet 1/8 and q=1/16)

would of course become

6/8 8 q.q.q.q. 88 (where 8=1/8 and q. = dotted 1/16)

[ibanezmonster]

Awesome, never thought of notating that way. I might try to think of some more complex examples eventually to see if you can do something similar.

[(poco) Sforzando]

https://www.youtube.com/watch?v=1a7fyKqX5Wg

[(poco) Sforzando]

Forgive me if I can't make heads or tails of either of your graphic notations. Must be the dementia of old age.

Don't know if this will help, but from the classic literature, perhaps the most unusual tuplet I've ever seen is from Wagner's Goetterdaemmerung, Act Three where the Rhinemaidens are warning Siegfried about the power of the ring. One measure in 3/4 is notated quarter note, and then a triplet equal to a half note consisting of a dotted quarter, eighth, and quarter. Now why do it this way, when the dotted quarter under the triplet is identical in rhythmic value to a standard quarter, and the measure is really nothing more than quarter, quarter, and quarter-note triplet consisting of an eighth and quarter?

(If that's not clear from my description, see page 258 from the score:
http://www.dlib.indiana.edu/variations/scores/bhr1272/large/index.html)

I've concluded that Wagner's reason for his notation lies in the prosody. The words are "Wir weisen dich Wahr!" If this were notated the "simpler" way, the singers would stress the weak second syllable from "weisen." And Wagner is very sensitive to the stress rhythms of the German language (all of Beckmesser's "mistakes" in Act Two of Meistersinger consist of emphasizing the wrong syllables).

[Luke]

Forgive me if I can't make heads or tails of either of your graphic notations. Must be the dementia of old age.

Don't know if this will help, but from the classic literature, perhaps the most unusual tuplet I've ever seen is from Wagner's Goetterdaemmerung, Act Three where the Rhinemaidens are warning Siegfried about the power of the ring. One measure in 3/4 is notated quarter note, and then a triplet equal to a half note consisting of a dotted quarter, eighth, and quarter. Now why do it this way, when the dotted quarter under the triplet is identical in rhythmic value to a standard quarter, and the measure is really nothing more than quarter, quarter, and quarter-note triplet consisting of an eighth and quarter?

(If that's not clear from my description, see page 258 from the score:
http://www.dlib.indiana.edu/variations/scores/bhr1272/large/index.html)

I've concluded that Wagner's reason for his notation lies in the prosody. The words are "Wir weisen dich Wahr!" If this were notated the "simpler" way, the singers would stress the weak second syllable from "weisen." And Wagner is very sensitive to the stress rhythms of the German language (all of Beckmesser's "mistakes" in Act Two of Meistersinger consist of emphasizing the wrong syllables).

I'm sure that is definitely the reason Wagner did this, and, indeed, if one imagines the alternative, one can see how misleading it would be. Even if the passage were purely instrumental, I think the same would apply.

A passage which to my mind is equally subtle is on page 245 of this score http://javanese.imslp.info/files/imglnks/usimg/5/50/IMSLP65456-PMLP49353-Janacek_-_String_Quartet_No._2__score_.pdf (it's from a larger volume hence the high page number; the passage in question is in the first movement). The passage could have been written in 2/4, or alternatively the duplet crotchet here could simply be dotted as in 6/8 - but both would be misleading because they would suggest a simple two-in-a-bar where in fact there is (or should be) an underlying three-beat metre being felt here (when the passage comes earlier it is over a two-note oscillating quaver pattern which puts it firmly in 3/4). Crotchet-tied-to-quaver would be better as it would imply the syncopation in 3/4, but perhaps would imply that syncopation too much - after all, the smooth, uninflected line does not suggest that kind of rhythmic upheaval, temperamentally speaking. Somehow the duplet, though in theory it is just as suggestive of a two-beat bar as a dotted crotchet would be, suggests the slight syncope just enough but not too much. But I'm not sure how, except that in its visual oddness it implies something slightly across-the-beat, and in its rhythmical evenness it implies something simple-and-plain. It's an intuitive notation, I guess, of the sort Janacek loved.

(Ives is another composer whose intuitive notations I adore, btw - they are there all the time, of course, but this sort of thing: http://javanese.imslp.info/files/imglnks/usimg/1/18/IMSLP53902-PMLP09680-Ives-ConcordSonata1921.pdf bottom of page 8 - is wonderful!)

PS Hi Larry. Please forgive my quaver/crotchet nomenclature. I know you hate it!

[jochanaan]

As a performer, my thoughts immediately turn to, "How do I count this?  How do I PLAY it?" But it can't be much harder than the trumpet rhythm in Bruckner 2, or some of Brahms' or Stravinsky's or Varese's patterns, now can it?

[ibanezmonster]

I have so much more to say about this... may be a little at a time, though, so stay tuned.