Jan 11


In drafting my last post on tuplets, which was mainly focused on ways to approach and decipher rhythmic difficulties, I got to thinking about the issue of notation in general. What are the purposes of notation? They are as manifold as the intentions of the composer, I suppose, but it might be interesting to start a discussion on what notation is and can be, especially in new music.

Why notate a certain passage a certain way? Some composers represent the sounds to be made or gestures to be enacted with mathematical precision; others might choose a graphical representation of the same event. Even if these two imaginary composers were presenting precisely the same musical event with the same intended result, the difference in notation will engage the performer differently, and result in a different performance, whether sonically, physically, or both. The form of the notation, not only its content, has a significant effect on the perception and performance of the music.

While it’s perhaps more easily seen in our imagined contrast between Mr. Nested Tuplets and Mr. Space=Time, it’s worth reflecting backward into the history of notation to see this as a more universally applicable idea. Anyone who performs Renaissance choral music from modern editions has to learn to ignore the implications of the modern addition of the barline when performing.  Similarly, performing Gregorian chant from neumatic notation and a 4-line staff is a completely different experience than reading modern notation of the same works.

Engagement with notation itself can be part of a method of constructing a work. Feldman’s manuscript scores which lack vertical synchronization, with differing time signatures occupying the same space on the page, are a lovely example.

What are your favorite examples of conscious and effective, creative, purposeful, obtuse, or ridiculous uses of notation? I’ve always loved Cage’s “Number Pieces” for the stark clarity of the single column of often single notes, and the way that the page reflects the same austerity as the music. Xenakis’s scores, (e.g. Pour Maurice) through their visual architectural rigor, manage to project a visceral humanity, thanks partially to an encounter with the impossible, the effect of which I’ll be addressing in an upcoming post on complex scores.

Jan 11

Huddersfield Contemporary Music Festival

We’re in the midst of BBC’s Hear and Now broadcast of highlights from the Huddersfield Contemporary Music Festival. Keep checking back to see when new episodes are available online, but right now it’s a concert of “theatical music” including pieces by Tom Johnson, Jennifer Walshe, and Mauricio Kagel (his fantastic pastoral Kantrimiusik). We’re also especially looking forward to the concert featuring works by Timothy McCormack and Peter Ablinger.

Jan 11


No, we’re not discussing old music here (not right now at least), but a great way to find new music. IRCAM’s fabulous database BRAHMS (which surely stands for something…) has recently gotten a facelift, but has luckily retained its incredibly useful functionality.

With a rudimentary knowledge of French (or google translate) you can use the œuvres par genre search to find repertoire for precisely the instrumentation you need. While the database can’t claim to be exhaustive, it does seem to contain some information not to be found elsewhere. The works pages also often contain links to the Contemporary Music Portal, where you can hear excerpts of unpublished concert recordings.

Jan 11

Tuplets and polyrhythms

A section of John Cage's "Living Room Music" which features quintuplets

How do I do this accurately at a slow tempo?

5 for 4 over a full bar of 4/4 at quarter=60? How do you do anything but fake that? All it takes is a little math! Slow tuplets can be a real killer, and if you try to perform them like you would an eighth note triplet (probably by feel), you’ll be all over the place. The least common multiple is your friend! In the case of our example (from John Cage’s Living Room Music, if you’re playing along at home), that would be 5×4 = 20. This number is the number of even pulses the bar is divided into that can accomodate both the quintuplet and the normal quarter note pulses. We could also have come to this from another angle: if the rules and standards of notation are preserved (tuplets over 3 beats need to have dots. Very few composers follow this standard; Carter does), tuplet notes will subdivide just like normal ones. This means a quintuplet quarter note split into 4 will yield 4 quintuplet sixteenth notes, just like its non-tupleted cousin will split into 4 normal sixteenths. Each normal quarter note in the bar could be divided into 5 quintuplet sixteenths. Either way we get there, 5×4 or 4×5 results in 20 quintuplet sixteenths, four of which add up to a quintuplet quarter. Knowing this, we can re-notate the rhythm as follows.

The quintuplets renotated

First the pulse, subdivided by accents, then written with ties

Now instead of a mysterious 5 floating somewhere in the bar we have attacks in relationship to the quarter note pulse, easily realized with a facility in subdivision. The purely mechanical accuracy of this method is, in many cases, only a first step; ideally, a tuplet like this should be realized without the syncopation accents implied by the re-notation. When you know exactly where each note lands in relation to the regular pulse of the piece, you can perform the tuplet smoothly, knowing proper points of reference throughout.

Any interaction of pulses can be rationalized in this manner – a more complicated example yielding a similar method: 5 for 3 over 3/32 in Aaron Cassidy’s I, purples, spat blood, laugh of beautiful lips. We can use our knowledge of the standards of tuplet notation to find how the pulses interact. First, we can imagine each iteration of the the 5 over 6 to have dots, which would make the first note of the quintuplet 9 pulses long, and the second note 6 pulses long. This 15 part division of the bar is in fact the LCM, allowing us to easily place the 32nd note every 5 pulses (15/3) and the 32nd note of the quintuplet on the 10th iteration of this pulse, leaving us with attacks on iterations 1, 6, 10 and 11 of a 3/32 measure hypothetically subdivided by 15 128th note quintuplets!

The same method can be used in the abstract to learn a polyrhythm. What does 5 over 3 in general sound like? Find the LCM (15), write out the digits 0 – 14 on a piece of paper, and circle every multiple of 3 and put a square around every multiple of 5. Following the numbers as a regular pulse, tap both hands at 0, the left at circled numbers and the right at numbers with a square. Voila, 5 over 3, mathematically done! Practice feeling each number as the ‘main pulse’, and each as the ‘cross rhythm’.

Two ways of feeling a 5:3 polyrhythm

Two ways of feeling a 5:3 polyrhythm

Generally, feeling the higher prime as a pulse will be easier, as it will feel subdivided by a lower prime. Take the above example: the 5/4 measure requires accurate placement of only triplets, while the 3/4 measure would require quintuplet level accuracy. An ability to shift between the two feels can help with accurate performances of polyrhythms and tuplets.

Jan 11

Neue Vocalsolisten concert recording

You can hear a full concert recording of Die Neue Vocalsolisten at Dutch Radio 4’s website, including some works that have yet to be released on CD. A real treat! I’m especially enjoying Karin Haussmann’s Klage right now.