Apr 11

IMSLP – sheet music online

IMSLP is a huge repository for public domain sheet music, which is wonderful if you’re looking for older music. Recently their servers had been down, due to a spurious legal challenge from the Music Publisher’s Association. Now they’re back up and running again, and you can find that there’s more than just old music on their servers! Luckily, there are some living composers who have chosen to post their works under Creative Commons licenses, giving us access to newer scores.

Michael Edward Edgerton is one of these living composers who posts his own scores on IMSLP. He is also a researcher into extended vocal techniques, and his works explore a kind of vocal parametric decoupling which includes precise notation of intraoral articulation points for consonants. Cantor’s Dust and Anaphora are two solo voice works worth checking out, if you’re interested at all in the possibilities of notation for vocal music!

It’s hard to know what is lost and what is gained in the move of parametrically decoupled actions from the dramatic choreography of the arms of string players to the movements of the tongue, vocal tract, and larynx of the singer, hidden inside the body. Of course the sonic exploration remains equally valid, but the visual performative intensity is occulted. We are presented with a kind of visual mystery in the performance of any vocal music, where the physicality of sound production is mostly interior and unknowable.

Apr 11

Just Intonation

Just Intonation is the tuning of pitches related by whole number ratios. The following will serve as a brief overview and introduction to the system’s theory and practice. The harmonic series is a good place to start when discussing Just Intonation (henceforth JI).

A harmonic series on low C

Partial numbers inside the staff, frequencies below

From a fundamental frequency (here the low C at ~65.4 Hz), the harmonic series ascends in multiples. If we refer to the partials of the tone, rather than the overtones, we can more easily see the math behind the present frequencies. Numbering the fundamental frequency as the 1st partial, the 2nd multiplies the frequency by 2, the 3rd partial by 3, ad infinitum. What does all this have to do with JI? JI deals in tuning intervals by simple whole number frequency ratios, and since we have demonstrated that the number of a partial is a multiplier of the fundamental frequency, we can use the harmonic series to find the intervals of these ratios. 2/1 is an octave, 3/2 the perfect fifth, 4/3 the perfect 4th, 5/4 the major third, 6/5 the minor third. What is significant about these intervals is that they deviate from the tempered intervals one finds on the modern piano. The simpler ratios sound beatless, and ‘pure’. If you are a choral singer or brass player, you probably are already used to finding this beatless sound by tuning wider fifths and lower thirds and sevenths in chords.

JI systems are sometimes referred to as “x-limit” systems, where x is some prime number. For example, a 5-limit system includes no prime numbers higher than 5 in any ratios, allowing for pure major thirds, but not true septimal or 7-limit consonances. 3-limit tuning is often referred to as Pythagorean tuning, and is composed entirely of just fifths. 5-limit tuning can approximate the major-minor system of Western music very well.

A few notable composers using JI

Americans: Ben Johnston, Harry Partch, LaMonte Young, James Tenney. Europeans: Gérard Grisey, Georg Friedrich Haas, György Ligeti. This is of course, no exhaustive list of composers, but a guide for the novice to what might be more familiar music, and an easier entry into the system. For a further discussion of the motivation to use JI, see Colin Holter’s fantastic paper “The Spiritual Construction of Tuning in American Experimental Music” at the Search Journal.

Notation of JI

The notation of JI varies depending on the composer and the circumstances. Ligeti often notated JI intervals simply by the fundamental on which the horn was to play (as in his last work, Hamburg Concerto). James Tenney sometimes notated JI intervals by writing cents deviation from ET. Perhaps the most exhaustive and most widely embraced system yet devised is Ben Johnston’s. Beginning from the assumption that the C Major scale is to be built from interlocking C F and G major triads, all tuned 6:5:4, Johnson introduces novel accidentals to shift these notes to different relationships. For example, in his C major scale, the supertonic D is ~4 cents higher than ET, while the A is ~16 cents low. If we are to use a properly tuned triad based on D, this requires an accidental to raise the A approximately 21 cents, Johnston’s +. Alternately, the D could be lowered, using -. The interval expressed by + or – is called the syntonic comma (81:80), and is the difference between a Pythagorean (or 3-limit) major third (81:64) and a 5:4 (5-limit) major third. Johnston’s system of accidentals continues similarly, with each successive accidental expressing a kind of fundamental shift related to a higher prime ratio.

Learning JI

Just Intonation tunings appear in traditional drone-based musics, like North-Indian Classical music, and can be easily practiced over a drone. If you play any string instrument, you can accompany yourself with a drone for practice, use a recording of a tambura, or even an electronic tone (preferably one rich in harmonics). Singing a just interval correctly feels ‘anchored’ in the fundamental tone and its harmonic spectrum. Aside from going by feel, if you are a string player of any kind you can also use the open harmonics of a string to learn simple just intervals. Being a computer enthusiast, I prefer to practice my microtones with the aid of software. Rote learning is the basis of the oral traditions that function within a JI framework, and is an indispensable tool. I use a program called Scordatura for the playback of JI microtones, and it is extremely flexible. Using CSE, a companion program to Scordatura, I can designate tunings wholly via ratio from any given fundamental at any tuning. It has made the task as simple as entering ratios in scalar order, and assigning them to keys on my midi keyboard. From this point on, I work by transcribing the pitch notation of the score to the re-mapped microtones of the midi keyboard (one octave of pitch extended over more than 4 octaves of keyboard (!) in my most recent JI undertaking, Johnston’s arrangement of Partch’s Barstow). I have a similar setup prepared for learning the tuning of Randy Gibson‘s upcoming work for ekmeles.

Of course, this is but a simplified overview – there are manifold internet resources for learning more about JI theory and practice. I’m happy to address questions or requests for elaboration on any of these points (and to accept corrections from those more deeply involved in JI than I). But if you’re interested, I would recommend as a first step getting your hands on a CD – or better yet, attending a concert – featuring JI music and hearing the difference a few cents here or there can make! Ben Johnston’s fourth String Quartet is a melodic and beautifully lucid introduction to JI.

Feb 11

Complexity and failure

“How joyous the notion that, try as we may, we cannot do other than fail and fail absolutely and that the task will remain always before us, like a meaning for our lives.” – Donald Barthelme ‘Nothing: A Preliminary Account’

The physical manifestation of the fear of failure is surely an element in the performative practice of complex music. Concentration on many levels of notation flying by at breakneck speed almost guarantees a slipup here and there. Is learning and performing a complex score really then a Sisyphean task? I would like to argue that complex scores require a redefinition of, or at least a reconsideration of the idea of failure in performance. A certain kind of failure is a necessary and aesthetically important part of all performance. The details of just how we fail and why are worth examining.

Firstly I would propose that the moral character of the performer is engaged by complex scores. Acknowledging the inevitability of failure does not absolve the performer from the responsibility to realize the score as faithfully as possible, using all the tools at his disposal. Likewise, if the composer intended for his work to be realized graphically or approached from a quasi-improvised angle, one would hope he would be clever enough to use notation which suggests as much, rather than the extremely detailed instructions we find in many complex scores.

The information density of complex scores represents in some ways not an evolution and continuation of notational practice, but a break which implies important performative consequences. The performer is transformed from an imperfect conduit for the composer’s ideal vision, into an integral and indispensible contributor to the work.

I recently read an article in Perspectives of New Music entitled “Re-Complexifying the Function(s) of Notation in the Music of Brian Ferneyhough and the ‘New Complexity,’” written by Stuart Paul Duncan. My writing here is in many ways a response to that article. It got me thinking about what the article refers to as the “High-Modernist” model of musical performance, and the break from that tradition that many complex scores represent. Some people take the progressive-historicist view that music notation, beginning at first as mere mnemonics, moving to a two line, four line, five line staff, specifying instrumentation, dynamics etc., moves along a straight line towards its goal, which is the ultimate specification of all parametric information. Certainly scores have become more and more prescriptive as time has gone on, but, as Duncan argues, not always for the same reasons. The “High-Modernist” model of notation and performance might be defined as a direct and absolutely prescriptive communication from the composer to the performer. The score is the work in an ideal form, towards which each performer strives; what is desired above all is accuracy and fidelity. With the increasing density of information communicated by complex scores, it’s easy to see how this kind of accuracy becomes more and more difficult, or even beyond the capacity of the performer, if not the instrument itself.

What to make then, of this extreme density of information? After all, if the composer is after such a complicated web of musical ideas, he could just as easily program it into a computer, rather than spend the time communicating it to us fallible human performers. Paradoxically, the completely prescriptive nature of complex scores involves the performers in a deeper way than a more traditional “High-Modernist” score might. In addition to the hours and hours of engagement with the score required by complexities of notation, rhythm, pitch, or other parametric information, which deepen the performer’s relationship to the work, the conflict between the various physical performative demands requires that the performer function as a kind of filter. If something really is “impossible” as written, whether because of context, or simply the performer’s human limitations, in some cases the performer simply must make a choice of what to do, and what not to do. Conflicting and competing physiological demands in the score can also create unstable and unpredictable sounds. Is this a kind of fakery that proves the illegitimacy of complex notation? I think not. Any human performance contains some artifact of that performer’s humanity; complex music highlights these artifacts, and elevates them, elevating thereby the performance to stand with the score as more of an equal. The late great Milton Babbitt wrote that his scores are indeed intended to be precisely realized and perceived by some ideal performer and ideal listener. In terms of information density, his scores are simpler than say, Ferneyhough’s, but certainly not simple. Does this mean that any imperfect performance (read: at a high enough resolution, absolutely every performance) of his music is a failure? Anyone who has had the joy to hear great interpreters perform his music knows that it most certainly is not. Surely, something about the involvement of actual human performers is necessary for the success of the musical enterprise, despite the fact that an objectively perfect performance which reflects in every way the notation is, depending on your view, either exceedingly rare, or totally impossible. A fascination with this failure and its subtleties is at the core of what we find appealing in any musical performance; the notational practice of complex scores only brings our attention to that failure’s inevitability.

I’ll leave the last word here to Cage: “Composing’s one thing, performing’s another, listening’s a third.”

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.