Intrepid soprano Christie Finn has written a lovely blog post about her relationship to absolute pitch and the tuning fork, specifically in our work on the upcoming Quando Stanno Morendo. I can verify both the chopstick difficulties and the tuning fork bruise.
Practice
28
Nov 11
Tuning – Vertical vs. Horizontal
I was talking with Sasha Zamler-Carhart, director of Ascoli Ensemble, about the ways that our ensembles approach tuning. Ekmeles’s approach to tuning Gesualdo in 31-note equal temperament is a mostly harmonically focused – 31ET being a keyboard temperament -and is about aiming for pure verticalities. Sasha’s group, specializing in Medieval music, and often reading from original manuscript parts, approaches tuning in an entirely linear sense. Of course they make sure they begin lines and cadence together, but reading from parts and singing in Pythagorean tuning – which is beautifully melodic, but only harmonically satisfying for major seconds fourths and fifths – has led them to consider tuning in this way.
Our most recent project, the premiere of Randy Gibson‘s “Circular Trance“, was an almost totally vertical experience. Scored for an array of sine wave drones in addition to the seven singers required, the piece’s complex just intonation tuning system requires us to constantly listen vertically, and to subsume our voices into the tuning of the drone. Perhaps the most linearly conceived work that I’ve ever performed is the first movement of Johannes Schöllhorn‘s “Madrigali a Dio”. The pitches for the singers are graphically specified on a 3 line staff representing the full compass of the voice, so that the pitches are only determined relatively within each voice, and are free to interact with the other voices at any interval, tempered or otherwise.
Despite these extreme examples I think I do my best work tuning diagonally, imagining both the melodic contour of my own individual part, and the way it will interact with the other parts as they go along. In reality, tuning with an ensemble of voices is a constant game of listening and subtle adjustments. Rules and approaches to tuning are a jumping-off point and a reference; but in practice, the voice is both a producer of an infinite continuum of pitch, and fallibly organic.
31
May 11
Irrational meters
I was going to write a blog post about what are called “irrational meters” (time signatures with denominators that are not powers of 2) – then I re-read a fantastic post by Helen Bledsoe, flutist for MusikFabrik (among others), and realized I should just link to her! She very lucidly explains the mathematical workings of Ferneyhough-style rhythm, complete with “irrational meters”, which really pose very little additional challenge, if you know how to interpret them.
The most basic point to remember about these meters is that the denominator, just like in more familiar time signatures, indicates the number of notes it will take to fill a whole note. 4/8 indicates 4 of something it takes 8 of to fill a whole note (namely eighth notes). A denominator of 5 would indicate that quarter note quintuplets are the basic unit of the bar, and the numerator, as in familiar time signatures, indicates the number of units in the bar. Thus, 3/5 would be a bar of 3 quarter note quintuplets! Of course, you can, instead, treat these changes of denominator as metric modulations and tempo changes – but I’ll leave some of the specifics to Ms. Bledsoe’s lucid explanations!
Head on over to her blog, Flutin’ High, for the full post!
23
May 11
Equal Temperament
Equal temperament or ET is the current tuning framework for most Western music. It is a kind of acoustical compromise, compared with the pure mathematical relationships of just intonation (JI). No intervals are ‘true’ in the system, but the equality of half-steps allows for free modulation to any key, ensuring that each would be as viable as any other. Pitches which in JI would be derived from the lowest primes are generally the best approximated pitches in ET: perfect fifths (3/2 in JI) are 2 cents low in ET, major thirds (5/4) are 14c+, and minor (7/4) sevenths are 31c-. In JI, all pitches are related intervalically to a fundamental (1/1); in ET, pitches are derived as equal logarithmic subdivisions of an interval, most usually the octave. (An interesting exception in this case is the Bohlen-Pierce system, which divides a perfect 12th into 13 equal steps) Thus, instead of the simple ratios involved in JI, the size of each ET halfstep is derived from the twelveth root of 2. Any ET division of the octave can be reached this way. For example, a 24 note scale’s smallest interval can be derived from the twenty-fourth root of 2.
The ET system used in most Western music is 12 note ET, also called 12ET. However, since the early twentieth century (and with a few notable exceptions, hundreds of years before), composers have worked in other equal subidvisions of the octave. 24ET introduces the quarter tone, 36 the sixth tone, 48 the eighth tone, and 72 the twelveth tone. These are the most common divisions, though there are many musics, composers and cultures who use different divisions (Klaus Huber, for example, in his later works, uses 18ET, creating an equal tempered scale of third tones). 19ET has been used as a better compromise for true JI intervals in tonal music than 13ET, differentiating between sharps and flats as differently tuned. 31ET is a system which was approximated by instrument makers and theorists in Italy in the 16th century via a kind of mean-tone temperament. It allows for diatonic (white note) chromatic (accidentals both sharp and flat) and enharmonic (double sharps and flats) genera, extending the range of possible harmonies greatly. Ekmeles will be experimenting in 31ET tuning in the performance of Gesualdo madrigals this Fall, as historical records indicate that Scipone Stella, a composer in Gesualdo’s court, built replicas of Vicentino’s 31ET keyboard instruments.
Non-exhaustive list of composers using ET microtones
Charles Ives (24ET), Alois Hába (24ET, 36ET, 72ET) Julián Carillo (18ET, 24ET, 30ET, 36ET, 42ET, 48ET, 54ET, 60ET, 66ET, 12ET, 78ET, 84ET, 90ET, 96ET [if you don’t know him, you should really check him out!]). James Dillon, Brian Ferneyhough, Liza Lim, and many other second modern or complexist composers make liberal use of ET microtones.
Learning ET microtones
Without the aid of rote learning, ET microtones can be exceptionally difficult to find. Acoustically, further divisions of 12ET rarely become more consonant, with the exception of 11th partial relationships which lie only a few cents away from a quarter tone. I reccommend the use of computer models, and have made use of several. I have occasionally used simple software synths for learning quarter tones. I reprogrammed a fine-tuning knob built into the synth to instead move only in gradations of 50c, and altered the pitches by hand on the fly. This is useful for melodic work, but makes harmonic hearing of quarter tones impossible. OpenMusic is an IRCAM-developed program made for computer assisted composition. A companion program, microplayer, can handle up to 72ET playback in multiple channels. To hear the score of an ET microtonal piece, I can’t just sit down and play it at the piano, so I enter it into OpenMusic, and can hear a completely accurate version of it, harmonically and melodically. When you have a limited amount of time to rehearse with an ensemble for a difficult piece, practicing with a computer model can allow you to devote that rehearsal time to music making, and not to panicking over whether you’re singing the right notes.
14
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.”
11
Feb 11
Performing Cage
Performing the music of John Cage is always a liberating experience. Working towards our performance of Song Books tomorrow, February 12th, I’ve been looking forward to the surprises and the serendipitous moments of beauty that are sure to arise. The process of learning and rehearsing this music requires a removal of personal decisions and the gradual creation of boundaries and limits; this is a freeing and creatively inspiring undertaking.
The following were decided by chance operations: The length of the total program, the number of sectional divisions in the performance and their lengths, the selections I will be singing, in what order I will sing them, how much of them I will be singing, where I will be singing them and for how long, what styles of singing I will employ, and the electronic changes I will make during performance.
The score, like a 200 page block of marble, has been chiseled away, leaving a few heavily marked sheets that denote the performance specific to my time and place. Rigorous rehearsal on these specifics, and confidence in their validity (despite their randomness) is a lesson in working on any music. Certainly nobody would know if I just fudged it, and didn’t follow what the chance operations dictated, instead shaping the material in the moment. However, fidelity to the material and a deep reading of the score will yield a performance with the possibility of transcending my momentary whim, and presenting my humanity (and hopefully Cage’s) in an authentic way.
All this without even recalling the fact that four of my colleagues will be performing their own programs simultaneously, which we will hear for the first time in performance! We, like Cage’s beloved mushrooms, will put forth an overabundance, a generous artistic wastefulness.
“If you look at nature, for instance, it often seems to be wasteful, the number of spores produced by a mushroom in relation to the number that actually reproduce … I hope this shift from scarcity to abundance, from pinchpenny mental attitudes to courageous wastefulness, will continue to flourish.” – John Cage in conversation with Larry Austin 1968
10
Jan 11
Tuplets and polyrhythms
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.
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
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.
13
Dec 10
Subdivisions
Composer Karim Haddad’s Motets present a complex rhythmic language based on the medieval concept of prolation taken to a modern extreme. The notation is beautiful and evocative, but tremendously difficult to realize as a performer.
Conceptually lucid, impossible to perform (currently)
Realizing this (thanks Karim!), the composer has also presented a ‘quantized’ version of the score, translating the many layers of tuplets into their duration in milliseconds, then mapping this information onto the closest approximation afforded by 2-8 subdivisions per quarter note. The result can be extremely variegated series of tuplet subdivisions of a regular beat, requiring accurate placement of say, the final septuplet of one beat, and the final triplet of the following beat, as in the below example.
Eminently readable and aurally identical
This notation, while immensely more familiar and readable, poses a unique challenge. It requires of the musicians the ability to switch subdivisions in some cases, every beat. This is not something that musicians are normally trained for; we are usually very good with duple and triple subdivisions of the beat and can fake our way through fives, and switching between them involves some grinding of gears. I wanted to train myself to instantly hear these higher-prime subdivisions in the same immediate way we hear duple and triple divisions.
I began by practicing each division on its own, putting on the metronome and simply subdividing, for example, an even five, ensuring that each attack was of equal length and unaccented. Of course 5s and 7s end up in groupings of 2 and 3, but I found it most useful to keep the subdivisions flexible, later improvising groupings with the metronome, exploring aspects of the subdivision. Then I would move between several subdivisions, alternating fives and fours, feeling the even pulse of each, and how they relate. After I felt more comfortable in each subdivision, I wanted a way to practice long strands of changing subdivisions like I knew I would find in the Motets. Using a favorite tool of practice and composition, random.org, I created a string of hundreds of random numbers between 2 and 8, presented in 4 columns. I put my trusty Dr. Beat on 4/4 and dove in, reading each number as a subdivision. It’s tedious work, but even a few sessions found me more confident in dealing with simple subdivisions of the beat. In a way, there’s no difference between triplets, sixteenth notes, and septuplets; they’re all periodic subdivisions, evenly filling the space between two pulses. There’s no special secret to learning them, only the familiarity that we have from years of duple/triple based music that has led us into rhythmic complacency and fear of the higher primes!
29
Nov 10
Elementary Training
Contemporary music is full of sundry rhythmic challenges. Before we even get there though, let’s make sure we are completely fluent in the rhythmic language of common practice music. My favorite workout for basic rhythmic exercises comes in Paul Hindemith’s perennial favorite Elementary Training for Musicians. If the title seems condescending, wait until you read what he has to say about singers!
“As for singers, nobody denies that most of them are launched on their careers not because they show any extraordinary musical talents, but because they happen to have good voices. On account of this advantage a singer is usally excused from any but the most primitive musical knowledge — knowledge such as could be acquired by any normal mind in a few weeks of intelligent effort.”
Ouch, Paul, ouch. The text takes you step by step from reading a simple series of vertical lines as regular pulses through the furthest traditional notational difficulties of Hindemith’s time. He even has a remarkable prescient turn in a page where he describes the derivation of what have been come to be known as “irrational meters”, with denominators other than powers of 2. But my favorite feature of the text is the way he forces a physical incorporation of the rhythmic concepts at hand with what he calls coordinated action. This consists of speaking the given rhythm while conducting with one hand, tapping it with the left hand while conducting with the right, tapping it with the foot while conducting, and every possible combination of limbs and rhythmic interactions.
Try tapping, singing, conducting, etc. as prescribed
While a given exercise may be simple with only your dominant limbs in play, a simple redistribution of the material across your body can force a radical re-learning of the rhythmic concept at hand. The literal embodiment of rhythm in a deep and conscious way (not just toe-tapping) has a transformative effect.
9
Nov 10
Ear training texts
Most of the time, the repertoire I am preparing for upcoming performances is more than enough to occupy my mental and musical faculties. However, when work comes in fits and starts, and I find myself without a project for a moment, I practice my musicianship skills. I’ve found different texts useful for different tasks and goals and will give a short summary of my favorites below.
Modus Novus
This book by Lars Edlund is a classic of atonal, interval-based learning. It starts off with melodic exercises consisting entirely of seconds and fourths, then adding fifths, then thirds, and moving further on into more complex structures. In addition to the melodies written expressly for the text, the book includes many examples from the orchestral, chamber, and vocal repertoire. Preceding the melodic exercises, Edlund includes several 3- or 4-note examples of the most difficult intervallic combinations involving the new interval. I’ve found Modus Novus to be exceptionally good for working on troublesome intervals in a musical context.
Wege zur Neuen Musik
While not as substantial or encyclopedic in scope a book as Modus Novus, I find the exercises quite useful, and it is sold in low and high voice versions. The melodies tend to be a little more mechanical and sequential, but are good for getting intervals in your ear on their own. My favorite parts of the book are the two voice exercises (bring a friend!) and the large section of exclusively vocal excerpts from the repertoire, ranging from Berg and Schönberg to Feldman and Ligeti. Sometimes it just feels better to be singing real music while working on your musicianship!
Elementary Training for Musicians
Paul Hindemith’s perennial text is a kind of all-purpose torture device for the masochistic musician. I’ll write about its excellent rhythmic exercises in an upcoming post; for now I’ll focus on the pitch-based aspects of the text. Unlike the other two texts listed here, Hindemith focuses on tonal (or at least diatonic) sight-singing. The rhythmic aspects of his melodic exercises are always interesting, with lots of across-the-beat accents and sequences. If you need a tune-up on more melodic and tonal reading, this is a very useful text.
Of course, it’s often useful to take excerpts from the literature and turn them into vocalises and ear training exercises. I’m currently working on a piece by Luca Lombardi that isn’t too difficult, except for one wide ranging and angular melodic line on a single syllable. I’m writing it out into my notebook in various forms and transpositions to use as a vocalise while I get the intervals clearly in my ear.