04
Nov 13

JI Composers: Christopher Trapani

This is the first in a series of conversations with composers who work in just intonation, and other microtonal systems. Questions from Ekmeles are bolded, the composer’s responses follow.

Why not 12-note equal temperament?

It comes down to this question, one I ask myself often: What exactly enchants me as a listener in the music I love? More often than not, it’s small expressive details that capture my attention, the fleeting surface gestures or stylistic inflections that make a performance distinctive. Replicating that kind of expressivity requires a full palette of pitch material; my works often run the gamut, mixing highly-detailed microtonality with tempered passages. Microtones are a vital component of almost every musical tradition: jazz, blues, country, electronic music, many folk styles, early music — almost everywhere except in the mainstream art music of the last few centuries.

Speaking more broadly, I’m captivated by the idea of consonance, and devoted to pushing the boundaries of what can be considered to “sound good.” Just intonation sparks my imagination because what appears to be a complex network of pitch relationships can be boiled down to multiples of whole numbers, simplest ratios that require extreme precision in tuning. I’m very attracted to this idea that simplicity and complexity can be a matter of perspective.

Why the systems and pitches you use?

My approach is simple: the system has to fit the project. I’m very concerned with making my music practical form a performance standpoint, so that the microtones can be reliably performed — whatever that might mean in a given context. I’ve often used the trick of retuning winds, plucked strings (guitar, mandolin, autoharp), or bowed strings (playing only harmonics and open strings) down by a quarter-tone, so that a player can use “normal” fingerings but still play reliable microtones.

I’ve also written for instruments which are specifically designed to produce microtones, in which case the system is more or less decided for me. I’ve worked extensively with the qanûn for instance, a middle-eastern zither equipped with small levers under the string that can produce microtones by changing the string length. I’ve used both the Syrian version (in Üsküdar and Widening Circles) which gives tempered quarter-tones, as well as a just intonation qanûn designed by Julien Weiss, for whom I wrote a solo part tailored to his particular tuning system in Cognitive Consonance. Or another example: the Fokker Organ, a MIDI-controlled microtonal organ in the Amsterdam Muziekgebouw, for which I also composed a short piece.

Another approach I’ve used is to write strictly tempered music for tempered instruments complemented by electronically created microtonal sounds, aiming for a fusion of live sound and synthesis or retuned samples that sounds like a single microtonal instrument. And there’s also my hexaphonic electric guitar, whose strings can be electronically retuned by a Max/MSP patch. I find that working with electronics offers the broadest range of possibility and precision, and a lot of my most fantastical pitch-related ideas are best realized in that medium.

A qanûn, showing the levers used for tuning

A qanûn, showing the levers used for tuning

What was your first encounter with microtones?

Wow, it’s coming up on a decade now… Shortly after I first moved to Paris in 2003, I caught a complete performance of Gérard Grisey’s Les Espaces Acoustiques. I’d heard Partiels (the third piece in the series) about a year earlier, and (weird to think of this in retrospect) only the theatrics at the end made an impression. But being enveloped by those lush harmonies in the concert hall was life-changing. Microtones were the key, it dawned on me around then, and I started devouring all the French microtonal music I could find, starting with Murail, Hurel, Leroux… For my first piece with microtones — a quartet for four clarinets written in 2004 — I decided I’d consciously train myself to hear microtonal intervals, and started constructing chords from slices of the harmonic series. But even in this first piece, I wasn’t doing just intonation drones, but working towards a richer polyphony, focusing on the voice-leading interactions between multiple microtonal lines.

My second microtonal revelation came when I discovered Turkish music. Often you hear that microtonal music has to be slow to be effective, that it takes the ear a while to attune itself to “unfamiliar” intervals. But in Ottoman classical music I discovered an entire tradition of fast and yet extremely precise microtones. The Turks rely on a combination of specially designed instruments and an internalized tradition that divides the octave (approximately but not quite exactly or consistently) into 53 parts. The idea that a microtonal theoretical framework could exist in tandem with a practice that tolerations deviations (which is in fact the way most supposedly tempered music is performed!) was illuminating for me and a source of inspiration for several pieces to follow.

Excerpt from Trapani's Cognitive Consonance

Excerpt from Trapani’s Cognitive Consonance

What piece of microtonal music that you didn’t write is most important to you?

I’ll go with either Harry Partch’s And on the Seventh Day the Petals Fell in Petaluma or Blind Willie Johnson’s version of “Dark was the Night, Cold was the Ground”


11
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.


03
Nov 10

Avant Garde Project

If you don’t yet know Avant Garde Project, you should! It’s a great resource for high quality transfers of LP recordings of classic 20th century music that are no longer available. A favorite of the moment:

The World of Harry Partch, featuring the man himself lending his intoning voice to a later version of Barstow.