19
Feb 14

JI Composers: Randy Gibson

This is the third 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. This is another specially timed edition, since Randy Gibson’s Fifth Annual Avant Music Festival begins this Friday.

Composer Randy Gibson - photo by Stern Weber Studios for Avant Media

Composer Randy Gibson – photo by Stern Weber Studios for Avant Media

Why not 12-note equal temperament?

I stopped using equal temperament a long time ago. I always had a hard time in my ear training classes, and growing up playing a pitched instrument, but never really considering pitch (I played the Marimba for many many years), my relationship to pitch was always unusual. When I began studying with La Monte Young, my ears were really opened to the possibilities of Just Intonation, and what had been some simple experiments developed into a richer understanding of how pitch can function.

I wouldn’t necessarily consider myself a “microtonal” composer. Rather, I’m interested in the harmonies that can be created through just intonation, these are often even more “tonal,” more consonant. I guess I feel like my goal is not one of microtonality, but one of harmony, although I get excited by some of the very small intervals that I use.

Why the systems and pitches you use?

I’ve been working in the same tuning system, refining and improving it, for the last 5 years, and everything I write is a part of it. It’s a simple system made up of very simple intervals, all over a unified fundamental. But there’s an incredible wealth of material that can be pulled from it, and the reason I keep returning to it is that there’s more and more to be discovered, and by keeping it the same from performance to performance allows us to continue to refine our understanding of the tuning and how to perform it.

In my most complete statements of the tuning we’re not even using all of the possible pitches. They’re all there in the drone, but we’re performing on a simple scale, creating harmony, exploring their resonance, and just this exploration of, say, the central chord, the lower half of the scale, the upper half of the scale, and the central chord again is taking us around three hours. This is the piece I’m presenting on March 1, Apparitions Of The Four Pillars In The Midwinter Starfield Under The Astral 789 Duet.

For something like Circular Trance Surrounding The Second Pillar (my piece for Ekmeles) or The First Pillar Appearing In Supernova (my new cassette for Cassauna), I’m just working with a single facet of the tuning, a single interval class and exploring all of the possibilities of that.

What was your first encounter with microtones?

I can put this into three parts that mirror my development as a composer.

The very first time I truly heard something microtonal, and I was aware enough to understand that it wasn’t “normal” pitches, was probably a recording of Cage’s Ryoanji that I credit as having been the inspiration for me to begin composing. Of course, the microtonality in this piece is completely abstract, there’s only a single pitch happening at once, so this doesn’t get to the harmony.

For that, I would look at my time playing in a Balinese gamelan in Colorado. The instruments themselves, of course, are not in equal temperament, they’re in their own pentatonic scale (I unfortunately don’t know the exact scale that the gamelan I played in was tuned to), but furthermore, the halves of the orchestra are tuned slightly apart to create beats, that shimmering quality of Balinese gamelan music. This experience led me to begin to explore how pitch and tuning could be used to create a feeling.

When I came to New York, I came to La Monte Young and Marian Zazeela. Dream House and their performances with the Just Alap Raga Ensemble were the big influencers here, the otherworldly sine wave drone of Dream House was revolutionary. I had originally known mostly about Young’s more conceptual pieces of the 60’s, these elegant instruction pieces were incredibly influential on my thinking, but it was Dream House, and ultimately the raga performances that really opened my ears to the expressive possibilities of just intonation.

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

There are probably two pieces, both by La Monte Young, that I think are the most important to my development: The Base 9:7:4 Symmetry in Prime Time When Centered above and below The Lowest Term Primes in The Range 288 to 224 with The Addition of 279 and 261 in Which The Half of The Symmetric Division Mapped above and Including 288 Consists of The Powers of 2 Multiplied by The Primes within The Ranges of 144 to 128, 72 to 64 and 36 to 32 Which Are Symmetrical to Those Primes in Lowest Terms in The Half of The Symmetric Division Mapped below and Including 224 within The Ranges 126 to 112, 63 to 56 and 31.5 to 28 with The Addition of 119 and his solo cello composition Just Charles And Cello In The Romantic Chord.

The Base 9:7:4 Symmetry… is the music heard at Dream House, and is a breathtakingly beautiful example of vertical composition. Every spot in that room is vibrant and individual, you get the sense that no-one else is hearing the same thing as you. As big and imposing as the composition is, it’s still incredibly private and personal. With enough time in the drone, whole new sound worlds open up and your thinking is forever changed, the vibrations are that powerful.

Just Charles And Cello was very important to my development as well. Taking a single chord from The Well Tuned Piano, that chord being The Romantic Chord, La Monte crafts a piece of music that is beautifully expressive and powerful. The casual listener might think that a piece that is maybe four hours long on a single chord might be “boring,” but it’s not, it’s completely captivating. I was at every single performance in New York in 2005 and it was the most beautiful thing I had ever experienced.


12
Jan 12

Circular Trance – Avant Premiere

We’re glad to be bringing back Randy Gibson’s Circular Trance in an extended version for this year’s Avant Music Festival.

  • Randy Gibson – Circular Trance Surrounding the Second Pillar with The Highest Seventh Primal Cirrus, The Utmost Fundamental, and The Ekmeles Ending from Apparitions of The Four Pillars

personnel for concert


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.


04
Oct 11

Circular Trance

Music at First presents the world premiere of a concert length work in just intonation for 7 voices and sine wave drones by Randy Gibson

  • Randy Gibson – Circular Trance Surrounding the Second Pillar with The Highest Seventh Primal Cirrus, The Utmost Fundamental, and The Ekmeles Ending from Apparitions of The Four Pillars

personnel for concert


20
Jun 11

The mathematics of tuning

Since we’re about to embark on a season of non-standard tunings, ranging from columns of septimal JI intervals (thanks to Mr. Randy Gibson) to 31-note ET (a speculative historical journey with everyone’s favorite musical murderer, Don Carlo Gesualdo da Venosa), I thought it might be interesting to have a quick review of the mathematics of tuning.

We’ve recently discussed JI and ET tunings, and they differ in mathematical foundations. Absurdly briefly put: JI is based on ratios; ET is based on logarithms.

I highly recommend Kyle Gann’s Just Intonation Explained for a basic background on ratio tunings, and to be able to hear exactly what all those numbers mean.

And though I hesitate to link to it for obvious reasons, Wikipedia actually has a very clear writeup on the math of equal temperament! I’ve linked you past the rambling and somewhat questionable narrative section straight to the goods, starting with the Chinese discovery of the logarithmic solution to equal temperament.


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.


21
Mar 11

Apparitions

Minimalist composer Randy Gibson, curator of the Avant Music Festival, is currently working on a piece for Ekmeles. I’m just starting to explore the sound-world he’s developed, and wanted to share some of the unique aspects of the tuning systems.

Randy is working with what he calls “pillars” of just intonation intervals to build scalar tunings. Just intonation, for the uninitiated, is a tuning system which involves small whole number ratios. These were originally developed by the ancients, and the ratios corresponded to string lengths of simple monochord instruments. Pythagoras is credited with the discovery of these ratio tunings, the simplest of which are derived from the lowest primes. Taking 1 (or 1/1) as the tuning frequency, multiplying by 2 will yield the octave, 3 (expressed as 3/2 to put it within the range of the octave) the pure fifth, 5 (again, 5/4 to drop it into the proper octave) will yield the just major third. You can also think of these intervals as being derived from the overtone series; the 2nd partial is the octave, the third partial the fifth, the fifth partial the major third etc. These perfect intervals were, for various reasons, gradually left behind for tempered tuning systems, which eventually led to the 12-note equal temperament we find on modern keyboard instruments.

The tuning of the piece for Ekmeles focuses on the prime number 7, a ratio favored by Randy’s teacher and mentor, La Monte Young. Most of Young’s seminal work The Well Tuned Piano is in septimal tunings, and the use of 7 is prominent in his work generally. Most simply, the seventh scale degree in this upcoming work will be tuned as 7/4. This is the natural, lowered minor seventh we encounter in natural brass instruments. The majority of the rest of the scale is constructed by building a “pillar” of 7/4 ratios on top of this first 7/4 ratio, yielding, in descending scalar order, 49/32, 343/256, and 2401/2048. Note the powers of seven as numerators (the denominators again function to move these ratios down within the octave range). Much like the simpler ratios noted above, the numerator of the properly reduced fraction also represents the partial to which the note corresponds. This pillar also means that the interval between 7/4 and 2/1, the septimal second, is also repeated between 49/32 and 7/4, 343/256 and 49/32, and 2401/2048 and 343/256. Randy fills out the scale by including several lower primes, 9/8 (a true major second above the tonic) and 3/2 (the perfect fifth, which lies between the 2401/2048 and 343/256 in the scale).

Intervals constructed from lower primes are easier to hear, but Randy’s scale is actually very singable! He’s provided the group with a sine wave drone, which includes most of the pitches from the scale in various registers, so much like Indian classical music, properly tuning these notes is a matter of resonating with the drone. The experience of singing just-tuned music is a physical one, in a way that is difficult to describe. Each interval takes on a unique character borne of its ratio, and the way the waves interfere. The piece is in its earliest stages now, and I look forward to spending the time internalizing this unique tuning system.


14
Mar 11

Avant Music Festival Wrap-up

We were so glad to be a part of the 2011 Avant Music Festival, and now you can see photos and videos from all the performances at their website. Take a minute to remember the great moments you loved if you were there; if you weren’t there, take a minute to see why you should come to the 2012 AMF! We’ll be premiering a new piece by curator Randy Gibson.


20
Dec 10

John Cage – Song Books

Et tout cela m'est advenu par la faute de la musique.

An excerpt from Song Books

The 2011 Avant Music Festival presents an evening of John Cage featuring Ekmeles, pianist Vicky Chow, curator/pianist Randy Gibson, and trombonist William Lang.

Ekmeles performs Song Books, Cage’s inexhaustible grab bag of songs and theatre pieces, categorized by their relevance or irrelevance to the theme “We connect Satie to Thoreau.” Each singer freely chooses a program to fit the allotted time, and each performs independently of the another. Several of the programs will be chosen and organized entirely by chance operations.

ekmeles personnel for concert