Software – Means of Synthesis
The earliest means of creating electronic music involved patching together various sound-producing and processing units – oscillators, filters, reverberators – with cords plugged into what looked like a telephone switchboard. The sounds emitted were recorded on magnetic tape, pieces of which could be spliced together and re-recorded over one another. In the 1960s, at the same time that the Moog and other synthesizers were appearing, various people began developing computer programs that digitally performed the same operations. One such program, Music 4B, was written by Godfrey Winham and Hubert Howe at Princeton University. It was run on large IBM mainframe computers. Digital files were written onto large tape reels which were carried to another building to be played back through a digital-to-analog converter, the essential component of CD Players.
I have been using a Fortran version of this software, Music 4BF, ever since the 1980s when I was able to modify it to work on an IBM PC clone. A composer using this software creates an orchestra which consists of several instruments each of which utilizes a number of unit generators – again oscillators, digital filters, and reverberators as in the old electronic studios. The instruments are little Fortran programs that can do complex mathematical operations on the inputs to the unit generators, loop through banks of oscillators or filters, and define different cases or pathways to follow. The sounds from each instrument can be played separately, but are usually all added together on one run.
The orchestra is instructed on what to play by a score file. This file has a short section at the beginning that directs the orchestra program to generate various stored functions – sine wave cycles to be sampled or used in frequency or amplitude modulation; envelope shapes controlling the attack and decay of notes or to shift timbres; and others required by the unit generators. The remainder of the program specifies all the events (notes) in the piece – when they should begin and end, which instrument should play them, what pitches they should play, how loud they should be, plus various other characteristics. The score program also may employ composer-written Fortran routines that can manipulate blocks of notes. As the score file is created, revised, and extended using a text editor, these routines along with the cut and paste functions become a seductive method of musical variation.
Note that none of the sounds in my pieces come from recordings of actual instruments, natural sounds, or vocalizations; nothing is sampled. Everything is generated by the coded instruments. I often claim to be like an instrumentalist playing a viola da gamba, pianoforte, or sackbut – or an orchestra using 18th-century instruments. I have had the dubious luxury of never having to teach a course in computer music, and have therefore never had to keep up with new generations of software. I have created a personalized working environment around my original computer program, and have eschewed working with laptop orchestras, real-time processing of live inputs, and other forms of sound processing.
One of the most pervasive instruments is called WHITES. White noise, generated by a random number generator (which paradoxically always generates the same series of numbers, preventing unpleasant surprises), is sent to as many as 13 parallel filters with very narrow band widths. The clearly pitched outputs can produce harmonic series, series of odd partials that sound like pan flutes, or clusters of even intervals. The relative amplitudes of the top and bottom tones are set by one of the score’s inputs; the other amplitudes are scaled evenly between these values. These clusters are often used as a background to other foreground instruments. Each interval cluster – for example, 13 perfect fourths spanning 5 octaves and containing all 12 pitches, or 10 major thirds, spanning three octaves – creates a different ambience. As there are many pitches in the clusters, they tend to harmonize whatever melodies are playing against them. At other times WHITES plays melodic lines, using either odd or all partials.
Another percussive instrument is called CYMBAL, although it seldom sounds like an orchestral cymbal. 16 oscillators are initially tuned, each a specified interval higher than the previous one. This interval can be any value as long as the frequencies produced do not exceed the audio range. The 16-tone clusters are also subject to a vibrato of varying speed and height. The resulting sounds range from a warbling whistle (when the interval between tones is a ninth of a semitone), to gong-like sounds.
An instrument called MARBLE has six modes, all beginning with sharp attacks and decays, but differing afterward. Some of these modes play three-note chords and echo the initial attack irregularly. Other choices produce sounds akin to a marble rolling down a ramp, a woodpecker, and a celeste. A drum-like instrument THUMP includes an upward glissando that may be spread over the entire length of the note or take place very rapidly at the beginning of the note. The other non-melodic instrument is WIND which also has a rarely used bird-call mode.
The other instruments are clearly pitched. Some send a complex harmonic series created by the unit generator BUZZ to various filters. A piano-like instrument changes the mix between two sets of filter outputs over the course of the note. A clarinet-like instrument has an option of tuning two of its three bands of sound slightly above and slightly below the desired pitch. Other instruments utilize simple sets of oscillators or frequency modulation that traverses a curve, continually changing the harmonic spectrum. Many timbral shifts in the pitched instruments occur over the length of the note; the speed at which the timbres change depends on how long the note lasts. This is not something that a keyboard-activated synthesizer can be aware of when a key is pressed. I believe this makes the music sound less mechanical.
Specification of Rhythm — Geometric Series
My Ph.D. dissertation for Princeton University in the 1970s was titled Rhythmic Applications of Geometric Series. The sounds of ping pong balls bouncing faster and faster; or conversely, rattling more and more slowly between my kitchen door and a wall two inches away in a boyhood basketball game, intrigued me. I started investigating the interrelationships of notes that accelerated or decelerated using the same ratios that define the tempered pitch system – powers of the twelfth root of two. For example, every second note accelerating at the rate that defines a semitone, projects a series of attack points accelerating at the rate that describes a whole tone. Playing notes that accelerated at one rate against notes decelerating at the opposite rate created interesting symmetrical patterns. I started composing pieces that applied these limited number of ratios to the length of successive measures, to the beats within them, and to subdivisions of the beats.
There was no rigorous prescriptive system on how these rhythms were to be used. Over time, the practice of saying, for example, that 8.0 seconds should be divided into 4 measures such that the fourth measure would be half as long as the first, and that each measure should have 4 beats each changing at their own rate, turned inside out. To match a musical phrase I was hearing in my head or could play on the piano but defied normal metric notation, I could stretch or relax the parameters defining the overall length, and the ratio between and within measures. I could also replay the phrase at a different tempo simply by multiplying the start times and durations.
I tried to convince myself that it was acceptable to question the notion that music must have a regular beat – just because it is used for marching and dancing; and hearts beat. A piece for piano and tape, Joint Resolution, asked the pianist to so familiarize him/herself with the tape part, that he/she could stay with the tape without counting. (After all, teenagers seemed to be able to remember every inflection in rock performances and sing along.) This proved too disconcerting for most pianists and even more so for sopranos in a later piece. Thus, all my pieces for the last 30 years have been for tape alone. My professor at Princeton, J. K. Randall, used to quip “that when you eliminate the performer, you also eliminate the listener.” I hope this is not totally the case.
All the pieces in this collection use recurring phrases shaped by this mode of specifying rhythm. They exceed the usual bounds of rubato, but seem to me musical utterances. I think they may resemble the rhythms of speech and bird calls, which are also non-metrical.
Pitch System – M3 mod 11
During the summer of 1977, at the MacDowell Colony, I became deeply engrossed in the results of multiplying the 12 pitches (0 to 11, representing C up to B) in the 48 forms of a twelve-tone row, by 3 modulo 11, with 0 and 11 held constant. The chromatic scale under this transformation becomes the three diminished-seventh cycles: 0, 3, 6, 9, 1, 4, 7, 10, 2, 5, 8, 11. Row forms have segments in common, but no two are alike. The most closely related rows, those originally a semitone apart before being multiplied, when played together will always have 9 minor-third, 2 major-third, and 1 minor-second intervals between them. Other duets, using row forms originally a tritone apart, always present the same six pairs of pitches, three perfect fourths, the rest major thirds. These passages with their inevitable parallel fourths sound quite medieval, especially as brass duets. Melodically, the rows are more like cousins than siblings. Canonic imitations sound more like fugue tonal responses than real responses. The score for Deep End illustrates this row transformation in detail.
Every piece I have composed since then has used this system. Many passages in each piece present several “transpositions” of the same melodies at different speeds, some starting together but drawing apart, others starting after one another and ending together, and others that pass each other part way through. The score of Under the Radar graphically shows such overlapping melodic strands as colored bars, differing in length. Quasi-tonal collections, C_F_G_A, B_D_E_F#, and B♭_D♭_E♭_A♭ are produced when the underlying row (before multiplication) has many minor thirds. The music can settle into these areas, becoming more tonal at crucial points. Notes are typically held until three or more notes have entered forming harmonic collections in the manner of the piano’s pedal.
Forms and Transitions
The data directing the computer to generate music – to be reviewed and revised – is entered one section at a time. Even when there are overlaps and overhangs, I tend to let the seams show. Each section for me seems like a musical room, perhaps in an art museum. When activity slows, we move to another room. Sometimes the next room has a similar character; other transitions can be abrupt and unexpected, like moving through the “doors” in the film The Adjustment Bureau.
There are three sorts of overall forms for these pieces. One kind is symphonic, for example, From an Undisclosed Location, and And Its Discontents. The opening and one or more other sections return two or more times. Other forms present one or two long sets of variations, perhaps with one abrupt change from the first to the second set, e.g., Genetic Drift. I tend to compulsively extract as many of the possibilities I can find in a musical idea, possibly seduced by the ease of copying and pasting. Finally, various medleys I encountered playing in high school orchestras and bands may have contributed to my sense of how music should go. Some of my pieces have several contrasting sections, most of which never return, e.g., Moving On.
Some of the pieces end in the same place as the beginning, perhaps returning from distant places. Others never return, ending up in a very different place from where they started. In every case I have been concerned that things should not go on too long or end too soon, and that the overall shape makes sense.
Comments on Some of the Pieces
My pieces are usually completed before I’ve selected titles for them. Some titles come from political buzzwords current at the time: From an Undisclosed Location refers to Vice-President Cheney’s hideout after 9/11, but has nothing to do with the piece. The Public Option, a health-care debate term, does suggest that the music is somewhat extroverted and meets the 10-minute maximum length often stipulated for performance opportunities. On the other hand, This Way Lies Madness and The Deep End do express fears I had while writing them that I was straying into uncomfortable waters. This Way Lies Madness has groups of thick blobs of sound that would be impossible to sustain for a whole piece. To abandon all traditional means of expression for this world seemed like madness. Fortunately, these blobs are followed by very serene passages.
The Final Approach and Moving On refer to aging and death. I can imagine a program for The Final Approach akin to Strauss’s Death and Transfiguration except as I do not imagine an afterlife, there is only a struggle against illness followed by a peaceful acceptance. Moving On more likely refers to a certain dance-like rhythmic energy. A Trifle One-Sided is unusual in that it breaks a single twelve-tone row into three short gestures, each of which then generates sections of the piece without the other two. But the title came to me when I realized that I had put more voices into one of the stereo channels than the other. I thought of the German army officer in Casablanca who says, “You would find the conversation a trifle one-sided,” as the desired interlocutor was already dead.
Genetic Drift slowly modifies a single quiet theme for the first half of the piece, before a second, more energetic theme breaks in, which in turn slows and quiets down. I thought that the several variations were analogous to different organs in the body being expressions of a single set of genes. Losses does have three WHITES choral sections that seem like ever more urgent lamentations, as well as one long section that I imagine to be satellites chattering to one another in outer space. ShortStops is the only piece of mine that has several breaks (rests) interrupting the flow of the music. Its quiet ending is my favorite part.
Inside Job, Round Trips, Under the Radar, and Ice Storm are introspective pieces. Under the Radar begins with a copy of the last section composed, also the ending. Ice Storm has sections that close with quasi-medieval cadences. And Its Discontents alternates angry, percussive sections with quiet, more lyrical sections. There are unexpected tonal cadences at the close of several duets.
In Your Dreams begins with serene and hopeful dreamlike music, but becomes more and more agitated, even nightmarish, before ending somewhat more calmly. Throughout the piece, a wide range of timbres are juxtaposed against backgrounds of white noise clusters that are tuned equal intervals apart: first perfect fourths, then minor thirds, major thirds, and various seconds, and finally perfect fourths again. Restful at the beginning, these clusters later sound like an organ in a horror movie soundtrack, and then like a roaring surf on a very windy day. The melodic material and chords often complement the cluster intervals. — Joel Gressel
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