This article is the first in a series on the ever-expanding world of computer music. Following on from Macro-music, we'll be looking at the basics of digital synthesis, the development of software techniques, hardware solutions for high quality synthesis, microcontrolled one-chip synthesisers, and the latest commercial 'add-ons' for microcomputers.

Macro-music is all about making music on large, expensive mainframe computers, and, in my idle moments, I dream about having a Cray-1 supercomputer (33 million operations per second) for my computer music studio. Anyone who caught the 'Horizon' programme on computer graphics will have seen what a computer like that can do for the visual artist, so just think what it could do for the cause of digital synthesis! (Pause for a great sigh of frustration...). Of course, the truth of the matter is that all the money in the world won't make a man happy, and even the Cray-1 won't necessarily balance out the creative input = creative output equation. Even more salutary to bringing one down from cloud cuckoo land are the experiences of the early pioneers of computer music.

When computing was a matter of vast arrays of gas-guzzling thermionic valves, some early computer programmers made the first tentative steps towards using their tricky charges for more frivolous activities than calculating annual turnovers and the like. At least, this was the attitude of their manufacturers. Music and sound synthesis was definitely at the bottom of the list of computer applications - except for one enlightened company, Bell Telephone Laboratories in Murray Hill, New Jersey. A young Massachusetts Institute of Technology graduate, Max Mathews, joined the Acoustic Research Department of Bell Labs in the early '50s to apply digital techniques to the analysis of speech transmission. The original work that Mathews initiated was for computer simulation of telephone speech after it had passed through mouthpieces, carbon granules, selector switches, and many miles of cable. The rationale behind this was that a successful simulation would allow new telephone systems to be tested without actually building them! The modus operandi of this program was to subject digitized speech to the synthetic brutalizations of the 'modern' telephone system so that it came out in all its grunged glory replete with the customary noise, distortion, and restricted bandwidth one's led to expect from this side of 20th century communications. Though this was far from what one wants in digitally-synthesised music, there was an important principle at work - that of the digitization of sound.

As every electro-musician knows, sound is a pressure wave that varies from moment to moment, and these pressure differences make themselves heard by vibrating the tympanic membrane in the middle ear. If these pressure changes can be turned into something the computer can understand, then you're halfway to the goal of sound digitization. An analogue-to-digital converter (ADC) provides the means of doing this by converting the pressure changes (in terms of voltage fluctuations from a pre-amplified microphone) into data (in the form of a stream of binary numbers). These changes can be measured 30,000 times per second and then stored in the computer's memory as a corresponding sequence of 30,000 numbers. The numbers can then be manipulated by various mathematical operations (as in the case of Mathew's telephone simulation program) and eventually returned to the outside world via the opposite conversion process - digital-to-analogue conversion (DAC) - as sound (Figure 1). So, the two key procedures for sound digitization are analogue-to-digital conversion and digital-to-analogue conversion. This, of course, meant that one of the first hurdles facing Mathews and his team was the development of suitable hardware to do the conversions. The fact that the digitization procedure allows any sound heard by the human ear to be reproduced from numbers is a very attractive proposition, and led Max Mathews to suggest that a computer "can make the sound of any instrument that exists today or of any instrument that anyone can possibly conceive of making in the future."

For Mathews, this relationship between music and the computer really started in earnest after a contemporary piano recital he'd attended with a friend one night in 1957. Of the various pieces played, only the Schoenberg seemed 'satisfactory' to them, and that prompted Mathews to start work on a program to show that he (or, rather, the computer) could do better. (Curiously, that's the only time that Mathews has shown an egotistical bent; the rest of the time he's been an unassuming and mild-mannered as Clark Kent!) Consequently, Mathews rents time on an IBM 704 computer, a machine so new at the time that the only model was on display at IBM World Headquarters on Madison Avenue in New York City. This led to the much applauded observation that digital music synthesis was born quite literally in a shop window! In fact, it was only the processing that took place in the middle of the window display; the final audible product was realised only after the 704-generated data (in the form of magnetic tape) had been passed through a 12-bit Epsco DAC back at Bell Labs.

Like any infant of the digital age, the first cry was a fairly primitive cri de coeur. The first program, Music I, generated just one sort of sound - a triangle wave with no choice of envelopes. However, pitch, amplitude, and duration were prescribable, and one person (a psychologist by the name of Dr. Newman Guttman) did actually write a piece using Music I, although, by most contemporary accounts, it sounded rather terrible. These limitations weren't helped by the difficulty of getting adequate computing time to improve on the original program or just for plain experimentation by interested parties. Fortunately, Bell Labs recognized the potential of these developments, and the next program that Mathews wrote, called, logically enough, Music II, which was capable of four independent voices, with a choice of sixteen waveforms stored in memory, was developed on an IBM 7094 at Bell Labs in 1958. The first more-or-less commercial result of this work was a couple of records called 'Music from Mathematics' released in 1959. One of these was issued privately by Bell Labs to show what could be done with the new digital technology and the other was from Decca (DL9103). Interestingly, the reactions to the early examples of computer music were much as they are now; composers were intrigued, but unsure about coping with learning a new language; traditional musicians were downright antagonistic; rock musicians were keen to explore new territory; and Joe public didn't really understand what was going on.

Higher sampling rates

Both Music I and Music II, as well as the subsequent series of programs, relied on the computer calculating the string of numbers needed to produce sounds after reading in and manipulating data supplied to the synthesis program by the composer. However, the much greater bandwidth needed for high quality music synthesis, as opposed to speech, put considerable demands on the design of digital synthesis programs. The main problem is that the faster a wave is changing (i.e., the higher the frequency) the more often it's necessary to put in numbers into the DAC to recreate a reasonably faithful version of the waveform (Figure 2). If each of these numbers represent a waveform sample, and the numbers are sent to the DAC with a sampling rate of 2n Hz, then it was demonstrated by Mathews that the maximum possible audio bandwidth was n Hz. This is the all-important sampling theorem, and the sampling rate bandwidth represents the Nyquist limit for digital synthesis.

What this means for digital synthesis is that a 20 kHz bandwidth would necessitate a new sample being sent to the DAC at least every 25 us (a 40 kHz sampling rate), and that just wasn't feasible for the first generation of computers. The solution adopted by Mathews in his program design was for the computer to calculate the necessary numbers at its leisure and store them on tape for playback via a DAC at a later stage. This technique of 'delayed playback' synthesis means that the computer has no real-time constraints as far as processing of DAC data is concerned. The big advantage of that is that the quality and variety of synthesised sound is limited only by what the composer and programmer feel like putting into the system. In fact, there are a number of advocates of delayed playback synthesis amongst users of microcomputer music systems (Hal Chamberlin, in particular), and, judging by his incredibly authentic rendition of Bach's D minor Toccata and Fugue, it's an approach that makes a lot of sense if real-time synthesis isn't a necessity. However, one of the big problems of delayed playback synthesis using high sampling rates (for high fidelity) is the large amount of data storage needed.

As a contemporary example, Hal Chamberlin's NOTRAN system (using a special music transcribing language), with a 20 kHz sampling rate and 12-bit DAC resolution, stores all the precomputed DAC data on floppy disks, but, in performance, feeding the data to the DAC requires a new disk to be replaced every 20 seconds! In the early days of computer music, data storage wasn't as straightforward as using floppy disks, and the typical 12 Mbytes of storage needed for a 5 minute piece meant that cumbersome and expensive tape playback machines were required. Even more to the point, as regards what the composer had to put up with, was the fact that 12 x 106 numbers took a great deal of processing, and a conversion factor of 100:1 was the norm when comparing the time required for processing with the amount of music that actually emerged.