Interview with Max Mathews
Author(s): C. Roads and Max Mathews
Source: Computer Music Journal, Vol. 4, No. 4 (Winter, 1980), pp. 15-22
Published by: The MIT Press
Stable URL: http://www.jstor.org/stable/3679463
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C. Roads

Interview with
Mathews
Max

Introduction

learned to play the violin. Did you study violin as achild?
Mathews: I studied violin through high school
Max Mathews is a pioneer in computer music, havand
have continued to play it ever since, taking a
in
first
sound
the
synthesis programs
ing developed
the late 1950s at Bell Laboratories.He is the author few lessons but not many. I like the instrumentof the classic text on the subject, The Technology
very much personally, although I call it an "inefficient" music instrument in that you have to
of
MIT
and
The
Music
Press),of Computer(1969,
numerous papers on the application of computer
practice more to achieve a given musical performance than with almost any other instrument.
technology to music and acoustics.
This interview took place in Cambridge,MasAnyway I'm stuck with the violin; I'm certainly
not going to learn any other instruments except thesachusetts in late June 1980. Dr. Mathews had
toInstituteresearch
visit
from
a
returnedcomputer and new instruments I might invent
recently
de Recherche et Coordination Acoustique/Musique myself!
(IRCAM)in Paris, where he and Curtis Abbott had
worked with his Sequential Drum and its interconnection to the 4C Machine.
Music I

Background
Roads: First, I'd like to ask you a little about yourbackground;where you went to school, what you
studied, and how you got interested in computer
music.
Mathews: I studied electrical engineering in all
my schools; Cal Tech first, and then M.I.T. I eventually got a Doctor's degree in electrical engineering. At that time and ever since I've been interested
in large, complex systems and in computers; first in
analog computers and then, when they became
practical, in digital computers. Leaving M.I.T., I
went to Bell Labsfor my working career.I worked
in the Acoustics Research Department applying
digital techniques to speech transmission problems
and, eventually, to music. I've always enjoyed music as an amateur musician.
Roads: I noticed in your demonstration and performance out at Stanfordthat you at some point
Computer Music Journal,Vol. 4, No. 4, Winter 1980,
0148-9267/80/ 040015-08 $04.00/0

Roads: It must have been in the early andmid-1950s that you started applying computers toward musical goals. Can you tell us a little about
your experiences with the programMusic I? You
brought that up on an IBM 704 computer?
Mathews: That was the only computer we hadthat was capable of doing sound processing.
Roads:That was at Bell Labs?
Mathews: Actually the 704 computer was in
New York City at IBMWorldHeadquarterson
Madison Avenue. We used to go in there and run
our programsand bring a digital magnetic tape backto Bell Labs.The digital-to-analog converter was at
Bell Labs.
Roads:What was the converter like?
Mathews: We had a 12-bit vacuum tube converter; it was quite a nice machine. It was made by
a company called Epsco, I believe.
Roads:Music I was capable of playing melodies,
was it not?
Mathews: It generated one waveform, an equilateral triangularwaveform, with the same rise as
decay characteristics. You could specify a pitch, andan amplitude and a duration for each note and thatwas it.
Roads

15

Fig. 1. Max Mathews, June
1980, Cambridge, Massachusetts. (Photo by C.
Roads.)

memory. Some hardwaresynthesizers today seemto give you this.
Mathews: True. The hardwaresynthesizers probably have to repeat the trajectory of the software
programs.
Roads: That must have been 1958. Was this stillon the 704 computer?
Mathews: By that time we had moved to the IBM
7094 at Bell Labs. That was a very, very effective
machine. We used it for almost a decade, not only
for musical purposes, but for our great preponderance of computations at Bell Labs in speechprocessing and visual signal processing. That was afine machine and some of the notable early operating systems were developed for that machine,
including Bellsys 1 and Bellsys 2.
Roads: Had you heard of anyone else doing anything similar at around that time?
Mathews: No. There were some people, Lejaren
Hiller in particular,who had done a bit with composing music-compositional algorithms-but as
far as I know there were no attempts to performmusic with a computer. In fact, we were the only
ones in the world at the time who had the rightkind of digital-to-analog converter hooked up to adigital tape transportthat would play a computer
tape. So we had a monopoly, if you will, on thisprocess.
Roads: This was 1957?
Mathews: Yes.
Roads: Some people made compositions withMusic I, is that not true?
Mathews: One brave soul, a psychologist named
Newman Guttman, made one composition. But it
was not hard to realize that we could do better. Music I sounded terrible and was very limited. It was
clear that if we were going to get better music out
we had to do better. It wasn't hard to see things
that could be added and changed.

Music III

Roads: So you developed Music II. As I recall,Music II was capable of four independent voices ofsound, and a choice of 16 waveforms stored in

Roads: In Music III,which you introduced in
1960, you introduced also the concept of the unit
generator, which is certainly one of the major conceptual advances which has made computer music
possible today. Can you describe why that became anecessary concept?
Mathews: I too think it's a very important concept, and more subtle than it appearson thesurface. I wanted to give the musician a great dealof power and generality in making the musicalsounds, but at the same time I wanted as simple a
programas possible; I wanted the complexity of the
programto vary with the complexity of the musician's desires. If the musician wanted to dosomething simple, he or she shouldn't have to dovery much in order to achieve it. If the musician
wanted something very elaborate there was the option of working harder to do the elaborate thing.
The only answer I could see was not to make theinstruments myself-not to impose my taste andideas about instruments on the musicians-but
rather to make a set of fairly universal building
blocks and give the musician both the task and thefreedom to put these together into his or her instruments. I made my building blocks correspond to
many of the functions of the new analog
synthesizers.

16

Computer Music JournalMusic II

So I had to contemplate rewriting the programoncemore and I wanted to make a universal program.
Also, I wanted to make it as universally available aspossible. At that time the Fortrancompiler wasavailable and was the most widely used compiler. I
was able to work out what I still believe was a very
ingenious technique so as to have almost all of thecomplexity of the programencoded in Fortranstatements which are portable, but have the inner loopsof the unit generators,which are computationallyMusic IV
rather simple but get executed so many times that
Roads: Yes. Music IV followed Music IIIin 1963.
they put a heavy load on the computer, proWhat was the advantageof Music IV over Music III? grammed in machine language. So the overall
Mathews: Music IV was simply a response to a
programwas both simple in terms of the amount of
in
the
It
had
and
the
coding required to put it on a new and different machange
languagecomputer.
some technical advantages from a computer prochine, and efficient in terms of running rapidly.
Roads:Even though you had developed Music V
It
of
a
macro
gramming standpoint. made heavy use
asa means of spreadingcomputer music out into
assembly programwhich existed at the time.
the world, a number of musicians had already got
Roads: So up until that point you had been prowind of what was going on at Bell Labs and weregramming in assembly language without a macro
starting to go there to find out more about what
facility?
Mathews: Macro assemblers were just invented
you were up to. Some of your colleagues, including
F.
R. Moore, Jean-ClaudeRisset, and JamesTenney,at that time. Indeed, Music IV debuggeda lot of thewere able to do some very significant work at Bellmacro assembler that was used at Bell Labs. It
made very heavy and rather sophisticated use of the Labs around that time. Can you describe the atmacro facilities, and I discovered a lot of bugs inmosphere at Bell Labs?Were composers visiting?
them that the designers hadn't anticipated, and that
Mathews: When we first made these music prothey were glad to fix.
grams the original users were not composers, they
So in essence Music IV was musically no more
were the psychologist Guttman and JohnPierce
and myself, who are fundamentally scientists. We
powerful than Music III and was only a little moreconvenient to use, but it was computationally quite wanted to have musicians try the system to see if
a bit more sophisticated.
they could learn the language and express themRoads:From Music IV a number of people madeselves with it. So we looked for adventurous
their own versions, like at Princeton.
musicians and composers who were willing to exMathews: Music IVBand IVBFand things like
periment. The first one was David Lewin, who wasthis were developed at least with the inspiration of
at Harvardat the time. We correspondedand he didMusic IV.
a composition mostly by mail, which was a bravething to do. Then JohnPierce met Jim Tenney at
the University of Illinois, where Tenney was studyMusic V
ing with Hiller. Pierce was very much impressedwith Tenney's music and his interest in computers.
Roads: Was the need to get these programsout
He invited Tenney to take a temporaryjob at the
into the world part of the motivation for developing Laboratoriesto try out the music programs.Tenneya machine-independent version of Music IV, that is, took the job and developed some timbres of hisMusic V?
own and also some pieces. To my mind, the mostMathews: Certainly. There were several motivainteresting music he did at the Laboratoriesintions. One was that again we'd changed computers. volved the use of random noises of various sorts.

I wouldn't say that I copied the analog synthesizer building blocks; I think we actuallydeveloped them fairly simultaneously. In any case,that was an advantage because a musician who
knew how to patch together Moog synthesizer
units would have a pretty good idea how to put together unit generators in the computer.

Roads

17

Roads: Yes, his Noise Studies.
Mathews: Then after Tenney, Jean-ClaudeRisset
was sent to the Laboratorieson a French scholarship to do a thesis in physics. Risset has a Ph.D. inphysics. His thesis involved analyzing the timbre of
the trumpet and developing a new technique foranalysis called analysis by synthesis, which is still,'I think, the most powerful technique for analyzing
natural music sounds.

is still in use today and which essentially has notbeen surpassed in terms of flexibility. But there wasanother rigid aspect that was part of the Music V
process which was the input process. I know thatyou turned to graphicalsystems of interaction at
one point. What led you to that?
Mathews: I was led to it by a desire to broaden
and make more facile the techniques for specifying
compositions. I think my graphicalexperiments
were very interesting; they did not, though, lead toa language which is as universally understood asMusic
the Music V language is. In some sense, I think toEarlyReactionto Computer
day the Music V language is much more important
Roads: Computer music today seems to be gainthan the Music V program,in that almost anyone
involved in computer music can read a Music V
ing acceptance at least in some limited quarters.
There are computer music centers established, and score or read a description of a Music V instrument
modern composers recognize that some form ofwith unit generatorsand understand it, and transcomputer literacy is an important part of their com- late it into whatever language he or she is using,positional training. But what was the early reaction whether it be Music 11, Music 10, or Music 360. It
both of the public and musicians to your demonprovides a well-documented and universally understrations of computer music? It must have beenstood way of describing a sequence of notes and
a
shock
to
some
their
quite
people.
interpretation and musical instruments.
Mathews: The reaction amongst all but a handful
The graphic languages didn't get to that level ofof people was a combination of skepticism, fear,
generality. I could describe an accelerando with aand a complete lack of comprehension. Amongst
single line, where the ordinate value of the line wasthemostinterested
that
was
the
the tempo, so if it sloped upward the tempo wasmusicians,
group
in the computer was the composers, while theincreasing and if it sloped down it was decreasing,
that
was
the
most
to
the
and
that was quite a nice, easy way of making accompugroup
antagonistic
ter was the performers.The group that understoodcelerandos. I had some experiments for drawing
the computer the least was "the general audience." melodic lines; that made graphicalsense.
The rock and popular musicians were willing tothink about the possibilities, but they also have thesame difficulties anyone dealing with a well-estabGROOVE
lished musical technique has. They are used towell-known and hence powerful methods for makRoads:After you developed this flexible sounding sounds. They're not very patient with "new"synthesis system and a means of graphicinteractechniques which are quite weak and tedious totionwith this system, what did you turn to then?
use, and which certainly require much more
Mathews:
I got into graphics at the end of Music
experimentation.
IV's history, and I did Music V as the next thing.
My graphicalinput work was at the very end of thelife of the 7094 computer. I spent a time getting
GraphicsInteraction
Music V in operation, then Risset carried out thebrunt of Music V work at Bell Labs. He worked on
Roads: That leads to my next question. When I
look back over your work, I see a very logical proanalysis-by-synthesis techniques and a catalog ofgression. You developed this series of flexible sound computer-generatedsound. After Music V I got insynthesis programsculminating in Music V, which terested in real-time work and developed the18Computer Music Journal

GROOVEsystem. That was quite a different
direction.
Roads: That was with F. R. Moore?
Mathews: Yes, he had come to Bell Labs by that
time.
Roads:The GROOVEsystem, as I recall, was a
hybrid system consisting of a minicomputer connected to an analog sound synthesis system, with anumber of input devices such as joysticks andknobs for conducting a score which had been prepared beforehand and input to the computer. It also
incorporatedgraphics, did it not?
Mathews: It had graphical displays. The point
about GROOVEwas that it looked upon the scoreas a recording of the control functions for the analog synthesizer. These are the functions of time
which specify the way the frequencies and all theother things one controls in an analog synthesizer
change with time to make music. Now, it basicallyrecorded these time functions in sampled form at
about 100 to 200 Hz, fast enough to record humangestures, and would store this on disk. The program
was a flexible way of playing back these functions
and combining them with other functions of timethat were generated by the performerplaying on thesensors of the instrument. These combined functions were then used to control the analog
synthesizer. In addition, the programhad very goodediting facilities so you could go back to thesestored functions and change them. You couldchange one sample of a single function without
affecting anything else.
Roads: So you could get a display or printout ofthese functions, allowing musicians to perfect what
they had done in real-time-edited improvisations,
so to speak.
Mathews: Exactly. The functions were displayedon a scope and you could move to a particular sample in the function and you would hear the
resulting sound as a sustained sound and you could
flip the editing switch on and change the value ofthe function at that point and hear what it was doing to the sound.
Roads: Yes, editing with real-time feedback. As
far as I know the most extensive use that was madeof this machine was by Emmanual Ghent. Was
there anyone else who worked with this machine?

Mathews: You'recertainly right that Ghent
worked with it more than anyone else. F. R. Moore
made plenty of compositions with it. Boulez and I
worked with it on the Conductor programwhich
was based on the GROOVEsystem.
Roads: When was that?
Mathews: That was 1975 and 1976.
Roads: The GROOVEsystem, which was developed in 1968, ran, as far as I know, up until 1979,
didn't it?
Mathews: Yes, eventually we couldn't maintainthe computer it ran on. I haven't reprogrammedit
because I think one should now use a digital synthesizer. Also I think a different way of storing thescore is better and more appropriatenow, such as
the way Curtis Abbott has used at IRCAM.

The Sequential Drumand 4CED
Roads:I understand that you have recently returned from IRCAM,where you attached a new
instrument called the Sequential Drum to the 4C
digital synthesizer.
Mathews: Yes. The Sequential Drum is anothersensor which you hit like a drum. The sensor sends
three signals to the computer. One of these is apulse which tells the computer when the drum is
hit and how hard it's been hit, and the other two
say where you hit the drum in terms of x and ycoordinates. The computer and the synthesizer use
these three pieces of information to synthesize asound. The musician decides how to use this information in controlling the sound.
In my case, I tried an interesting principle inwhich the pitches to be played are a sequence inthe computer memory. Each time you hit the drum
you automatically get the next pitch in the sequence. I did this because most traditional music
has a very rigid pitch line and the musician is notallowed to deviate from the composer's intention.
I actually built two drums; one I used at Bell Labs
and the more recent one I took to Paris. The computer there was the PDP-11/34 and the synthesizer
was the 4C Machine. I was very fortunate that Curtis Abbott had written a programwhich I could
adapt to this sequential principle. It's a program
Roads

19

one can do many things on. It is one of the first
general real-time programs.I think it's a good program partly because it resembles Music V andMusic 10. If you've learned these languages it becomes quite easy to learn Abbott's program.It's
also a good programbecause he has figured out theright structure for describing a series of complex
events in a score and for synchronizing and controlling events which are determined by a score with
events determined by the input sensors like thedrum.
Roads:As I understand it, in Curtis Abbott's program, wherein a traditional pfield in a language like
Music 11 might specify a value which would betyped in by a composer, in the 4CED programan
instrument, instead of being fed by a pfield would
be fed by an external event which might occur at
any time.
Mathews: That's right. A note can be initiated bya performeror by a score.
Roads: These scores themselves can be structured
into rather complex entities. One score event might
trigger a whole series of score events. One can, forinstance, attach a subscore to a particular event. So
not only do you have this complex instrument connection to real-time, you also have a complex scoreconnection to real-time, as I understand it.
Mathews: That's quite correct. The score controls the real-time processing of events in the 11/34
computer. It allows one to put together a whole series of events in a treelike structure where one
starts going up the trunk and when one reaches aside branch that branch starts whatever it is doing
and at the same time one proceeds on up the trunk
perhaps starting other side branches. So you can get
a lot of things going simultaneously. The side
branches all end, and the trunk continues on, so theoverall synchronization is quite simple since it all
depends on how fast you climb the trunk.

violins. Some of them are closely related to normal
violins, in that I've worked very carefully on theresonances of normal violins, and made electronic
circuits which introduce these same resonances
into the electronic violins. The electronic instruments all have regularviolin strings and they all
have bows. So the source of the vibrations is thesame as in a regularviolin. But thereafter the soundgets modified electronically. It is possible to tune
the resonances very accurately, and it is, of course,
possible to have as much energy as you want in thesound. It also makes it possible to use some of thethings we know about timbres to change completely the timbre of the violin. Notably, we canmake it sound like a brass instrument or like ahuman voice. The other thing I've most recently
done is incorporatevolume expansion to increase
the dynamic range of the violin. The normal violin
I think suffers from having a very narrow dynamic
range. One can expand the entire spectrum of theviolin, but it's more interesting to expand only aportion of the spectrum. This way you not only geta change in the dynamic range, but you get amarked change in the spectrum.
I've also made some physical changes in the violin. My latest instruments are played in a vertical
position, as one plays a cello. I've learned to playthe violin that way myself, and I'm convinced that
that's a superiorphysiological position. In short,
I'm going back to the old style of the viols. I've introduced some other human-engineering changessome very low frets which one feels with the fingers but which do not constrain the pitch of thestring to the pitch of the fret. So one can do vibrato
or a glissando and for that matter, one can tune thescale to whatever variations one might want.

IntelligentInstruments

Roads: This Sequential Drum is only one in a
number of new musical instruments you've developed, including a new violin.
Mathews: Yes, I've made a number of electronic

Roads: Do you see a time when families of instruments such as the ones you've developed would
be used in concert for a new kind of musical performance-an orchestra of intelligent instruments?
Mathews: In truth, I don't know whether the intelligent instruments will be used in concert form
or whether they'll be used in the home, or whether

20

Computer Music Journal

ElectronicViolins

Fig. 2. Max Mathews with
one of his electronic violins. (Photo by Nathaniel
Tileston.)both will happen. Certainly one could use the increased capabilities to enhance performances byvirtuosos. One could also use the capabilities tomake a wider range of music available to the amateur player.
Roads:Do you also see new kinds of musical interaction resulting from the use of intelligent
musical instruments? One of the implications ofyour Sequential Drum is that the performeris in a
new kind of relationship with both the score andthe instrument.
Mathews: That's certainly true. With the intelligent instruments both the score and the control
from the player form separate inputs to the instrument. The score does not have to pass through theperformeras it does with traditional instruments.
Also, the score doesn't stand between the musician
and the instrument, as with Music V. So I think
this is a much more powerful and flexible
arrangement.
Also, we will have very interesting situations
when we have several intelligent instruments andseveral performers interacting with one another,where part of the interaction flows directly from
one instrument to the other. That's a very pregnant
situation.
Roads:This implies that these intelligent instruments will be in some way cognizant of each other.
Do you foresee a day when these instruments will
actually be able to listen to one another the waythat musicians listen to achieve ensemble quality?
Mathews: I don't think they'll listen with microphones. I think the basic information of what each
instrument is doing will be transmitted to the other
instruments over a digital channel. This gets intoanother important question of how one makes multiple, independent computers work together on asingle problem. That's one of the most interesting
unsolved computational problems today.

Experiments with Inharmonic Timbres
Roads: You've recently concluded a series of experiments dealing with "stretched"inharmonic
tones. What was the motivation behind that project, and what were the results?

Mathews: It's clear that inharmonic timbres are
one of the richest sources of new sounds. At thesame time they are a veritable jungle of possibilities so that some orderhas to be brought outof this rich chaos before it is to be musically useful.
So John Pierce and I have been studying one smallclass of inharmonic sounds, those which have overtones like normal sounds except that the overtones
are stretched farther apart than normal overtones orcompressed closer together than normal overtones.
Roads: So the relationship of a pseudooctave
might be 2.2/1 or 2.3/1, not 2/1?
Mathews: Exactly. Our initial experiments were
aimed at finding out what properties of normal harmonic music carried over to music that was made
Roads

21

with stretched overtones. We found some things
carried over and some things did not. The sense of"key" carried over better than we expected.
Roads: So you can actually detect "keys" in sequences of completely inharmonic sounds.
Mathews: That's right. You play two samples anda person can reliably say whether they're in thesame or a different key.
Other properties do not carry over. The sense of
finality in a traditional cadence does not carry over.
A person who hears a cadence with unstretchedtones says, "That sounds very final to me." Whenhe hears the same cadence played with stretchedtones, he'll say, "That doesn't sound especially
final." But we have been able to make other inharmonic materials which do convey a sense of
cadence.
Roads:Yes, very strongly so in the one's I've
heard. These modified sounds relied on the criticalband phenomenon, as I recall.
Mathews: They were related to a theory of thecritical band and how it affects the consonance anddissonance of sounds, which was primarily developed by Plomp and Levelt.

Roads:If we can detect "keys" and some form of
finality within a cadence or progressions within inharmonic tones, then some of the theories ofharmony in the past must not be as cogent as someof their proponents have thought them to be.
Mathews: Our results are contradictory.We
looked at two theories. One was the Rameau theoryof the fundamental bass, and the other was theHelmholtz and Plomp theory of the consonanceand dissonance of overtones. The destruction of thecadence would support the Rameau theory and thepersistence of the sense of key would support theHelmholtz and Plomp theory. So we have one result which supports one theory and one which
supports the other, with the overall conclusion thatthe world is a more complicated place than we had
perhaps hoped it was. We will have to dig deeper
before we can say what is causing the various perceptions we find meaningful to music. Butunanswered questions such as these make life
interesting.

22

Computer Music Journal