Tae Hong Park
102 Dixon Hall
Music Department
Tulane University
La Nouvelle Orléans, LA 70118 Etats-Unis
park@tulane.edu
An Interview with
Max Mathews
Max Mathews was last interviewed for Computer
Music Journal in 1980 in an article by Curtis Roads.
The present interview took place at Max Mathews’s
home in San Francisco, California, in late May 2008.
(Voir la figure 1.) This project was an interesting one,
as I had the opportunity to stay at his home and
conduct the interview, which I video-recorded in HD
format over the course of one week. The original set
of video recordings lasted approximately three hours
total. I then edited them down to a duration of ap-
proximately one and one-half hours for inclusion on
le 2009 Computer Music Journal Sound and Video
Anthology, which will accompany the Winter 2009
issue of the Journal. The following article is a lightly
edited transcript of that edited video recording.
The Early Years
Parc: Could you tell me a little bit about your
background: where you grew up, where you went to
school—a little bit about your background that we
don’t usually hear in interviews.
Mathews: Oh, I’d be glad to. I was born and grew
up in the middle of the country in Nebraska. My
parents were both schoolteachers. They both really
liked teaching sciences. My father taught physics,
chemistry, and biology in high school and was also
the principal of the high school. It was a small
school, with class sizes of about twelve students,
and it was a very good place to begin an education.
My father let me play in the physics, biology,
and chemistry laboratories, so I enjoyed making
lots of things—making motors that would run,
making barometers out of mercury, playing with
mercury—you could do that in those days.
Parc: Hopefully you didn’t hold it in your hands.
Mathews: Oh yes, I held it in my hands, et moi
am still here at 80. One of the important things I
Computer Music Journal, 33:3, pp. 9–22, Fall 2009
c(cid:2) 2009 Massachusetts Institute of Technology.
learned in school was how to touch-type; that has
become very useful now that computers have come
along. I also was taught in the ninth grade how
to study by myself. That is when students were
introduced to algebra. Most of the farmers and their
sons in the area didn’t care about learning algebra,
and they didn’t need it in their work. Donc, the math
teacher gave me a book and I and two or three
other students worked the problems in the book and
learned algebra for ourselves. And this was such a
wonderful way of learning that after I finished the
algebra book, I got a calculus book and spent the next
few years learning calculus by myself. I never really
graduated from high school; I just stopped going
là.
This was in 1944, and instead I took an exam
for the Navy and enlisted as a radar repairman
and essentially fell in love with electronics at
that time. [Editor’s note: Mr. Mathews moved to
Seattle.] I did find out that the two schools that
the teachers in Seattle recommended were Cal
Technologie [California Institute of Technology] and MIT
[Massachusetts Institute of Technology]. Since [mon
wife] Marjorie was in California and was going
to Stanford [University], I chose Cal Tech, et
that was a very lucky and wise choice, as the
undergraduate education I got at Cal Tech was
superb. The techniques I learned in math and
physics in freshman and sophomore classes at
Cal Tech were the techniques that enabled me to
pass the doctoral qualifying examinations when I
went to MIT for my graduate work. On the other
main, even though I graduated from Cal Tech in
electrical and mechanical engineering, when I got
out of Cal Tech I didn’t know how to simply build
a simple audio amplifier; but at MIT I learned
how to build complicated computer circuits out of
the rudimentary operational amplifiers that were
around at that time.
Another great stroke of luck came when I was
refused employment at the 3M Company after they
had offered me a job, as a result of a back injury that
I had, so instead of going to Minneapolis—which I
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Chiffre 1. Max Mathews at
his home in San Francisco
in late May 2008. (Photo
by Tae Hong Park.)
Chiffre 2. Max Mathews
and an IBM mainframe at
Bell Laboratories.
(Courtesy Max Mathews.)
favored, since my family still lived in Nebraska—I
went to Bell Telephone Laboratories (Chiffre 2),
where I went into the Audio Research Department
to study new and better ways of compressing and
encoding speech so it could be transmitted over the
very limited-channel-capacity wires and radio that
were available in those days.
Developing a Computer Music Language
Mathews: I also was very lucky that I had a boss
who was very smart, very famous, very lucky,
and very powerful. His name was John Pierce,
and he’s best known for the invention of, or the
propagation of, communication satellites. Pierce
was very interested in music. He was interested
in information theory, how much information
there is in speech—which is a good question [à
answer in order] to know how to compress speech,
and how much information there is in music. Il
himself liked to play the piano and to compose
pieces.
He invited me to many concerts, and we went
ensemble. At one of these, a local pianist played
quelques [Arnold] Schoenberg, which was very good,
we thought, and some [Karl] Schnabel, which we
detested. In the intermission, John suggested to me
that perhaps the computer could do better than
ce, and that since I had the equipment to convert
computer-digitized tapes into sound, I could write
a program to perform music on the computer.
Parc: It seems to me that you really got into the
research in computer music after that particular
concert where you heard Schoenberg with John
Pierce. Was that an important turning point?
Mathews: Bien, that was the actual provocation for
my writing Music I. Now, if we hadn’t gone to the
concert, I think I would have gone on to write music
programs anyhow, because I was very interested
in this. My interests came from two things. Un
was that, although I’ve always loved to play the
violin and I’ve had an amateur string quartet going
most of my life, I was never very good at it, et
so I wanted to be able to make better music that
didn’t require such manual dexterity as almost all
[musical] instruments require. I also felt that there
were many composers who would compose a piece
for an orchestra and who would never hear the piece,
or its performance would be delayed for years, and so
[the computer] would provide a way for composers
to write something and hear it almost immediately.
Parc: Was there anyone else doing this sort of
thing—anywhere in the U.S. or around the world?
Mathews: There were a lot of people who wanted to
get music out of computers. [Years later, we learned
que] in Australia there [had been] a significant
effort. There were some people in the United States
10
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who could get printers to produce pitches, et ils
would write a program that would play Mary Had a
Little Lamb or something like that with the printer’s
sound. But I certainly think that my program was
one the earliest ones that would actually generate
arbitrary sound waveforms. [Editor’s note: Mr.
Mathews is being modest here; there is no evidence
of any previous program with such a capability.]
Sampling Theory and Corollary
Mathews: Essentially the sampling theorem shows
that there are really no limits to the sounds you
can make from samples. Any sound the human can
hear, you can make with the right number, accuracy,
and combination of samples, so the computer is a
universal instrument. Other instruments, the violin
in particular, are beautiful, lovable, but they always
sound like a violin—or at least it’s very difficult
to make them sound not like a violin. And I think
the sampling theorem is true, but I now think
there is a corollary to it, and that is that of all the
classes of sounds you can make from a sequence of
samples, most are not musically interesting, plenty
are unpleasant, and some are even dangerous.
If you are trying to make music, there is a
psychological tendency to make sounds that are
dangerously loud. I myself feel that the temptation
for composers is that if they have made a timbre
that doesn’t satisfy what they wanted to say, ils
hope that by making the sound louder it will have
the kind of power that they really intended. That’s
led to [the use of] earplugs and should lead to the use
of sound-level meters and things like that.
The Right People
Mathews: We need better understanding of the
physical correlates of beautiful sound—beautiful
as judged by the ear and the cortex of the listener.
Computers have contributed to our understanding—
computers in the hands of the right people. Deux
of the right people were Jean-Claude Risset and
John Chowning. Now, I wrote a number of papers
describing Music III. The fundamental paper was
published in the Bell System Technical Journal. Mais
the paper that had the most important impact in
my opinion was a paper I published in the magazine
called Science. And the reason it was so important
was that Risset, who was studying for a doctorate
degree in physics at the University of Paris, et
John Chowning, who was at Stanford also studying
for his musical doctorate degree, read the paper
and saw the potential in this and were interested
in it.
Risset persuaded his thesis professor to send
him to Bell Labs to work with me, and he ended
up working more than two years in two separate
sections, discovering some of the fundamentals of
timbre for traditional instruments. John Chowning
both read and understood the paper, and he came
back essentially for a day’s visit to Bell Labs. Nous
talked more about it, and he returned to Stanford
and wrote his own computer programs. Risset and
Chowning together made enormous advances in the
production of beautiful music.
Now, what was Risset’s contribution? At that
temps, people realized that the spectrum of sounds
rather than the time waveform of sounds was a
better way of characterizing how the ear would hear
these sounds. By spectrum, I mean the average spec-
trum of, let’s say, a single note or a sustained sound
from the instrument. People knew a little bit about
the attack and decay characteristics. They knew the
piano had a sharp attack and a short decay. Using
Music IV and V, Risset could produce these spectra
controllably and accurately, but they didn’t sound
like the instruments. And what Risset discovered
was that it was important to control the attack and
decay of each overtone in the spectrum indepen-
denté. His initial example was the brass timbre,
where he showed that during the build-up of a note
(the attack phase), the higher-frequency components
had to increase faster than the lower-frequency
components; otherwise, it didn’t sound like a brass
sound. By manipulating separate attack and decay
functions for the different overtones, Risset was able
to make useful approximations to a lot of different
types of timbres and to extend the instrumental
sounds so that you got interesting variations of the
sounds of the instrument—which was not [actually]
what Risset was after. He wasn’t trying to imitate
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instrument sounds, but he wanted to get the same
richness that the instruments had and vary it.
If one wants to individually modulate the attack
and decay of a lot of components, it’s a very expen-
sive process computationally—and in those days, le
expense of the computer was significant. Chowning
discovered a more efficient way of modulating the
attack and decay of the overtones, and this was a
different application of frequency modulation: FM
synthesis. This was a different use of FM than any-
one else had made. It was essentially done with two
oscillators or very few oscillators, so it was a much
more efficient technique than Risset’s technique,
and it led to similar results of musical interest.
In addition to being smart, Chowning also was
lucky in that his innovation, his discovery of the
FM synthesis techniques, came at just the time
when complex computer chips were understood
well enough so that it was feasible to design
special-purpose chips to do particular operations—
in this case, FM synthesis. In addition to his
musical and technical talents, John has another
talent. He is a super salesman, and he was able to
convince the Yamaha Company to spend several
years and a lot of money and a lot of effort to
design and test and redesign this FM chip. Mais
when they had finished the design and incorporated
the chip into what I characterize as their second-
generation synthesizer, the real winner was the
DX-7 synthesizer. The reason it was a winner was
that it was very inexpensive compared to alternative
moyens. I think the DX-7 was about $2,000 dans 1983. The number of people making digital music, I would say, increased from a few hundred worldwide to thousands, particularly in the domain of popular music. This almost overnight swept the United States and the rest of the world. As I say, Risset’s and Chowning’s reading the Science article was the start of a very essential and important movement in computer music. Another early musician who was involved was Jim Tenney. Tenney was a student of Lejaren Hiller at the University of Illinois. John Pierce visited Hiller and hired Tenney to spend a couple of years at Bell Labs. Hiller himself was interested in composing music with a computer program, which was also a big interest of John Pierce. It was not quite a significant interest for me. I was interested in having a computer perform music. Actually, the composing of music using computers predated the performance of music with computers. I did do some experiments of, let’s say, my own, for computer-related compositions—never with great success, but with a certain amount of interest. But it was a much more difficult problem in terms of the logic of the program to produce it, and that was one the reasons I shied away from trying to compose music on the computer: It was too difficult for me. I felt that one of the important problems in computer music was how to train musicians to use this new medium and instrument. One procedure was to invite a small number [of people] when we could to come to Bell Labs for visits—maybe long visits, as with Jim Tenney or Jean-Claude Risset, or perhaps very short visits. But that was a relatively slow way of getting the media into as broad a usage as we thought was appropriate. So one of the things that I did was to write a book. [Il] was essentially an instruction manual for how to use computer music. It’s this book that came out in 1969, The Technology of Computer Music. It was mostly intended as an instruction manual for using the Music V program. À ce moment-là, the big [Bell Labs] Computation Center computer, or any digital computer, was not fast and powerful enough to make interesting music in real time. I really missed the possibility of playing the computer as one would play a traditional instrument, so that one could hear and modify the sounds, timbres, things you were making as you made the music—the kind of things that performers are so expert at doing with traditional instruments. And furthermore, you couldn’t really play in a musical ensemble where you played with other performers, which to me has always been a great joy: to relate to [what] other people are playing. F. Richard (Dick) Moore, who is now at the University of California at San Diego, and I put together what we called the GROOVE system, which was a hybrid system. The control end of the system was a digital computer, and the sound-generating end was a modular analog synthesizer. [Digital] sound-wave synthesis has to be computed at audio sampling rates, which are [nowadays about] 44,000 samples per second. [Par contre,] the control end of a digital 12 Computer Music Journal l D o w n o a d e d f r o m h t t p : / / direct . m je t . e d u / c o m j / l a r t i c e – pdf / / / / 3 3 3 9 1 8 5 5 3 6 4 / c o m j . . 2 0 0 9 3 3 3 9 pd . . . f par invité 0 7 Septembre 2 0 2 3 system only has to be able to follow the motion of a performer who is controlling the music, and this requires sampling perhaps a hundred times a second. Dick and I put together a system with a small but fast digital computer at one end and connected a number of different sensors to the computer, so that it could track the motions or changes the performer was making in the sensors. The output in the digital computer was a set of, in this case, 14 analog signals that were sent to an ana- log synthesizer that had a lot of voltage-controlled equipment. Controls that were available on the GROOVE system consisted of a normal electric keyboard and a rather remarkable three-dimensional “magic wand” which you could move up and down, left and right, back and forth, and potentiometers would record the position. But in addition to potentiometers controlling [and measuring] these three motions, there were motors on the device, so that the computer could also move the wand. So you could not only move it by hand but also feel the position or feel whatever the computer “wanted” you to feel (or the program you had written). It was never very popular, for one very good reason: it cost about US$ 20,000 in 1960s dollars to
build. Donc, as far as I know, only one was ever built.
But we did use this device to make quite a few pieces
of music. One of those pieces is Emmanuel Ghent’s
Phosphones, and we have a good video of Mimi
Garrard’s dance company performing to this. Not
only did Ghent get the GROOVE system to make
the music, mais [he also got it] to control the light
sources that were illuminating the dance company.
[Editor’s note: See this work on the 2008 Computer
Music Journal Sound and Video Anthology DVD.]
The GROOVE system worked at Bell Labs in the
late 1960s and continued on until the early 1980s,
when that computer was then finally retired. Et
a number of composers would come out to Bell
Labs at night when we were not using the computer
for speech research, which was its other function.
Emmanuel Ghent was one of these; Laurie Spiegel
was another notable one; Richard Boulanger came
down from Boston. So a fair amount of interesting
music was made. [Pierre] Boulez came out and tried it
and asked me if I could use these kinds of techniques
to control the tempo of a tape recording, so that if
Chiffre 3. Early controller
conception. (Courtesy Max
Mathews.)
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you had the accompaniment for a soloist on a tape
you could then control the tape to maintain a good
ensemble with the performer. I probably changed my
interpretation of Boulez’s request to what I call the
Conductor program, which I am still interested in.
The philosophy behind the Conductor program
(voir la figure 3) was that the performer of a computer-
based instrument should be doing a job more similar
to what the conductor of an orchestra does than
to the way the violinist plays the violin. With the
Conductor program, the score of the piece to be
played was in the computer memory as a sequence.
Eventually, MIDI files became the preferred way of
putting the score in a computer program. And the
job of the performer was to control the expression
of the way in which the score file was performed.
Now, what are the expressive factors that could
be controlled? Bien, the tempo, bien sûr, et le
micro-tempos in the piece, which are one of the
most important expressive factors. In watching
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Boulez conduct, [I saw that he has,] in my opinion,
a very precise motion of his conductor’s baton, donc
he beats time in a very detailed and exact way and, je
believe, hopes that the orchestra will follow his beat.
Donc, I made the rules of my Conductor program do as
closely as possible what I thought Boulez was doing.
Another expressive function is the dynamics,
bien sûr. Still another expressive function is the
balance of the various voices in the ensemble. Toujours
other expressive functions are the timbres of the
voices. All of these things can be controlled with
the performer’s conducting motions. But one needs
to be very careful about overloading the performer;
you can only control so many things. And the way
of limiting what the conductor had to do at any one
time was essentially to write in the particular factors
that needed to be emphasized in a given part of the
performance. Par exemple, bring out the flute in
this section and assign a given controller to the flute
for that particular section, and then later on, où
the oboe was the critical instrument, to change the
assignment of the limited number of controls.
So the Conductor program really divided the
expressive quantities into those that would be
written out in detail in the score and those which
would be assigned to the human conductor. Ce
then led me to an instrument that I have been
working on since the mid 1980s—the Radio Baton
as a controller. The idea of the Radio Baton was
that it would be a controller that could sense the
motion of the conductor’s hands and use those
motions to control the expressive quantities of the
instruments. Donc, initially I built an instrument called
the Radio Drum. This instrument had a set of wires
in two dimensions: x-going wires and y-going wires
underneath a plastic cover. When you would hit the
plastic cover, that would cause one of the x wires
to contact one of the y wires, and then you could
tell where you had hit this grid. The instrument had
a contact microphone on the back plate, et le
strength of the pulse from the contact microphone
could tell how hard you hit it. So you could then use
where and how hard [you hit] as controls to control
whatever aspect of the music you wanted.
This was a relatively easy instrument to build.
I made one for IRCAM [Institut de Recherche et
Coordination Acoustique/Musique] and took it over
to Paris. One of the percussion players at IRCAM, un
very good percussion player, played a Bach chaconne
with this. Boulez listened and pointed out a wrong
note in the score, and I was delighted to hear that,
because then I fixed the wrong note and it was
forever OK. But the instrument was overall not a
success. One of the problems was that the wires kept
breaking at the points where they hit each other.
Another problem was that you only got information
from the instrument when you hit it physically, mais
if you just waved the baton (or the drumstick in this
case) around above the instrument, you didn’t get
any information. Donc, when I got back to Bell Labs, je
talked to one of my associates there, Bob Bowie, et
he thought very long and hard about making a radio
sensor that could track the motions of a little radio
transmitter in space. At least he came around to this;
he tried several other things before this. This turned
out to be the instrument that I kept on working on
for the 19 years I was at Stanford. With it I achieved
not a full three-dimensional sensing, but at least
what I call a two-and-a-half-dimensional sensor.
Donc, the instrument consists of this radio-receiving
antenna, and if you are close enough to it, you can
see from the pattern of the metallization that there
are four separate antennas on this plate. Here’s the
current version of the stick. If I remove the pad, toi
can see at the end of the stick a metal ring, lequel
is the transmitting antenna. So the strength of the
signal depends on how far you are from the receiving
antenna. Tom Oberheim and I have been working
on this device together for about a decade. Il a
joined me out here in California, and I have joined
him.
Amazing Place and People: Bell Labs
Parc: Bell Labs must have been an amazing place,
offering a healthy environment for collaboration and
creativity.
Mathews: I think you and I and everyone in the
world has wondered about that, because it was
a very, very fruitful environment. You put your
finger right on one of great things about Bell Labs:
that we had experts in various fields in physics
and chemistry and mathematics, and they were all
14
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willing to listen and talk to each other and spend
enough time listening to understand the question
that someone from another field might have and
possibly, if they got interested, to actually help that
other person solve the question. I had a number
of mathematical questions come up that I was
unable to deal with, and I was always able to find
a mathematician who often was able to advise and
sometimes solve the problem for me. One of those
exceptional mathematicians was David Slepian.
more or less finding the right people and then letting
them alone to do their thing and then finding out
what they had accomplished and understanding
what they had done. Among other things, it left me
a certain amount of time to do my own work.
Parc: It seems like it was a great environment
for creativity and innovation. I think that sort of
environment is perfect for smart people to come up
with smart things.
When I changed to a university job, I’ve been sort
Mathews: Oui . . . it was . . .
of disappointed that the interactions between real
experts in various fields are much more limited, et
I don’t understand why this is. I think one possible
explanation is that the support for the research
department, at least the research area at Bell Labs,
came as a lump sum to the vice president in charge
de recherche, and then he assigned various amounts
of money to the various departments, and it was a
very generous support, so that no one really had to
spend time writing proposals, going out searching
for money, and competing with associates. So maybe
that certainly made people much more willing to
interact. But there may have been other reasons.
My job for most of the time when I was at Bell
Labs was managing the Behavioral and Acoustical
Research departments. And these were experimental
psychologists, physicists, some engineers—mostly
electrical engineers—and some computer scientists.
I always felt that my job was to try to recruit people
who seemed both very smart and who seemed
interested in problems that were broadly related
to the work of the Bell System communications.
But when I say “broadly,” we could study how the
human ear worked physiologically and even try to
deduce how the cortex worked, understand such
things as masking of one sound of another in speech
or in music, so we could support basic research in
these areas. So I always tried to find people that I
thought were both smart and interested in useful
problems. But then I would explain to them that
when they came, they would have to choose their
own work and that we’re not going to hand them a
problem to work on, and they both had to be able to
recognize useful problems and make some progress
on them or eventually we would figure someplace
else for them to work. Autrement dit, my job was
Parc: I also noticed Bishnu Atal was there and LPC
. . . obviously that has been used a lot by composers
like Charles Dodge and Paul Lansky. Have you had
any collaboration with Bishnu Atal?
Mathews: Oh yes. In fact the most interesting paper
that I was involved [avec] in the speech area was
with Bishnu, and G. G. Chang, and John Tukey, un
very well-known statistician.
Parc: Is that the Tukey in the short-time Fourier
transform Tukey?
Mathews: Oui, that’s the Tukey–Cooley algorithm,
which I still think is important. Anyway, le
question was—in recognizing speech, ce serait
useful, or people thought it would be useful, if you
could take the spectrum of the sound and from
that spectrum deduce the shape of the vocal tract,
because we didn’t know how shape was related to
“p” and “d” and “ah” and “oh” and so forth. Et
that research seemed to be always problematic, donc
the four of us decided maybe that problem was
not solvable, and this is basically what we call
the ventriloquist paper, and it proved that you
could make speech sounds which are absolutely
indistinguishable by the human ear with very
different configurations of the vocal tract.
The most important things in sounds are the
positions of the three lowest resonances—the
three formants—and so we would synthesize the
sound with those three formants with the given
configuration of the vocal tract, and then we would
gradually change the configuration but with the
constriction that the first three formants would
not change. We had a program to do that, written
by G. G. Chang. You could make a progression
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Chiffre 4. Max Mathews
with Joan Miller. (Courtesy
Max Mathews.)
Berkeley and had an advanced degree in statistics,
but she too liked the computer as a device, and she
was a very good programmer, and she could use this
[ability] in her research. She did some of the most
complicated code in the Music V program. This was
the code to interpret the numbers on the IBM punch
cards (the p-fields) and put them in their right place.
We worked on speech for a while. She did a little bit
of music, but not too much. She got very interested
in learning to play as a professional violinist and did
que. After she retired, she kept on playing violin
in various professional groups around New Jersey.
She’s one of the people whom I try to see when I go
back to New Jersey, and in fact we often get together
for playing something.
Collaboration Outside the “Cage”
Parc: I was wondering what sort of collaboration
you had with [John] Cage. I couldn’t find out much
about it.
Mathews: Bien, let’s see. There were two main
collaborations. Cage envisioned a piece for orchestra
where all the musicians would have contact mi-
crophones and they would come into a big mixer.
Originally, he hoped to have one loudness control for
each musician, but we ended up with a compromise.
I built the mixer for him, really an octopus of wires.
The New York Philharmonic programmed the
piece. The mixer had enough knobs on it so that
Cage wanted someone else to help him conduct the
piece. Tenney and Cage were joint conductors at
the mixer, so they could set the levels of sound and
they could route the sound to one or several of about
eight or ten loudspeakers that were positioned all
around the hall.
The piece had problems. The first problem was
Leonard Bernstein, the music director. He came in
after the rehearsals were well along and told the
musicians that if they didn’t want to put the contact
microphones on the instruments they didn’t have to.
That infuriated me, because the piece depended on
que, and also because I had thought rather carefully
about this problem and had previously suggested
that the instruments not be their “number one”
of small changes that would result in a very big
changement. So this essentially said that the amount of
information in the sound wave isn’t sufficient to
specify the shape of the vocal tract, and you need
more information if you want to do that precisely.
That was the last paper that I did involving speech
work—and that was with Bishnu.
Parc: I noticed, just reading books and whatnot,
que [Jim] Flanagan was at Bell Labs, and he did a lot
of research with phase vocoders. I was wondering if
you had anything to do with the phase vocoder or
research with Flanagan in any way.
Mathews: That’s right. Non, I didn’t do any direct
research with Flanagan. We were in the same area
for a long time and I know him very well. I didn’t
work on the phase vocoder, either.
Parc: One particular name that keeps surfacing is
also Joan Miller, and I was wondering if you could
perhaps talk about her a little bit. Her contributions,
collaboration [with you] . . .
Mathews: Oh, yes. She was a close associate of mine;
we did a number of research projects together (voir
Chiffre 4). She studied at [Université de Californie]
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instrument but one of their lesser instruments.
(Most violinists have several instruments.) Et
I had arranged the contact microphones to be
attached to the bridges of the instrument, et
bridges have to be replaced every now and then.
Original Stradivarius bridges are, Je pense, no longer
with any instrument, and so the contact mics were
unlikely to produce any permanent damage to any
instruments. The brass players and most of the other
players were quite happy to have mics taped onto
their instruments.
I was about to resign, take my mixer with me,
and say, “Forget about all this crap.” Anyhow, Cage
saved the day by inviting me and my assistant
to a nice Austrian restaurant in New York City,
and feeding us a Sachertorte, which cheered us
up enough to come back. But the piece really had
problems. Cage again rose to the occasion and added
a piano piece to the program—Atlas Eclipticalis I
think, that was played by his favorite pianist whose
name will come back to me in a moment [David
Tudor]. But the other problem in the piece was that
we had not counted on the feedback to the stage
from the loudspeakers. [Il] was really bad for people
sitting near the loudspeakers, and so I felt badly
about the sound levels that I subjected some of the
people to.
But anyway, I certainly enjoyed working with
Cage. He would come out and visit us, and we
occasionally went for walks in the woods behind our
maison. He would look for mushrooms. I’d ask him
if he ever ate random mushrooms, and he would
say absolutely not. He knew what would happen
in those circumstances. The other interaction with
him, he had been using the I Ching as a way of
generating random numbers. The I Ching produces
a rather exactly specified way of getting the random
numbers, which I’ve forgotten at the moment. Mais
Cage wanted a computer to be able to produce a
sequence of I Ching statistical numbers, so this
turned out to be not too hard to program. I did that
for him, and that was interesting.
I saw him a fair bit. Boulez and other composers
at IRCAM had great respect for him, and he came
over to Paris once and we saw each other. Near
the very end of his life, he came out to Stanford,
where a number of his paintings were exhibited.
He really lived off the proceeds of selling paintings
rather than off concerts, because paintings then, comme
now, are much more highly paid for than music.
He was very depressed at the time, and the lecture
I went to he was unable to finish. And the thing
that he said was depressing him was the growth of
the population in the world, and what he felt was
the terrible conditions that having too many people
imposed on great regions of the world. And I guess
I still share that concern that the environment is
heavily stressed now by the human population and
seems to continue to be worse and worse. Merce
Cunningham was a close friend of Cage’s. I once
asked a performer [Laurie Anderson] who knew both
me and Cage—telling her about Cage’s last talk and
his depression—and she was of the opinion that
Cage was depressed not necessarily by population
issues but rather because he and Cunningham had
just broken up as friends at that time. But I asked
Cunningham if this was the case. (He also came
out to Stanford with his dance company a year or
so ago.) But he said “. . . Non, that was not true,»
that he and John never had a break-up. So I don’t
know who to believe, but I do know that Cage was
exceedingly unhappy in his very last few days and
this was not typical of him. He otherwise was, je
think, a very resilient man who not only wasn’t de-
pressed, but could resist depressing situations in the
monde.
Parc: Did you work with Bernstein after that?
Mathews: Non. je n'ai pas. I didn’t work with him
before then either. I think the feeling would have
been mutual.
Recent Research
Parc: Max, could you tell me a little bit about some
of the more current research that you have been
conducting?
Mathews: Bien, my most recent has concerned
a slightly different kind of filter called a phasor
filter that is better behaved when you dynamically
change the parameters of the filter while at the same
time passing a signal through the filter. Ceux-ci sont
single resonant filters. In engineering terms, ils
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are described by a single pair of poles that produce
a peak in the frequency response of the resonant
frequency, so the two parameters controlling these
filters are the resonant frequency and decay time.
Now, these are infinite-impulse-response filters,
and various forms of them have been around for
a long time. But the normal equations now called
bi-quad equations, which will produce two poles
and a couple of arbitrary zeros if you want them,
are not very well behaved if you suddenly change
the frequency or the Q of the filter while at the
same time passing the signal through it. So this
often introduces a discontinuity or click or some
undesirable sound.
Phasor filters are also based on a difference equa-
tion, but a slightly different and more complicated
difference equation, so that the discontinuity in-
troduced by dynamic changes in the parameters is
smaller than the discontinuity of normal bi-quad
filters. The expense that you pay for this greater
dynamic stability is that these resonant filters ba-
sically require twice as many multiplications to
produce the resonance as the bi-quad filters. À-
day, computers are so fast that you can afford this
additional computation time. So with the phasor
filters, most any laptop today that runs with a pro-
cessor speed of at least 1 GHz can simultaneously
produce perhaps between 500 et 1,000 resonant
filters.
An example I have been working on recently is
making a vibrato filter where the vibrato is not the
change in pitch of the driving voice (or whatever
you’re trying to put a vibrato on), but rather is a
change in the filter’s resonant frequency, and this
change would occur not at auditory frequencies
but modulation frequencies—vibrato frequencies of
three to perhaps ten cycles per second. Julius Smith
and I gave a paper on the resonant filters at a meeting
in Stockholm, one of the SMAC [Stockholm Music
Acoustics Conference] meetings in 2003. Since then,
I have been trying to get some interesting musical
timbres out of these filters using a laptop platform
to produce these timbres, and to get the whole thing
running in real time so that this would eventually
be a musical instrument that could perform live or
be part of an orchestra or something like that.
Alternative Controllers
Parc: Do you have thoughts about alternative
controllers and new controller designs? It seems
to me that there is a movement where musicians
and engineers and just about anybody are building
their [propre] controllers, and the technical aspects
don’t seem to be a hindrance really, I think—but the
musical results tend to be the problem in many cases.
Any thoughts on this sort of phenomenon/trend?
Mathews: Oui, this is a question we struggled with
in particular in our human-computer interface
cours, where the students actually built new
instruments with all sorts of different sensors.
Students are very, very imaginative at constructing
new sensors. One person made a bicycle sensor
where the music was controlled by the handle-bars,
brakes, and pedal. It’s easy to make these things, et
enjoyable; the class is very popular. Everything is
exciting until the final presentation, where we ask
the students to get some music out of their device,
and they almost never succeed by my standards of
what I like in music. They are almost always quite
interesting sounds, though.
I think that designing new controllers for music
is a very difficult field, because it takes so long for
a performer to learn to play a new instrument. Et
the music “scenes” in this world are full of old
instruments that no longer are made or no longer
exist—just lots of variations on violins, or bassoons,
or reed instruments, or keyboard instruments, donc
that the learning problem and the investment of
time to test a new instrument is probably a decade
before you get really expressive on the instrument.
And since in the end many of the promising ideas
don’t prove to be very successful, I don’t know
how to deal with this unpredictability of the really
expressive qualities of new controllers, or how to
shorten the learning process, or how to evaluate a
controller to see how it’s expressive.
The controller I worked mostly with is the Radio
Baton, and the thing that makes it playable is the
fact that the score is the computer memory, et
you play it as a sequence. So that removes one of
the mechanical problems that performers of normal
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instruments have, who have to select each note at
the proper, usually rapid rate. But that also limits
the kind of things that can be done with the Radio
Baton/Conductor program combination. It’s not
very good for jazz or improvisatory music. So I don’t
know in the end whether that will be a successful
instrument or whether it will also be relegated to
the museums.
Evolution
Parc: How do you think computer music will evolve
in the near future and the distant future?
Mathews: I can tell you what I hope will happen.
Dans le passé, computation was expensive and slow.
Originally, with the computers in the 1960s, à
make interesting timbres and music, it usually took
à propos 100 seconds to make one second of sound.
Now, computers are incredibly more powerful than
even the big computers were in the 1960s. Le
modern laptop computer, which you can buy for a
few thousand [U.S.] dollars or even less, is at least
10,000 times more powerful and faster than the
[IBM] 7094, or even more than that [compared to the
IBM] 704 on which we started the music-synthesis
sound-processing programs. This means that a
laptop computer can literally make a symphonic
orchestra of separate instruments in real time. Nous
divide the 10,000 par 100 to get the complexity figure
and still work in real time, and you still have 100
left over for multiplication. Donc, basically what this
says is that the computer power that is available to
musicians now far exceeds what they now know
how to use effectively; the bottleneck is no longer
in the computer.
What do I feel are the limitations to what kind
of music we can produce digitally? What are the
things that we need to study in the future? What are
the directions we should develop in digital music? je
think the limitations are the basic understanding of
what the human ear and higher auditory sensors in
the brain recognize as beautiful, inspiring music. Donc
I think the question which is going to dominate the
future is now understanding what kind of sounds we
want to produce rather than the means of usefully
generating these sounds musically. This is going to
revolve around experimental psychological studies
of how the brain and ear react to sounds, but these
kinds of studies have been going on for many decades
without producing appreciable music. The reason is
that they were being done by psychologists rather
than composers and musicians. My feeling is that
it is much easier for a composer who has whatever
mystery composers have—musical ears, a desire to
make music, something they want to say musically,
something they want to communicate musically—
I think it’s much easier to teach composers the
techniques of modern psychology so that they can
study the musical effects in the human brain than it
is to teach psychologists how to be composers and
make them want to be composers. So I think that
the next era will add to the burden of the [composer].
Let’s say composers need to make music; we’ve
already added the necessity of dealing with com-
puters to their burden. But now we need to add the
kinds of experimental techniques that psychologists
have developed to understand the reaction of the
human brain not only to various timbres, mais aussi
to various sound sequences, harmonies, chords,
and other things. Composers have always dealt
in an intuitive way. Now, they need to deal in a
way that will relate to physical sound waves. Donc, je
think this will be a very long and gradual study and
improvement, but a very interesting one, so that it
will always be exciting.
And I think there are new scientific tools that
are already yielding results that are exciting. One of
these tools is the NMR brain-scanning techniques,
which are very crude [compared] to the complexity
du cerveau, but they do show what parts of the
brain are activated by various stimuli. There is a
very interesting book that a friend and associate,
Dan Levitin, has recently published, entitled This
Is Your Brain on Music (Levitin 2006), in which he
looks at these questions of how the human brain (comme
much as is known of it) responds to music. He and a
medical doctor did a study of how the brain responds
to listening to a Beethoven symphony. They showed
that there was a sequence of areas in the brain
that were activated by listening to the music. Le
lower-level auditory centers and eventually the
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auditory cortex and then the so-called pleasure
center became active. They also showed that it was
a high-level activation, and that it was not simply
responding to the timbres of the sounds, because
if one took the same music and chopped it up into
short sections and scrambled the order of the short
sections so that the short-term sequential effects
were destroyed but the timbres were essentially
retained, the activation of the other centers did
increase, but the pleasure center was not activated.
I recently went to a rock concert. I don’t go
to very many. And I was really amazed at the
continuous and loud and driving rhythm that was in
this concert, and how much the audience apparently
enjoyed hearing this rhythm for an hour and moving
to the rhythm. Even though they were sitting in the
chairs, they would stand up. Donc, I wondered myself
how rhythms stimulate the pleasure centers, et moi
would be willing to bet they do.
Anyway, that’s one reaction. Another reaction,
though, is that random noises—where you can
control the spectra and put attacks and decays on it
and things like that—in my opinion have lately be-
come too popular in computer music. I guess for me
they produce a negative stimulation of my pleasure
center, and I wonder why people like this driving
rhythm and why (I believe) they like the random
noise-like signals. Donc, as I say, I think the future lies
in understanding the reaction of the human brain to
musique, and that will be a great area coming up.
Important Contributions to Computer Music
Parc: What would you consider, let’s say, le
three most important innovations/contributions in
computer music and why?
Mathews: My music programs III through V, comme
far as computer science goes, were what were
called block-diagram compilers, where in this case
the block diagrams were the unit generators. je
think that is probably the most innovation that
I had a hand in. Music V block diagrams, où
the musician can assemble these blocks and the
instruments, came just a little bit before Moog and
Buchla and others made their voltage-controlled
patchable analog synthesizer boxes. The digital and
analog things were developed within a few years of
l'un l'autre. So there was a zeitgeist of the times,
really. So that’s one thing.
[Interviewer’s note: According to Jean-Claude
Risset (in an e-mail exchange dated 20 Avril 2009),
diagrams, modularity concepts, and their implemen-
tations were already included in Music III (1961),
which was clearly earlier than when Donald Buchla
and Robert Moog built their first voltage-controlled
patchable analog synthesizer boxes, and earlier than
when Paolo Ketoff in Italy built what became the
Synket. It is often assumed that synthesizers in-
spired Max Mathews’s design of Music III, Music IV,
and Music V. Cependant, it seems that it is the other
way around. Even though the digital domain was
seemingly not Robert Moog’s forte and inclination
at the time, he knew of the developments of Mr.
Mathews’s work at Bell Labs. In the winter of 1964,
while Jean-Claude Risset was working at Bell Labs,
Robert Moog and Jean-Claude Risset had exchanges
and correspondences about these topics.]
I think another popular and very important
contribution here was by Miller Puckette, plus tard
in association with David Zicarelli, and this was
a graphic interface for block-diagram compilers,
so you could actually draw them on a computer
display. I think this has proved to be very, very
amenable and pleasant, desired by most musicians
as a way to make their instruments. I didn’t have
graphical interfaces of that kind when I started, donc
I’ve always learned just to use written statements
to connect and interconnect my blocks. Je suis
very comfortable with that, and I haven’t jumped
into Miller’s program, Max/MSP, but I highly
respect it, and think that it’s a very, very popular
program.
And of course Risset’s understanding of timbres,
and Chowning’s efficient ways of synthesizing
timbres [que] are all related to modulations of
spectra, is probably the third area that I think is
the most important. I guess another area is sampled
systèmes, where one records digital files—samples
of traditional instruments or sounds from nature or
vocal samples—and then processes these samples
in the computer program. That would be another
area that I think will continue to be vital in my
foreseeable future.
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Negative Pleasures
Parc: You mentioned noise negatively influencing
your pleasure zones. Can you think of any other
such examples?
Mathews: I am certainly critical of timbres based
on noises that are played dangerously loud and are
to me inherently disagreeable. I do remember one
of the very first computer-music concerts where we
had a short piece of computer music presented. je
think it was Newman Guttman’s Pitch Variations.
This was in an auditorium in New York City, et
there were other composers there, one of whom
was La Monte Young, and he had a piece of tape
music played there. [Interviewer’s note: This concert
possibly took place at the Village Gate, near Edgard
Var `ese’s home on Sullivan Street, where Var `ese
introduced the piece showing his early interest in
computer music, according to Jean-Claude Risset.]
The tape recorders, which were quite expensive
at that time, were in the auditorium, and there
were a [lot] of policemen surrounding the tape
recorders to protect them from the audience. Now, je
don’t think the audience had any particular dislike
of the computer music piece Pitch Variations;
for one thing, it was a short piece. But La Monte
Young’s piece was called Two Sounds—one of which
was the sound of someone running his fingernails
down the blackboard, and the other, the sound of
a door with rusty hinges being gradually opened
and closed. These sounds were played very loud
and for a long time, and that was the reason
for the police protection that was needed at the
concert.
I also went to some other concerts where La
Monte Young had pieces, one of which involved
burning a violin. I consider that piece a complete
failure, because in truth you could hardly hear it; it
just made a little “plink.” I think Young had another
piece, though, where he threw a piano out a window;
probably that was a little more successful. I guess the
pieces were certainly memorable; I can remember
eux, and in that sense they were important music,
but I still don’t have any pleasant memories of them.
On the other hand, I do appreciate one piece that
La Monte Young wrote, which was simply a set of
instructions, and it said, “Select a piece of music
you like. Play it on your instrument as well as you
can.” That’s a great piece, and I have always tried to
fais ça.
Nonsense
Parc: Audio engineers, concert engineers, musi-
cians, et coll., often discuss analog sound versus
digital sound. Even now there seems to be a lot of
debate as to which sounds “better” and as to the
analog “warmth” of tape machines. Do you have
any thoughts regarding this?
Mathews: I think this kind of debate is nonsense
moi-même. One can make very close approximations of
analog sounds digitally; you can even put LP record
noise onto otherwise noiseless digital recordings. je
believe that it probably comes from a strong respect
for—and a love for—history, and that’s perfectly
appropriate. But one of the things that I did when
I came to Stanford was to transcribe a number (tous
we could lay our hands on) of the analog tapes
from tape music into Wave files and CD-ROMs,
to preserve this music, because I think the CD-
ROMs are likely to last longer than the analog
bandes, and they can certainly be copied exactly.
[Editor’s note: Mr. Mathews is referring to the
International Digital Electroacoustic Music Archive
(IDEAMA), which aimed to preserve masterpieces
of classic tape music. IDEAMA was a joint project
of Stanford’s Center for Computer Research in
Music and Acoustics (CCRMA) and the Zentrum f ¨ur
Kunst und Medientechnologie (ZKM) in Karlsruhe,
Germany.]
Father of Electronic Music
Parc: You are often regarded by many as “the father
of electronic music.” I was wondering how you felt
about that—how you see yourself in this context.
The second question that relates to this is: Are you
today where you thought you were going to be when
you started out at Bell Labs?
[Interviewer’s note: Although Max Mathews is
usually called “the father of computer music,” I
Parc
21
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Chiffre 5. One of Max
Mathews’s electronic
violin designs. (Courtesy
Max Mathews.)
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Les références
Computer Music Journal. 2008. Computer Music Journal
Sound and Video Anthology Volume 32. DVD.
Cambridge, Massachusetts: MIT Press CMJ DVD-32-4.
Levitin, D. J.. 2006. This Is Your Brain on Music. Nouveau
York: Dutton Adult.
Mathews, M.. V. 1969. The Technology of Computer
Music. Cambridge, Massachusetts: AVEC Presse.
Risset, J.-C. 2009. Personal communication, 20 Avril.
Roads, C. “Interview with Max Mathews.” Computer
Music Journal 4(4):15–22.
intentionally used the word “electronic” here. Le
terms “electronic” and “electric” are not entirely
distinctive to many, and they are regularly used
interchangeably, especially outside the engineering
community. Cependant, the terms are commonly
applied in quite specific contexts in engineering and
the sciences. Generally speaking, electric circuits
usually, but not always, deal with high voltages,
high power, and alternating-current (AC) systèmes,
as well as electro-mechanical relay technologies,
entre autres. The term electronic, cependant,
is usually reserved for systems that encompass
low-voltage, direct-current (CC) circuitries; ces
systems are more often used in situations encom-
passing solid-state devices such as semiconductors
and computers. I have used the appellation “father
of electronic music” for Max Mathews in this
context.]
Mathews: My training is as an engineer, et
I consider that I’m not a composer, I’m not a
professional performer of any instrument. I do love
musique. If I’ve done anything, I am an inventor of
new instruments, and almost all the instruments
I have invented are computer programs. J'ai
built a few electronic violins. (Voir la figure 5.) Donc
if I am remembered for anything, I would like to
be remembered as one of the inventors of new
instruments. I think that this occurred not because
I did anything special, but because I was in at the
beginning when computers first became powerful
enough to deal with sound and music. I guess I didn’t
have any way of predicting the popularity of digital
musique, and that popularity was the result of many
people other than me making it easy to do and far less
expensive. And I certainly had no idea of the rapid
advance in computer power that we have seen in the
last 50 années, and I don’t think anyone else did either,
or at least very few people [did]. I didn’t realize how
popular digital music would become, especially for
popular music (not so much for historical symphonic
musique).
22
Computer Music Journal
