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# Importance of an Overall Plan to Composition

SS: We're back again with Roger Reynolds, and what we're going to be talking about in this segment is mainly Transfigured Wind. And Roger, we've covered a little bit of Ambages and a lot of other things previously, but we didn't get to a very important part of the process, and I'm not sure that we will except if you care to bring it up, of another orchestral piece which is Archipelago. But maybe we can catch up on that later, unless the discussion works out that way. But what we're interested in right now is to try to look at the overall plan that you devised for Transfigured Wind. I take it from what you've said before that Transfigured Wind II was really worked on at the same time as you did Transfigured Wind I?

RR: I explained when we were talking before that I make plans to begin with, and of course the plans also don't come into existence suddenly. They are worked through in stages. I try out ideas and gradually settle in on the way they should be. We have here one of the earliest plans in relation to Transfigured Wind (view an image of the initial plan). And what you can see is that, at the top, there is a proportioned series of one, two, three, four segments; and on the bottom there are also one, two, three, four segments; and what happens in the middle here, is that those two sets of four are interleaved. The first thing that happens is that the flute plays a solo, then the ensemble enters with a commentary, the flute plays another solo, there's another commentary, another solo, another commentary, another solo, another commentary. You can see that this has, as I explained, an outward tendency. And the first thing that I was doing, given that I knew I wanted to make a piece of around thirty to thirty-two minutes in length, the first thing I did was to settle on numerical series -- in fact they're logarithmic series1 -- that would, when intertwined, give me the duration that I wanted. Now it's not so simple as to say that I simply choose a series and make it happen.

Obviously the idea of interleaving series is the first step. What then happens is: what kind of interleaving? What is the duration of these parts? What is the implication, for example, if I start with a duration of modest length here for the flute? How long do I want the response to be? How long does it need to be? It would be possible to think of a statement or response process where a statement was quite long at the beginning and the first response was brief. In fact, I decided that it would be in an expanding sort of proportion. Then, once having decided on the basic idea of the interweaving of two sets of four, one representing the solo instrument and the other representing the ensemble, then the next step was to (- if we can move the camera up to this one -) ... the next step was to actually get into the details. Now I have to say that the detail here in this plan is probably more extensive than in any other piece that I had done up to this time with the exception of Archipelago which you mentioned. We may or may not have time to get to that, but the basic idea is that Archipelago was for me a watershed piece. I went to Ircam2 - I was there in residence (in Paris) on and off for two years. The opportunity came in the early 1980's at a time when I was in a mid-career situation, and it offered me a chance to really rethink the way I considered musical form and also, most importantly, what I was going to do about the integration of technology into my composition. And so this piece [Archipelago] was rather elaborate.

View "compositional plans" for Archipelago:

[Back to Transfigured Wind,] we have here, in a second plan, the four segments that are provided by the solo flute, but you can see everything else has gotten more complicated. Here we have the shaping or the positing of the kinds of opportunities that are going to exist in terms of the computer's role. So basically what has happened is that, instead of having, as we did in the earlier diagram, two factors, I now realize that we have three factors. We have the solo flute, the ensemble response, and the response of the computer. So I have to build that into the diagram. Now, at the bottom, here again are the same proportions - one, two, three, four - for the ensemble, but now I've broken the ensemble down into a number of strata. You can see those as woodwinds, percussion, brass and strings, and above for the computer part - this is the ensemble part, this is the computer part - you can see that those are each also broken down in a way that you can think of as a mosaic. And I see this as a shaping of opportunity - as the proposal of a certain set of opportunities that I will have.

Now because I have it in this rather, I'm sure for many people, horrifically objective form, it helps me enormously because I can foresee the kinds of problems that I'm going to get into if I try to realize this. And I can build my materials and my methodology in such a way as to foresee, and already have accommodated, the kinds of difficulties that I'm going to get into. For example, we see that when we get to a place like this, there are one, two, three, four, five, six, seven, eight layers of things happening. What that means, of course, immediately, is that those layers ... they have to allow for one another's presence. I have to think of the representation of an idea that includes the participation of woodwinds, the participation of percussion or brass or the solo instrument or the computer. I have to think of these in such a way that they don't obscure and obfuscate one another but tolerate and even benefit from one another's presence. So what the plan does is to give me a map of the future in such a way that I am obliged not to just charge into this (as you can see) fairly complex project blindly or intuitively, but with the sense that I have already laid out the opportunities and already spotted what might turn out to be problems that are inherent.

SS: Well this approach really does remind me of an architect designing a building, developing and working from a plan. And to other people the plan may look impossible on paper, but the architect is able to see the problems in the plan that are going to come up when people start hammering in nails and laying bricks.

RR: One of the things that you can also see from here is the idea that what a lay person might think of as a unity, as an inseparable identity, such as the orchestra, is in my view, here, something which can be, and indeed in this project will be, thought of as a composite resource. I'm thinking on the one hand, of course, in a rather traditional way, that there are primary families in the orchestra, but also that I'm going to think of them as potentially independent resources. What does that mean? It means that they have to have a role in the design of the whole and it means also that they have to have materials, they have to have ways of presenting themselves which are identifiable, experience-able, if you will, as independent entities that will, when necessary, work together.

So you could think of it as, let's say, taking a Beethoven or a Mozart symphony and extracting the horn parts, the brass, the strings, the woodwinds, and sliding them in time relative to one another, so that the potential that they have to work together when they are in phase is always there if you wish it to be and, in this case, if you planned for it. But at other times you can have what you could think of as a representative of a certain passage of a movement of a minuet, of a rondo or something which is separate from, out of phase with, its other parts.

To me this is in large part the way life is, where we do from time to time have the great experience of everything coming together and fitting. But frequently the components of our life, the components of our days, are not ideally in phase with one another. An opportunity comes at a moment when you're otherwise occupied; you're too tired to take advantage of it and so on. So for me the idea is that first of all we look into the presumed identity of the orchestra or of the sound of the solo instrument and we use the computer to analyze it - open it up - and allow us to take something that we have thought of always as integrated, as this, and go ummmhmmmph [RR gestures interlacing the fingers of his left and right hands together to form a composite surface, then pulling them apart] so that now we have two things. Each of them is indebted to the original sound, but is only a partial representation of it. If we put them together, the thing is there, but if we separate them, put them out of phase with each other, we get a very strange kind of experience which in my view teaches us something previously unknowable. It's rather like, let's say, envisioning the microscope or telescope. It allows you to confront an aspect of your reality which has always been there, it is there, but it's something we haven't been able to see before or apprehend directly, and therefore it's something that is only in an abstract way a part of our thinking, a part of our dreams ....

One of the things working with computers has done to and for me is to cause me to always think of any unitary thing as potentially multiple, and on the other hand to think of any multiple thing as potentially unitary. And to work with that idea is what fascinates me so much at this moment, for example, about Greek theater: because of the idea of the chorus which is multiple but speaks as one and the protagonists who are evidently singular but frequently speak as representatives of an entire class or society. I find this endlessly fascinating.

So this "breakdown" which I fully understand may be a bit unexpected for people - even for a lot of musicians - as I indicated in our earlier conversation, is not something that I just started doing one day. It began in a very much more elementary way. At this point, I feel entirely comfortable with this way. In fact I feel a lot better about starting a piece when I have something like this, because the project - otherwise a terrifying expanse of the unknown - is in fact now a set of knowable and definable issues. I can know where everything fits, and I know how to go about solving each problem or, from another perspective, fulfilling each invitation.

SS: I'm reminded of something at a master class you gave at the 2000 June in Buffalo contemporary music festival in New York. One of the young composers had brought in a piece - there was something in it that was very repetitive, I can't remember exactly what it was. One of your suggestions to him was: you know, this would come alive if you could string this passage out in time, split it up a little bit - or each time it doesn't have to appear exactly in the same place. It was this same idea of coming-apart/putting-together that you're talking about here that you appeared to be trying to give to him.

RR: One common problem for young composers is that the music moves too rapidly. They have little sense of the amount of time that an idea needs in order not simply to be indicated but to be experienced. I've been saying all along that it's a totally different thing to offer an opportunity and to have an experience. I have a tendency to write rather long pieces. This isn't because I want to be grand. It's because, for me, music is about experience and time, and when you have a longer period of time there's a richer and more complex path that you can follow.

If one is talking about, again, a young composer at June in Buffalo3, what frequently is necessary is to suggest how it is that perhaps a rather interesting brief idea can be made larger. Now, obviously, you don't want to inflate something like a balloon so that it's larger than it ought to be, but when there is an idea which is promising the question is how do you get somebody who doesn't yet grasp that into a mode of discovering how to make it larger, how to make it begin to inhabit more varied temporal terrains. So for me, the idea of breaking things into components and pulling them out of their temporal coordination with one another produces some very interesting - what I think one might call shear forces. You know, in physics, if you start sliding the planes of a physical object in opposite directions, it's the most powerful way to break or distort. When you think about breaking a stick, it's one thing to break it this way (cross-wise), it's something else entirely to break it that way (length-wise).

SS: That's true.

RR: The cohesive power of that sort of coordination, I think, also adds up. And experience when things are not gelling temporally has a profound effect on our emotional lives. This is something that interests me a lot.

SS: Is this a good place do you think ... unless you want to say some more about this aspect right now ... is this a good place to get into what you do with these segments, which are at this point undefined. I'm talking about compositional algorithms, editorial algorithms4 as you refer to them.

RR: Well, the first thing that needed to happen here was that the material for the solo was written, and out of that material the needs of each of these responses were assessed. Now to some degree the material that happens in the first response is indebted to the material in the first solo proposal. We can call the solo the proposer and the ensemble the respondent, but not exclusively. The solo part itself is indebted to a row, to a set of numbers (numbers as proportions and numbers as enumerators); the ensemble is also indebted to (as you can see) the design .... So far as timbre is concerned, there is the subdivision into the percussion, brass, woodwinds and strings and so on. And up here, over on the side, there's a set of six-letter acronyms which have to do with ways in which the computer can modify, elaborate, dissect, and reassemble the given sound.

Now, in the same way that the ensemble is to some considerable degree dependent upon the material in the solo already written, the tape is totally dependent upon that. Because what happens is this: after the material has been composed - and this is not only true for Transfigured Wind, but a rather large number of the pieces that I make with computer - I then go to a performer and I work with that performer as though he or she were preparing for a performance, a public performance of that material. In this case, that performer was my friend and colleague Harvey Sollberger. Harvey had played a lot of my music before, I knew him very well and we worked very hard on this material as though it were going to be performed in a concert. Then we recorded it.

Once the material is recorded there are two kinds of information there, and this is an important thing for me, something that computers have opened the door to which has not ever existed before. There is the design and content of relationships that I composed and there is the musical performer's intelligence that Harvey, as a very fine flutist, brings to it. So when this material goes into the computer, when it's digitized, it consists not only of what I did but also of what he did. And that means that the performance information, the performance necessities, now become a part of the composition itself. How Harvey shapes things becomes part of my material, and in the context of the computer part, his inflections, his timing, his way of balancing things is everywhere in the piece. Just as my relationships are everywhere. And I find this extraordinarily interesting and rich. Primarily it's rich because it allows for a kind of expressive dimensionality, which is very valuable and actually comes into the world of contemporary music very rarely. Why? Because, normally, there is a demand, a first performance; and after that the organizer, the orchestra, the soloist, the festival organizer, wants a new first. They're not interested in re-playing.

The kind of richness that comes from inhabiting music for a long period of time is largely absent from the experience people have with contemporary music. I think it's one of the major difficulties with people, let's say, "warming up" to it, because it's in fact not performed. It's executed, and sometimes I mean that almost literally. In my case, because I work only with players that I really know well, and we worked very hard for a long time at shaping [my material], there's an investment on the part of the player which I think calls forth an investment on the part of the listener. It's a very rich thing. So the material that is composed is also recorded. The composition and the performative information become essential to the computer part. I am, of course, influenced by the way, let's say, in this case, Harvey shapes the ideas. This generates more response in me. So when I start writing the ensemble response, I'm not only responding to my own composed piece, I'm responding to the way he's treated it.

SS: You have more material to shape at that point.

RR: Yes. Anyway - as we've already indicated in our earlier discussion - behind the solo parts, the proposals, there are two factors: one is a body of conditions - rows, numbers, etc., etc., this design; and, on the other hand, there also is - in this case which is quite unusual - the existence of a prior piece, Ambages, which I "mined" as a part of the making of the new solo proposals. When I'm ready to do this, you see, I already know - because of this design - I know what is going to follow the first ensemble response. I have a certain orientation or foot hold in the future of the piece. So my obligation is not to go blindly forwards, but rather to figure out what is needed here, partially in view of what has already happened and partially in relation to something that I know is going to happen later but hasn't yet. I mean, metaphorically, this is the difference between the composing of the piece and the experiencing of it as a listener. Anyway, the process then actually moves forward rather linearly and I composed the whole piece more or less as you see it here.

SS: So at this point you are going from the first note to the last, more or less .....

RR: More or less. Now, if, for example, let's say I looked at this plan and I saw that there was a particularly important or problematic place. I might, in fact, jump ahead and compose that. I want to make sure that I know how I'm going to deal with that. So I might go to this difficult place and fix it. I already know how I'm going to do that moment in the future, and now I go back.

For me of course, this is one of the enduring and extremely important distinctions between improvisatory music making and composing. Composing is done "out of time." It allows you to move into the future, into the past, wherever you need to be, and to consider what it is you would like to be true about that future or that past. When you're in a live, improvisatory engagement, this kind of thing is obviously quite impossible. You're in a one-directional mode, and you can't know what it is that's going to happen later. I mean, you can of course imagine, you can posit in your mind while improvising, but in the case of a composer - while he or she is composing - you can be anywhere ...

SS: Right.

RR: ... and I think that's interesting.

SS: It's my impression that a lot of younger composers - it may be because they're overwhelmed with electronic possibilities these days - but, in the studio, they are almost ad libbing it, so to speak, and just doing the recording on the spot and playing with things as they go. I don't know how many of them plan like this or understand the importance of it.

RR: Well, let's be clear. By explaining what it is that I do, I'm not advocating that as a way. I'm simply pointing out that, at least in my case, this is where I've come. And it is important to emphasize that it has taken me, after all, some forty years to get here. It would not be expected that you could dive in to the work of a mathematician, or a physicist, or a doctor, or in fact any discipline that is on-going, and in which one develops greater skill and orientation over time, that you can jump in after forty years of development and say, "Well, I'll do it that way to start with." It makes no sense. What I am saying is that I believe that there is value - a very great value - in preparatory stages. And I don't quarrel with your comment about young composers ... whether I would say "ad lib it" or not .... That may be a little bit ungenerous. The problem is, if you are a young composer at this point, where do you look for a model: one to resist or to partially adopt or to embrace?

SS: Good point.

RR: You can look back to the sixties, in magazines like Die Reihe, and so on - when Darmstadt began - and the composers in Europe were not at that point opposed to talking about what they themselves were doing and what their colleagues were doing. So you get [György] Ligeti5 writing about [Karlheintz] Stockhausen6 and Stockhausen writing about [Pierre] Boulez7, [Luigi] Nono8 or whomever, and you don't see that happening now. And I think it's a great loss.

SS: Getting back to this chart, what I wanted to then point out, for insertion later or maybe you want to talk about it now, it's maybe a little too involved to get into at this particular time, are the actual algorithms themselves. You've become rather famous, in some circles at least, for things like SPIRLZ and SPLITZ. It seems to me that they fit in, at a micro level, what you're doing at a macro level here.

RR: This is an early diagram which shows the shaping of a piece called Variation 9 for solo piano. And you can see it's informal, it's sketched - there's some erasures and so on. Here's what happens to it a little bit later. It gets much more explicit.

SS: And it should be noted that in your book Form and Method, there's a very interesting long section about Variation in there - it goes into great detail.

RR: Here is a diagrammatic representation of the idea of SPIRLZ. At the top, let's imagine that this is a diagrammatic representation of a four-note musical motive - a long medium note, a shorter high note, a slightly longer low note, and then a note which rises in pitch. Now, the idea here is that the algorithm takes segments from this, as though a knife were cutting it into pieces and spiraling out. [Motions in spiraling gesture at diagram.] Let's say that the first set of sections is taken in fairly large bites - 1, 2, 3, 4, 5, and so on - so that, if you were circling this way [gestures counterclockwise], you would see: I cut out that, then I cut out that, then I cut out this, then I cut out that. When I come around to cutting out this segment at the end of the motive, I'm out of bounds, so I stop. Now I go back. I move the center point a little bit and I start again with smaller windows, and I cut out segments again counterclockwise. Then I move the center again, cut again with a smaller window, move again, cut with a smaller window yet, and so on.

So what is it that's happening here? Basically, this short musical idea is being represented in a very uncommon fashion by going forward and backward in it, starting at the center. So the idea is that the identity of the whole is presented to us in an out-of-order - in a sense, a permuted - form, which, of course, is part of what improvisors do. This particular instantiation of the algorithm has a tendency to "arrive" - in a tonal sense - to cadence. How is it that that happens? It happens because the chunks that are being cut out are getting shorter, and they are more and more concentrating on the latter part of the motive. And, as you see, if we carried this through more cycles - 1, 2, 3, 4 [motioning down the diagram] ... if we carried it five or six cycles, at the end we'd be having very little fragments only of the very last portion of the motive.

Now, obviously, the algorithm doesn't need to work only in that way. There are lots of other ways in which the principle of cutting something out in a spiraling fashion can be exercised. One can start with small segments and gradually have larger chunks. One can start at the closing and go backwards. One can start in the middle and not move, just always stay centered. One of the interesting things about this is that you see from this that the size and orientation of the chunks are not correlated with the changes in the theme, or the little motive. So that its edges - the first note, the second note, the third note, the fourth note - are not respected by the algorithm. What does that mean? It means that the formal effect of the algorithm is in conflict with the formal identity of the material. Now, of course, I can arrange it such that the algorithm and the material are in a direct and "correct" relationship to each other. Or I can work at it this previously described way. The thing that's interesting is that there's a kaleidoscopic situation where you have two competing organizational norms which are impacting on one another - again, something which I think in our time (as contrasted, let's say, to Haydn's time) is truer representation of the way we live. We are subjected to enormously powerful forces that manipulate us in contrary ways all the time. It is not surprising to me, therefore, that ideas would occur in music and art that play off that kind of reality in our experience. So this is the one of the two algorithms - SPIRLZ - which produces a unitary outcome. That is, the samples which are cut out as the algorithm generates its output are put (in the result) into a direct, unbroken sequence with one another, so you extract segments: middle, forward, back, forward, back, forward - new cycle: forward, back, forward, back, etc. And it all emerges as one line, a sequence of segments.

The complement to it, SPLITZ, is a contrapuntal or a multi-linear process. So again, if we have a prototypical motive with 1, 2, 3, 4, 5 parts to it, what we're doing is cutting it into odd and even pieces and separating them so that the odd pieces are down here (there have to be more odd pieces because the odd must begin and end) and above we have the even pieces. Then I reverse the order of the even pieces. So what does this in effect mean? - That the beginning and end of the algorithm's output contrasts the beginning and end of the subject, of the motive. In the middle, the fact that I reversed the order of the even pieces has little effect. So you go from a highly contrasted form of the thing you are processing, to a situation which is almost normal, and then back into a situation which is highly contrasted. Now, again, to explain it all in detail takes a long time, but essentially these two algorithms are very straightforward ideas.

SS: Well, I'll tell you, verbally and with your hand motions, in a few seconds I understood what took me a great deal of time and only partial understanding when I read the words before. It's very difficult, it seems, to explain some of these things just verbally on the page, where in a sense they're very simple.

RR: But there's a strange thing here if you think about it. An algorithm, even though I wouldn't venture to give a mathematical definition of it, an algorithm is essentially an automated process by which you can accomplish a rather complicated goal in a straightforward way. The way we learn in school, or used to learn, how to do long division - traditional long division is an algorithm. It's a way that allows us to come through a fairly complex purpose in a straightforward and manageable way. We don't even need to - in fact probably most people don't - understand why it works. But it does. Now that we have calculators, nobody cares about that anymore. But, in music, so far as I am aware, there is only one algorithm used in any society ever, and that's canon. And canon is an algorithm in the sense that you have a theme - or, as I would explain it here, a "motive" - and everything that comes out in the end in the canonic texture is a product of that initial identity transformed in some way: made longer, inverted, made shorter, multiplied, stacked on top of itself, and so on. So the essential things are: you know what the material is, and you know what the handles are (if we were to move it into the realm of the "machine-like"). The handle is: how many semitones up or down? And another handle is: is it twice as long or half as long? Another is: how many voices are there at a time and where do they come in? But it's a partially automated way of creating something which has potentially great richness. Of course, it can also be quite arid.

SS: Sure, it's one of the greatest games of all time in music.

RR: But it strikes me as being really odd, especially given the frequently remarked relationships between music and mathematics, that there is no other algorithmic procedure. I developed these in the early 80s. And, although they became more sophisticated in terms of the kinds of handles and the degree of explicit definition, they remained essentially the same. I thought I would use them in a piece or two and then go on to others. But I have to say, now that I've been using them for 20 years, I don't even begin to see an end to their use, and I feel that they remain provocative. As I say, we could spend all afternoon on just that, especially the nature of their complementarity and why, therefore, they establish, let's say, such a large space, such a large conceptual or operational space. I treat the algorithms as, in effect, one of my methods. I would never create material, or a form, with an algorithm. But the methodology - the way of treating material such that it begins to serve formal purposes - that seems to me something that can be partially routinized or automated. Form itself, and material, seem to me too sensitive, too important, too particular to a piece to be done algorithmically. That's not to say that algorithms couldn't in time be invented that would be so rich that these concerns would cease to be an issue. The reason that I call them editorial algorithms is that I feel that they have merit in that they make their effect by subdividing and re-ordering in a particular way an original thing. They do not transpose, they do not distort in other ways, the relationship of the parts of the subject entity.

The identity of the original object, the subject, remains there and can always be detected. What comes out of it is a kind of kaleidoscopic proliferation of that thing's parts, but organized in a certain way that, in SPIRLZ, normally one hears very quickly. One hears this "rocking" because of the consistent time relationships. You hear it going BEE-dah-BEE-dah-BEE-dah-BEE-dah-YAH-do-YAH-do-DI-do-DI-do and so on. Of course, I can change it so it isn't quite like that. But normally it is.

But with SPLITZ, when you hear something processed by this algorithm, it's, on the one hand, strange and fragmented and broken - but, on the other hand, it's disturbingly orderly in a way that you can't quite grasp. I love the "can't quite" part of it. It's intriguing but not obvious. And I think the same thing is true of canon, of course. It can be - as in "Row, Row, Row Your Boat" - it can be trivial; but it can also be, as in the Bach Musical Offering - not trivial. So those are the algorithms that actually were created in the context of Archipelago and then, secondly, refined in Transfigured Wind.

SS: Is there more on this particular topic that you would like to talk about now, or would you like to go to the score [of Transfigured Wind]?

RR: I think we should go to the piece.

## Notes

1. Logarithmic Series - Number series provide a basis for grouping and ordering elements in music. In many traditions these are simple (2, 4, 8, 16, ...). In more recent times, the Fibonacci series (0, 1, 1, 2, 3, 5, 8, 13, 21, ...) has attracted artists. Logarithmic series can vary widely in their specifics, but are used by Reynolds, in integer approximations, to create the effect of accelerating or ritarding formal shapes. [Return to text]
2. Ircam - a research and production facility founded by Pierre Boulez in the mid-1970s, is located at the Pompidou Center in Paris. It has carried on a unique program whereby innovative music is composed often directly involving either musical experimentation requiring substantial scientific consul, or tools which are in some regard indebted to scientific developments. [Return to text]
3. June in Buffalo - Initiated by composer David Felder, it has continued, at the Music Department of SUNY Buffalo, for over 25 years. It has been an important meeting ground for young composers who, through it, come into contact with older colleagues and also hear their own music well-prepared and presented in a collegial atmosphere. [Return to text]
4. Editorial Algorithms: SPLITZ and SPIRLZ - While working at Ircam towards the realization of Archipelago, in the early 80s, Reynolds conceptualized two complementary algorithms at the suggestion of David Wessel. The composer terms these "editorial" processes because they confine themselves to the principled proliferation and recombination of fragments derived from a given source or input. They may be automatically applied to digital sound files directly, or employed "by hand" in a compositional (rather than computational) mode. SPIRLZ produces continuous, cyclical and monophonic results whereas SPLITZ is discontinuous and polyphonic. [Return to text]
5. Ligeti, György - Ligeti (b. 1923) has been one of the major iconoclasts of post-World War II European composition. After escaping the constraints of a Communist-controlled Hungary in 1956, he concentrated at first on very dense, atmospheric textures that employed his noted "micro-polyphony". Ligeti's music later became more lean, wry, and virtuosic. He responded to the canonic writing of Conlon Nancarrow and contemporary studies of Central African music by Simah Arom, the effects of which can be heard in his piano etudes and in subsequent concertos. [Return to text]
6. Stockhausen, Karlheinz - Stockhausen (b. 1928) was an early advocate of utilizing an awareness of physics and psychology to inform experimental thinking about music. A central figure in the origins of electronic music and the Darmstadt Summer Courses, Stockhausen became, in latter years, more influenced by mystical and notably grandiose enterprises. He has been working on a week-long opera, Licht, for the last several decades. [Return to text]
7. Boulez, Pierre- Boulez (b. 1925) is a polymath, a major force in the evolution and practice of music since the Second World War. Originally active as a pianist and composer, he began what has become a major conducting career in connection with the seminal Domaine Musical series in Paris and also at the Darmstadt Summer Courses. Boulez is a prolific writer and founded, in the mid-1970s, the Ircam music research facility at the Pompidou Center in Paris. [Return to text]
8. Nono, Luigi - Nono (1924-1990) was at first a strict serialist, independently minded, and strongly influenced by political beliefs. Over time, his work became more phenomenological, concentrating on subtle modulations of sonority often evolving at extremely slow rates. In his later years, Nono worked extensively with electroacoustic elements, both pre-recorded and, eventually, with the real-time modification of performed sound. (1924-1990) [Return to text]
9. Variation - This 1988 work is one in a series written during the same period in which Reynolds utilized the editorial algorithm SPLITZ as a primary methodological strategy. Three thematic elements (linear, chordal, and figurative) are algorithmically transformed in relation to a pre-existent overall plan, and the composite of the computer's algorithmic output is then "mediated" by the composer so as arrive at a final text. [Return to text]