PREFACE (WITH SOME PRACTICAL REMARKS)

This paper has grown out of my engagement in teaching improvisation practise and composition at Aalborg University, Denmark. The use of parameter concepts for exercises has always played an important role here, and they were familiar to me both from previous music history studies and from practical compositional activity. It has been important to me both to clarify theoretical foundations as well as to document and describe the works of my students.

The term experimental music has been employed here for both European and Anglo-Saxon tendencies. While this term is most clearly established in the Anglo-Saxon tradition and the European one has several other names, such as "new music" or "contemporary music" (what is meant by this last one is, however, often music sounding closer to tradition), it has been deemed practical and not too disturbing to let the term include the radical tendencies of the European tradition.

When quotations are not in English, they appear both in original and in translation by the present author within square brackets.

Recordings are generally not part of the literature lists. With one exception, they have been stated directly in the lists of examples from concert music. In one case it was stated in a note.

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Only a selection from the archive of compositions could be included here. Access to the archive may, however, be given on demand.

INTRODUCTION. PURPOSE OF THIS STUDY

In the 19thirties, a Danish industrially produced lamp came to existence having the bulb hidden inside a lotus-flower like pattern of metal pieces, still well-known in its homeland as the "PH-lamp". Its inventor, Poul Henningsen, was concerned with the idea of avoiding sharp boundaries between dark and light and thus creating a more pleasant light environment. Moreover, coloured parts of the metal pieces had the effect that the light sent out was composed of mixed colour shades.

"Der Klang hängt nicht mehr grob in sich zusammen, sondern muss ... durch ein feines dicht gewebenes Netzwerk zusammengehalten werden"

["The sound does not stick together as a rough mass any more but must... be held together by a tight, finely wowen network"],

said Karlheinz Stockhausen and Herbert Eimert in the first issue of "die Reihe" from 1955 about their new music

Both examples express an interest in creating shades and intermediary steps between extremes. This can be described with the German word Vermittlung. It is hard to translate but can mean 'putting extremes into connection with each other', 'finding missing links', 'mediating', 'creating understanding' and the like.

When such concern for the detail becomes systematic, it can be highly innovative. It can reflect a real need for breaking new grounds and cultivate new sensibility. Cubism in painting cultivating a variety of simultaneous perspectives could be another example. Spectral music as developed in the IRCAM context from the nineteen eighties and on could be one more example. The aim is, however, not to add details to well-known shapes but about satisfying an appetite for creating new shapes and qualities.

European serialism in the 19fifthies focused especially on parameter concepts allowing for new shades, nuances, combinations and their systematic construction - in the middle of having abandoned traditional forms and attempting to create totally new ones. This way of thinking was not absent in its contemporary American counterpart either. Since then, parameter concepts have remained common in contemporary music. The historic connections have, however, been blurred by political conflicts and ensueing polemics and this has to this very day, unjustly, made it difficult to see the overall perspective and, consequently to some degree, the usefulness of this approach.

It is a very modern idea that music is sound which can go in any direction, or at least, this is very much a re-discovery compared to mainstream developments in Western music for a thousand years or more, as they have been prior to the new developments after the second World War. But it has come to stay and we deal with it in practise. The composer, the improvising musician, the music therapy client playing with his/her therapist might be circumstepping all this cultural heritage in both playful and thoughtful ways, sensing the sound qualities, compiling them one after another according to immediate likings, exploring various fast and slow processes of sound and concluding the whole thing out of a feeling for what fits into the context.

This kind of music creation cannot just be explained in the classic terminology dealing with symmetries, metric structures, sonata forms and with intervallic and harmonic concepts. We need a practically oriented music theory oriented towards sound broadly conceived with which to put perspective into practise and inspire ourselves to new discoveries. It would also be practical if we, in this context, could deal with how new and old forms of material could combine - for instance, how traditional melodies and rhythms can be part of such open processes.

So these are the purposes of this study:

- to clarify historical backgrounds and underlying ideas of what I shall be calling parameter analysis, a method originating in European serialism and developed by me in teaching, preceded by compositional experience.

- to document compositional activity by students in my intuitive music classes at Aalborg University, Music Therapy department, which has dealt with both group improvisation and composition training since 1983, employing teaching based on the principles described here and outlined in more detail in Bergstrøm-Nielsen (1999)

- and in so doing, to systematically examine how each individual parameter has been used, to provide examples of precedent historical uses, and examples of how the awareness of it could be trained in practise. Further, to relate to relevant literature in those cases where specific treatment of the parameter in question has been found, so as to contribute to a common body of knowledge in this field.

The word parameter has been known in mathematics and statistics since the latter half of the 18th century. It comes from Greek, meaning "to measure against something, to compare". The mathematical meaning is that it is a characteristic variable which makes it possible to compare functions or systems. ⁽¹⁾

Helmer Nørgaard's statement (1962) is, as a general characterization, well-suited as a first introduction to what is dealt with here:

"...Stockhausens parameter-teori... kan kort beskrives som et komplementær-måleapparat - anvendt på al musik - som vil give en helt ny form for analyse"

["...Stockhausen's parameter theory ... may in short be described as a complementary measuring apparatus - which will yield a totally new form of analysis"].

Nørgaard also relates this to the open situation of expanded musical material and a new desirablility of being able to overview and handle it:

"... ved parametrenes hjælp kan [man] styre uden om de skær som altid viser sig, når perspektivet bliver større"

["... by the aid of the parametres, [one] can circumnavigate the rocks that always emerge when the perspective grows"]

PARAMETER ANALYSIS. THEORETICAL BACKGROUNDS.

PARAMETER CONCEPTS IN EUROPEAN SERIALISM

Serialist music in the fifthies was a movement centering around the Darmstadt summer courses which became an international meeting-point after the war and around the electronic music studio of WDR in Cologne, involving composers like Henri Pousseur, Luigi Nono, Luciano Berio, Karlheinz Stockhausen, Pierre Boulez and many others. Individual works could be very different, but there was a strong, common tendency to work systematically and to break away with classicist forms of composition. Composers took inspiration from Webern and the previous Vienna school of twelve-tone music (Schönberg, Berg).

Electronic music became a catalyst for approaching the description of musical sound in a new way. It seems natural that in the multi-disciplinary context of composers, sound engineers and still more kinds of people, basic acoustic concepts would be employed to describe the sound that came out of the generators, which was recorded on tape and arranged according to composition plans in the studio. ⁽²⁾ Sound was described with regard to frequency. Durations could be measured in centimeters on the tape, as one can still see it in the aural score section of Stockhausens' Kontakte playing score from 1960 ( ⁽³⁾). Timbre could be analyzed as a continuum between vocal/sound and consonant/noise, as Stockhausen did with Gesang der Jünglinge (1956) in which he mixed vocal sounds with electronic ones into a compositional universe in such a way that they appeared to be transformed into each other. Other parameters that could be treated systematically included dynamics, distribution of pauses, density of sound, ways of tone attacks, and placement of sound in physical space. Further examples are understandability of text, employed in Stockhausen's Gesang der Jünglinge and characteristics of form and degree of change, employed in Stockhausen's Kontakte.

For Stockhausen and others, "parameter" was understood in close analogy to the mathematical variable. It should thus be possible to conceive of it as being in principle a continuum, a dimension which in itself is continuous. Frequency can for instance be conceived of from the highest to the lowest audible. A simple glissando will make a part of this continuum manifest. There are no a priori "steps" in a continuum. It is like the rails of a railway - they extend all the way with no interruption. But stations can be placed arbitraily. ⁽⁴⁾ Thus, conventions like scales, including of course chromatic and quarter-tone ones etc, specific rhythmic values as more "basic" as others become relative. The parameters are there like colours on the painter's palette - it is up to the artist to mix them in his or her own way and to choose colours from an infinite variety.

Stockhausen's early definition of serial method (1958 p.58) testifies to the central importance of the continuum:

"Alles Separate zunächst in ein möglichst bruchloses Komtinuum einzuordnen; und dann die Verschiedenheiten aus diesem Kontinuum herauszuarbeiten und zu komponieren"

["First, to fit all isolated phenomena into a continuum, and then work out and compose contrasting elements from this continuum".]

The word "parameter" was later often used in a less exact way, to denote just any characteristic of sound, but the exact terminological meaning and the continuum aspect was in focus here.

The antithetical concept to the serial view of parameters could be called a modal view. A mode is a fixed framework, for instance the way a scale is set up, maybe with additional rules for upward/downward movements etc. This is, as Maegaard (1964) rightly points out (p.25) not necessarily in any direct contradiction to the serial principle, since those parameters not varied can be considered modal. Continuing this line of thought, it is also relevant to note how the historic variation form can be seen as an interesting forerunner of the openness discussed here. For instance, such extensive works as Bach's two (!) collections of Preludes and Fugues through all keys, The Well-Tempered Piano I and II, his Goldberg variations, Beethoven's Diabelli variations can be said to perform extensive and systematic variation within a precisely defined framework. In such works, the variation may be felt to lead to a vast universe of different phenomena. Exactly a precisely defined framework or starting-point seems necessary for variation of a systematic kind. ⁽⁵⁾

Whether there are any "primary" and "secondary" parameters has been the object of disagreement. In music history, first pitch, then durations, then dynamics, later timbre became dimensions which were elaborated compositionally in detail - at least when judging from Western written sources during the last thousand years. Some composers (Boulez (1963)) would argue that those parameters not so elaborated on yet need more exploration to become really "serious" members of the core group. Others would maintain that they all have the capability to become really important and can thus be considered equal.

The traditional view is illustrated in a very down-to-earth manner in the following quotation taken from a discussion among German musicologists:

"De la Motte: Ich wollte noch einmal bei der Klangfarbe einhaken. Ich habe inzwischen Appetit bekommen und deswegen ist mir etwas zum Thema des Essens eingefallen. Mir scheint folgendes: Es gibt in der Kunst Grundnahrungsmittel, die Kartoffeln, Gemüse, Reis oder Nudeln vergleichbar sind. Es gibt dann ausserdem Verschönerungen, Reiznahrungsmittel: Curry, Paprika, Sambal-Olek und andere Sambals.... die Klangfarbe entspricht dem Sambal oder Gewürz, die Tonhöhe und der Rhythmus Reis oder Kartoffeln. Ich kann mir kein zwei- oder dreistündiges Werk, eine Oper z.B. vorstellen, die mit Sambal, also nach meiner Definition mit Klangfarbe komponiert ist. Das kann ich zehn Minuten lang ertragen, und dann muss ich endlich eine anständige "Kartoffel" essen. Etwas seriöser formuliert würde die Frage heissen: Ist die Klangfarbe tatsächlich ein Parameter gleichwertig der Tonhöhe und der Zeitdauer? Ich glaube nicht".

["I just caught appetite and so something occurred to me around the theme of eating...In art, there are basic articles of food comparable to potatoes, vegetables, rice or noodles. Then there exists also embellishments, stimulation foods: curry, paprica, sambal-olek and other sambals...Timbre corresponds to sambal or to spice, pitch and thythm to rice or potatoes. I can imagine no work lasting two or three hours, for instance an opera which has been composed with sambal. I can stand that for ten minutes, and then I have to eat a decent "potato". A little more seriously formulated the question would sound: is timbre really a parameter equal to pitch and time duration? I believe not"] ( Stephan (1969) p.70).

Another argument having been proposed in this direction comes from Adorno who points out that instrumental timbre historically "has not been processed by the human subject". ⁽⁶⁾ That is, instruments are taken over as they are and their sound may therefore be considered as fixed modes, not as variable parameters. Obvious counter-arguments are that composers of electronic music are indeed able to control the timbre - and that advanced instrumentation, like that of Richard Wagner, Rich Strauss and on, before that time did something similar by melting together the sounds of several instruments in sophisticated ways. In more recent times, this was further developed in spectral music.

Since we are dealing with creative possibilities, not just with observing what has till now been usually the case, the statement of Hans-Peter Reinecke which followed immediately on the comparison with foods stated above appears striking in all its simplicity:

"Wenn man fragt: Ist die Klangfarbe etwas Gleichwertiges?, dann würde ich vielleicht auch sagen "nein". Aber die andere Frage ist: Kann sie etwas Gleichwertiges werden?""

["If one asks: is timbre something equal [to the other parameters]? then I might also answer "no". But the other question is: can it become equal ?"]

THE SERIAL COMPOSITION AS AN INTEGRAL WHOLE OF INDEPENDENT PARAMETERS

Stockhausen employed the principles of serialism with great consequence. To him, equality of parameters was an important point, and this has lead him to reflections on the nature of the new universes of sound. The equality means that "alles zu allem überleitet" [everything leads to everything].

"Für die jetzige musikalische Sprache ist das sehr typisch: keine Melodie mit Begleitung, keine Haupt- und Nebenstimme" [for the musical language of the present this is very typical: no melody with accompaniment, no main nor subordinate parts] ⁽⁷⁾

This makes it possible to integrate seemingly very different types of material in a composition, as was the case in electronic works such as Gesang der Jünglinge, Hymnen and Telemusik. ⁽⁸⁾

Listening adaequately to this music is a more meditative kind of listening than traditionally according to Stockhausen. There are "keine bevorzugten Höhe- und tiefpunkte" ["no favourite anticlimaxes and climaxes"] ⁽⁹⁾, and this meditative way of listening is contrasted to the one known from radio programs playing music according to listener's wishes ⁽¹⁰⁾

Considering the choice of parameters in which to differentiate and considering which divisions to make within them as something which is relative and which depends on the composition in question, as well as also considering parameters theirselves as having equal importance, has deep-going and far-reaching aesthetic consequences. It is from this perspective that Stockhausen said "...serial thinking... is relativity and nothing else" as late as in the beginning of the seventies ⁽¹¹⁾ (Cott 1974). Tonality and traditional form were means of maintaining hierachies, centres of gravity as it were, in musical structure. As Maegaard puts it, the modern situation after the World War entailed a sceptical attitude to traditional melodic themes as musical elements, parallel to sceptical attitudes towards anecdotes in literature and figurative painting, he adds. (p.32). Relativity became the keyword of modern physics and replaced the notion of fixed laws of nature one had believed in since Newton. ⁽¹²⁾ And a slogan then employed by Boulez was, according to Maegaard (1964) "Man må akceptere kompleksiteten" ["one has to accept complexity"].

The widespread use of rows not only for scale tones as in the times of Schöenberg, Berg and Webern, but in other parameters as well, indicates that unified construction ideas and conceiving the composition as an integrated whole was common.

The concept of 'row' was programatically used as the title of the magazine of the serialists, but it is a popular misunderstanding to think that there was always only one row covering the whole composition in all parameters. ⁽¹³⁾ Laying down the design of a serial composition must be conceived of as a complex analytical process, involving a dialectical relation between the sounding material and the composers' intuition. Gredinger describes this in die reihe 1 (1955) explaining the importance of choosing relevant divisions and proportions of material:

"Anzahl Herz, dB, cm/sek sind bloss abstrakte Bezifferung...Das Mass erst schafft unsere auf uns Menschen bezogenen Grössen, organisierten Grössen, die ein proportioniertes Nächtsgrösseres, Nächstkleineres zur Seite haben...die Folgen einer Wahl...getroffen mit dem Willen zu bestimmter Form."

["... the number of Herz, centimeter per second, -dB are just abstract nominations... only the measuring unit gives us dimensions related to humans, organized units which have something which is the proportionally next bigger and next smaller step... the results of a choice...being made with the will to create a specific form"] (p.39)

The selection out of the infinite number of divisions of parameters, which parameters to focus upon etc. is strategic. After analyzing, the selections and decisions made as well as the working out of details combine to make the result a modal arrangement, but an individual one - out of the infinite possibilities has to be born something finite, even if it may suggest a vast perspective. Thus Stockhausen (1974) stated during a discussion with his audience in Darmstadt:

"... serial organisation is just a way of thinking that guarantees the equality of elements in a given form -- on a un maximum de variation et un minimum des élements - c'est une organisation économique".

[one has a maximum of variation and a minimum of elements - it is an economic kind of organisation]. ⁽¹⁴⁾

It is interesting to note that the notion of serialist music as "pre-formed" or "totally predetermined" does not originate from the then young composers of the fifthies theirselves, but from older ones. ⁽¹⁵⁾ From Eimert (die reihe 1957) it becomes apparent that is had already become a pejorative one at that time - he defends the music against allegations that the composition is a mechanical process or even a symbol of totalitarian attitudes, which had appeared in the public debate. They have been alive ever since - see also the section "modern music and cultural repression" below.

As a non-biased alternative to this terminology, it could be instructive to look at the concept of "network", employed by the serialists theirselves. It was used programatically by the editors, Eimert and Stockhausen, in the preface to die Reihe 1 (Eimert et al. (1955)): "der Klang ... hält nicht grob in sich zusammen, sondern muss durch ein feines, dichtgewebenes Netzwerk zusammengehalten werden"

["the sound is not staying together like a rough mass but must be held together by a fine, tightly wowen network"]

Here, the aspect of differentiation is emphasized. And this may lead us to contemplate what could be the creative challenge for the composer, instead of the both pejorative and abstract label of predetermination mentioned before, which was furthermore imposed by critical colleagues, not coming from those who were themselves the originators of the serialist development. Eimert mentions the concept of network again in his article in Eimert et al. (1957) in a context stressing the unity of the composition (p.12) - this unity is guaranteed by the systematic character of the construction which does not, as in previous twelve-tone music according to Eimert, suffer from being only partial, still connected to romantic and expressionist traditional phrasing -

"stöhnend aufgesetzten Ausdrucksvaleurs der Seele" ["groaning expressive values of the soul being pasted on"].

Instead, the composer has to make decisions concerning all dimensions, or parameters, of the music. And instead of the pre-determination of style, there are individual differentiation and balancing of parameters for each work. Also Ligeti, in his analysis of Boulez' Structures, compares the composition to a network ⁽¹⁶⁾

Serial method was based on combined analysis of the material and on synthesizing the chosen parametric properties into a whole. "Network" was a contemporary word for this procedure. Employing a term which then came into use and which has asserted itself as common terminology ever since, serialism was the start of parametric thinking. It has come to stay as a concept associated with composition, even through many different tendencies to the present day.

PARALLEL AMERICAN DEVELOPMENTS, DIFFERENCES, ENCOUNTERS, SIMILARITIES

American experimental music had a character different from the European one. John Cage was profoundly influential, putting forward his idea of indeterminacy, inspired from American traditions and from Zen buddhism. ⁽¹⁷⁾ Paraphrasing the ideas of indeterminacy, Childs (1974) states, in his dictionary article on the notion of indeterminacy, that it involves the possibility of any sound and any relation between sounds being potentially musically interesting. This seems to describe widely accepted principles among experimental composers of the fifthies and sixties. Cf. also the use of the term in such music history books as Bosseur (1979), Brindle (1986), Cope (1972), Feisst (1997), Nyman (1999) and Sutherland (1994).

This openness appears to be indicative of the typical American view of experimental music aesthetics. Indetermination endeavours to achieve both differentiation and new sounds and structures - but rather as a liberation of sounds and of the aesthetic awareness, not as symbolic of new constructions. The general cultural background was new currents of "anti-conformism" that gave birth to critique of modern society with threats coming from atomic weapons and pollution. These currents influenced the "beatniks" on the West Coast and their successors, the hippies. And one popular statement expressing this critical individualism was "to do one's own thing". (Hamm (1975))

Indeterminate composition could certainly, however, take on systematic forms and also employ parameter concepts ⁽¹⁸⁾. I am deliberately saying "dimensions" instead of parameters since this latter word does not appear with Cage, but the meaning here seems to be utterly synonymous. In "Variations III", cop. 1963, they are called "interpenetrating variables" - and here, they are not even specified, thus underlining the aspect of openness in a very perceptible way. Morton Feldman employed, as early as in 1950-51 in Projection I for cello solo, a coordinate system dividing registers simply into high, middle, low, and he arranged the tones to be played by observing the spatial sequence on the paper, not with metric notation. Details of exact pitch and exact rhythm were thus made indeterminate, including an opening up to the total possibilities beyond the 12 tone system as well as those beyond the metric notation. At the same time, the pitch parameter was given new basic divisions for orientation - cf., in the text above in the secion "The serial composition as an integral whole of independent parameters" about the necessity for the serialists of choosing how to divide parameters.

Indeterminacy was an aesthetic view originating in the victorious nation after the World War. It presented itself with much less emphasis on seriousness and a much more immediate pursuit of freedom notions than did serialism. This must be understood on the background of the different political situations. Until 1955 there was not even a thing called West Germany yet, but an "occupied zone". The serialists emphasized visions of new, responsible construction analogous to the reconstruction process so vital to their society.

Their views could appear diametrically opposed, and with John Cage's visit to Darmstadt in 1958 and that of Earle Brown in 1964 there were great cultural clashes, even if the Europeans could not remain untouched after this. For the Americans, Europeans could appear pedantic, and for the Europeans, the Americans could appear schockingly hedonistic or even indecent.

But, as a creative strategy, both were practising parametric composition. For the serialists this was the central technique, for the indeterminationists it was one aspect of technique among others. There seems to be a common tendency arising out of a general need, whether European or American. Cf. also the approach of Kenneth Bruscia described below which came about even without previous knowledge of the significance his concepts has long had in music history. The idea of music as sound seems to be related to and even to be able to entail, the idea of a number of parameters or dimensions of sound as what to deal with in this open universe. It appears as a universal discovery in the latter half of the twentieth century. ⁽¹⁹⁾

MODERN MUSIC AND CULTURAL REPRESSION

Life in Germany these days was unsecure: people were living in an occupied zone, and the invasion by Sovjet in Hungary in 1956 arose fears that something similar might happen in other parts of Europe. The radical musicians had the pioneering spirit of building up something completely new from scratch. But in concert life there was also a strong current of turning to the music of older times.

Before the war, and especially after the Nazi occupation of Austria in 1938, a large number of artists, including composers like Schönberg, Eisler, Bartok, Stravinskij, fled to the USA. Under the depression of the thirties, support of modern music from private funds declined drastically and some composers survived by teaching and writing film music (Brincker et al (1983). Atonal music went into Hollywood film music and became known as background for horror scenes, which might still be the dominating association to such music by many music lovers. It is an ironic fact of history that this music to an important degree originated with exiled dissidents to entertainment culture and that their European successors after the war experienced additional resistence precisely because of their cultural ancestors' contributions to the film music of the nation now occupying them! To many people, the new music which was so different appeared scary, and film background music was a part of their backsground for thinking so.

It seems no coincidence either that around 1956, the culminating year of public anxiety because of the Soviet invasion into Hungary, there was a veritable "battle" in which the public music discussion also culminated in several pamphlet books and a law suit for slander (Bergstrøm-Nielsen 1980). As a result, composers had seemingly no choice but to give in verbally and admit that they were on a wrong path, but had now loosened up their systematic working method into something more "healthy". In the seventies there was often mention of a "post-serial" era, but it still remains to be demonstrated more clearly whether this label has any substantial, descriptive and analytical significance. ⁽²⁰⁾

For such reasons, actual continuities in the developments from serialism and on have been less clear to music public and even to music historicians than could be desirable. However, and even in spite of this, the parameter concept has not only survived but also gained foothold in music terminology.

PARAMETER THEORY IN MUSIC LITERATURE

While examples of uses of the word parameter are legio in music literature, there seems to be relatively few writings dealing in a comprehensive way with parameter theory.

One writer using "parameter" as a main concept is Landy (1991). This book is music analytically orientated, besides also discussing sociological issues. In "Part 1 - Introduction" he discribes what he sees as the general background:

"As in the sciences where one became more acquanted with various minutely small and extremely large worldly phenomena, composers searched to expand their own dimensions." (p.8)

After summarizing a few developments within pitch, namely the equality of all twelve tones with Schönberg's dodecapony and Haba's work with micro-intervals, he states that parallels could be found in other dimensions, too. And makes the reflection that

"Early avant-gardists were certainly aware of this potential, but lacking apparatus to make such expansion feasible, most early 20th century composers limited themselves to dreams and manifestos" (p.8)

This assumtion could deserve closer attention, but it is not further elaborated here and documented. As to "apparatus", there are several examples of instrument building endeavours in previous instrumental music (Partch, Futurists). Of course, electronic music after 1945 played a major role in music history, both with the serialists and in the USA, but the question remains, exactly how decisive was that role. After all, instrumental composition remained crucially important for the serialists along with electronic music. One could imagine that "apparatus" just as importantly, or maybe even more, also included compositonal devices - like, previously, the systems of Schönberg and Haba the author mentions. But also sociological issues contribute to making a sustained development possible at all - how marginalized the music is plays a role. - An accepted notion of "open sound" and of a suitable notion like "parameter" could thus seem to be possible parts of the "apparatus" making experimental music advances possible!

The author gives reasons for his use of the parameter concept:

"Although parametric research is not the only form of experimentation within recent music, it has been singled out for this introduction due to its relative importance in most experimental music along with its link to music tradition (studies of melody, rhythm, harmony, and so on)" (p8f).

And his definition of parameter is the following, quoting Josef Häusler from 1969:

"Musical parameters are all sound or compositional components which can be isolated and ordered" (p.9).

This is a very broad definition. It includes not only those dimensions that can be continuously varied, like pitch, duration etc, which can still be seen as analogous to a mathematical variable. It includes also those components the ordering of which falls into discrete steps or classes. This becomes apparent when the author mentions Olivier Messiaen's Mode de valeurs et d'intensités from 1949 as an example, a piece which is known as a forerunner of European serialist composing and which was an inspiration for the early serialists. He explains how each pitch has its own unique length, dynamic level and attack and views the resulting assembly of pitches with their individual characteristics as one parameter:

"In this case four parameters were fused into a single new one" (p.10)

After an intermezzo with characterizations of parameter approaches with some important composers, John Cage, Iannis Xenakis and Karlheinz Stockhausen, Landy proceeds to stating lists of parameters, with explanations and examples.

"Parameters of primary importance" are for this author pitch, duration, tempo, dynamics, timbre, "sound types" and space. "Parameters of secondary importance" then consist of density, "simultaneity", "(dis)order", "energy" (a special designation found with Xenakis), ""freedom" ("This term is an unhappy one but will be used as a heading for a number of potential parameters" p.15), "compositional bearing" (polarity of rationalized-intuitive way of composing with Stockhausen), form, "formel" (fromStockhausen).

As these lists suggest, there are clearly elements of personal choice and selection - if not, as some would probably say, subjectivism.

To put this into perspective, one could quote Reinecke (1967) who advocates the view that parameter descriptions must refer to "mathematisch erfassbare Eigenschaften"["mathematically describable properties"]. This could, as a counterpart, be called a strict, narrow definition.

Even if Landy, as we have seen, employs a wide definition, he nevertheless follows the tradition for putting the most objectively measurable dimensions first in the list - as "Parameters of pimary importance". With the possible exception of tempo it seems that they could all be made to fit into Reinecke's requirement. ⁽²¹⁾

For the description of given, finite historical periods one might discuss the issue whether standardized criteria of description could be relevant. But dealing with creative strategies, as they are relevant to teachers, composers and musicians, it appears that the list of criteria, in this case parameters, cannot be finite, whereby it would assume a normative and confining status. By accepting to let the list be open, it can become an adequate tool for describing strategies which aim at new developments. By following the tradition of marking out those parameters capable of exact description, an important area within which intersubjectivity is guaranteed is defined. Stating an exact definition of how the term is understood is also important, if the term is not to just mean any kind of "characteristic" and thus lose any general comparative perspective.

Christensen (1996) does not speak of parameters but of "basic listening dimensions". However, his theoretical model overlaps with traditional parametric views. Special attention is here given to theories about the ear and its biological functions.

He distinguishes between microtemporal and macrotemporal dimensions, thus connecting to the idea of the ultimate relatedness to each other of the parameters, the "temporal continuum". ⁽²²⁾ In one of several models, "Microtemporal listening dimensions" are "Timbre, Harmony and Pitch height" (p.15). This is so because space is "the ability of localization and orientation" and timbre "the ability of estimation and identification" - they are seen as basic because they are biologically essential for survival. We are equipped with the ability to hear immeadiately where something around us is going on and what kind of sound source - whether it is our own species or not, whether dangerous or not, etc.

Such first orientation having taken place, our attention may then move on to the "macrotemporal listening dimensions", movement and pulse. The question "is it moving?" may be answered - again, as a requisite for survival: "The listening mind is informed whether the sound source is approaching, passing by or receding, and has the chance to decide if it is necessary to run away or whether it might be a better idea to find and follow the moving sound source in order to fight, scare or eat it" (p.13). Pulse, however, is "awareness of regularity" and also contributes, together with movement, to time experience (p.14).

Following and modifying Stockhausen (1963b) he assigns the dimensions mentioned to a time scale:

Timbre: 1/16.000 - 1/32 sec.
Pitch height: 1/6000 - 1/16 sec
Pulse: 1/8 - 2 sec
Movement: 1/4-5 sec

The qualities of the dimensions are further discussed in the remaining long parts of Christensen's book which is mainly dedicated to a large number of detailed analysis of music works following the models. It ends with some additional remarks and a concluding, composite model.

Christensen takes a new starting-point among parameter theorists, if he can be called that despite not using the word. Instead of sticking to classical acoustic notions, he builds his theory on human listening attention. It is thus quite logical that timbre is seen as "microtemporal" because "All kinds of sound are characterized by their timbre ... But only certain kinds of sound are characterized by clearly defined pitch height" (p.16). We learn from acoustics that timbre is the result of several pitches combined but even so, we cannot hear those individual components. We only perceive pitches when they have been sustained a bit longer. It can be said to be thought-provoking that Stockhausen was already aware of this in 1961, but Christensen has put this observation into a larger biological/psychological perspective.

Wishart (1985) deals with fundamental problems of electronic music and its development. He undertakes an philosophical and theoretical, critical discussion of some traditional notions of acoustics. The very idea that properties should, at the best, be exactly measurable, is seen as a problematic dualism that may have originated in Descartes' distinction between "primary and secondary qualities of perceived natural phenomena" (p.18). Recent 'catastrophe theory' having lead to a new branch of mathematics called differential topology concerns itself, however, with studying systems in states of unstability. In the realm of music, one has for instance focused on the stable sound produced by a flute after the initial attack - but it seems one has to to some extent neglected the attack.

Specifically concerning the pitch-timbre continuum, Wishart attacks the widely accepted notion that sine wawes are more fundamental than resulting timbres. Fourier analysis is an acknowledged mathematical procedure which can transform a graph of amplitude against time into a graph of amplitude against frequency - that is, an oscillogram, now commonly seen in computer wawe editors into a spectrogram, the kind of diagram featured also by spectrum analyzers. One cannot argue, according to Wishart, that the first graph is more fundamental. If we are dealing with complex sounds, the second method is more lucid and less aperiodic than the first one.

The human ear carries out a Fourier transformation by synthesizing a composite sound from sine wawes. Some research, however, suggest that this is not possible above 4Khz, but still we hear timbres. Still one more thing to consider is that extremely short sounds are amgiguous and indeterminate. The implications of this is discussed further on in the context of theories of modern physics.

Wishart's view thus converges to a certain extent with that which Christensen took on biological/psychological grounds, concerning the pitch/timbre issue. His scepticism also takes its starting-point in an experiental orientation (p.7ff), and it leads to a broader perspective on the acoustic and mathematical foundations of sound, pointing out the possibility of relevant theoretical description of sound which is unstable and complex. In other words, a more holistic view of matters seems possible without sacrificing descriptive methods.

Even if Brindle (1986) has a chapter on "Integral serialism", the term "parameter" does not appear to be in use with him. However, a number of specific dimensions are listed systematically in the index under "Indeterminacy": form, pitch, rhythm and duration, dynamics and expression" (p.218). He couples this systematic treatment of various characteristics with indeterminacy, which he takes as synonymous with "aleatory" (p.215). Thus, he gives up the division between those two concepts which refer to distinctly different geographically based traditions, procedures and attitudes. Nonwithstanding the problems in doing so, one can nevertheless observe that he treats a number of dimensions independently which are often referred to as important parameters. He thus follows the general tendency of viewing musical sound as multi-dimensional and capable of variation within the dimensions. ⁽²³⁾

The discipline of Music Therapy has since the seventies been a fast-growing new one. It operates within a multi-disciplinary perspective in which psychology plays an important role, as well as musical disciplines. Since freely improvised music is in many cases the music medium in which the therapist and client work together, there has been a need for new music theory and terminology, and the literature features instances of descriptive systems with detailed terminologies.

Bruscia (1987)'s Improvisation Assessment Profiles utilizes "scales" to describe among other dimensions texture, timbre and volume - for instance "Texture variability". In this way he clearly employs parameter views, keeping to general properties appearing in a continuum. I addition to theze descriptive elements in this terminology, categories are coupled to psychological assessments such as, in the case cited, "Rigid" to "Random". As this example shows, Bruscia associates the music characteristics with psychological characteristics in a one-to-one manner. The author discusses this procedure in Bruscia (1994).

It is especially worth noting here his reasons for employing such concepts:

"Obviously, there are many different ways of listening to or analyzing music already in existence, as we all remember from our early days as students of music theory. But my experience as a music therapist has been that these traditional methods of musical analysis are inadequate for clinical situations in several ways. First, they usually focus almost entirely on tonal and harmonic structures (which are not always present in client's improvisations), and consequently neglect the more basic musical elements such as rhythm, volume and timbre. (Even our definition of musical "form" is based almost entirely on melodic themes and tonal processes)." (Bruscia (1994)) p.2)

So Bruscia's endeavour could be said to employ such basic concepts which traditional music theory does not encompass. And then he turned to commonly known and more broad concepts. In this way, he discovered basic new knowledge which were common to the composers of experimental music dealt with here - without being aware of it!

Like Bruscia, Deuter (1998) is concerned at the same time with sound description and its psychological interpretation. Just one example is "regularity" versus "multitude", valid for "rhythm". Such opposite concepts are seen as polarities with a continuum in between, differing from rigid oppositions. This is therapeutically relevant because pathologic phenomena very often result in rigid ways of personal being and expression, which is in turn reflected in the music. It can therefore be a relevant task for the therapist to support the client in finding ways of loosening up such rigid oppositions in improvised music playing.

The continuum view is further reinforced by the author's endeavour to set up meta-polarities on psychological grounds which can serve to facilitate overview and to further systematisize psychological interpretations.

Deuter also stresses the equality of parameters: "In this, there is no hierachy of the individual fields or a "first" and "then" of neither their appearance nor their meaning" (p.84). Here, the clinical view of music therapy coincides interestingly with that of the radical serialists ⁽²⁴⁾ In music therapy, there can be relativity and equality because there should be no pre-conceived rules for the music, but an acceptance of what the client plays.

While Bruscia and Deuter employ parameter concepts based on continua, that of Ansdell is different. It is rather based on oppositions, for instance with Ansdell's own words:

"rhythm is initially divided into structured or unstructured, with structured at this point the positive pole. However, at the branching of the structured pole in the map there is again a "positive/negative" polarity where the structuring of the rhythmic element in the client's display can either be "precise but flexible" or "rigid". In this way, there is a dialectical process of thinking in opposites and moving on to greater precision. The descriptive map presented includes "the basic categories of musical organisation (rhythm, melody, harmony, form, etc.) but also categories which pertain to the unconventional analytic perspective of listening to personal process through musical process. These are the categories of force, articulation, continuity, aspects of physical behaviour, facility in playing - focusing back from the qualities of the product to the state of the producer" (p.22)

Hegi (1998) concentrates on "timbre" (German: "Klang"), "rhythm", "melody", "dynamics" and "form". He does not provide lists of descriptive words but is rather concerned with general interpretations of their meaning and presenting case stories - and what is important here, the case stories are presented as illustrations of the ways of working of the individual components. It is also interesting, however, to note the connotative properties of the word "component" which, like "parameter", has the sound of something exact. In the case of dynamics, he also makes this systematic presentation of possible combinations with tempo:

louder and faster
softer and slower
faster but softer
slower but louder

The unifying and exact-sounding terminology of "components" as well as the author's interest in transformation processes suggest a view of the music material having points in common with both the serialists and Deuter ⁽²⁵⁾

Ansdell takes up a question of interest regarding the multi-disciplinary relation between psychology and musical disciplines. He critisizes "a post-Freudian intellectual tradition where the process of interpretation can often mean that description is subsumed within explanation" (p.18). In other words, there is a danger of jumping to conclusions without grounding the interpretation sufficiently in a precise perception of the phenomena. He states that the ""what?" dimension ... is the foundation for any further process of knowing" (p.18), the "why?". He also tells this story: "The difference between our eagerness to explain rather than to describe is nicely illustrated by the story of the young boy who presented his mother with his latest painting consisting of vivid splashes of red, blue and green. "That's lovely, James. What is it?", asked his mother. "It's red, blue and green", replied James." In other words, he stresses the necessity of exact, descriptive terminology - his own motivation for setting up the system.

SUMMARIZING AND CONCLUDING STATEMENTS

- Thinking in musical parameters owes much of its current dissemination to the intensive work of European serialists in the nineteen fifthies. Further backgrounds include similar American developments. The use of the word is widespread, also outside music, but it may mean almost anything, ranging from displaying the pure fashion of using a word having connotations to exact science to something very definite. One can, however, observe a common tendency in describing experimental music and in describing music therapy improvisations to employ a multi-dimensional thinking of music sound going beyond traditional concepts and taking inspiration from acoustics. Some of this activity employs the word parameter, some does not. It may derive from the established use of parameter concepts within experimental music or, as can be seen within music therapy, arise independently, out of a descriptive need and, presumably, of a common intellectual climate of the historic periods we live in.

- It is crucial to define exacly how the term "parameter" is to be understood if it is to serve music analytic purposes. A narrow definition is that of Renecke (1967) who, following Meyer-Eppler, acknowledges only what can be laid down mathematically exact - this means in his interpretation "frequency, amplitude, spectral composition, duration "etc. - and such things as timbre and perceived dynamics etc. are then to be regarded as subjective dimensions. Following his line of thought, one could also argue that "pitch" is unprecise because it synthesizes perception of slightly different tones into an illusionary one and the same. Theorists need to contemplate how narrow or broad they wish to make their criteria. - One more point to consider: A definition may stick to requiring that there is in principle a continuum between extremes if a characteristic is to be called parameter, thus staying with the analogy of mathematical variable, or it may not, like Häusler's definition which was employed by Landy (1991). And various criteria may be laid down for defining individual parameters.

- When making a list of parameters, there has developed a certain practise to state first those parameters being easiest to define in exact ways. Given the existing variety of approaches, this is a practical procedure, allowing for fast orientation and comparison and yet also for individual definition and selection of parameters. It allows for a synthesis of what has been handed down from historic experimental music practise and new developments and purposes of analysis.

- Some keywords of parameter analysis in a "classic", strict sense (taking Stockhausen serialism and certain works of Cage as models) are continuum, enabling all possible degrees and shadings, and independence or, depending on how radical the view, equality of parameters, hence the possibility to freely combine from a "palette" of a number of parameters. This openness may entail an individual analytic-synthetic procedure for each creative task - be it a music work to be written or analyzing what happened in a music therapy improvisation improvisation before making the next. The analytic-synthetic aspect could also appear the form of alternating thought and intuition during improvised playing, as is relevant to the practise of improvising and the teaching of it.

- The concept of parameter is mentioned passim in music literature, often without going into much detail. And we have seen a focus on composite systems of parameters with the authors Landy and Christensen, rather than on the single ones; likewise Brindle employs such a way of thinking even with no mention of the word. Parameter theorizing, seen in the context of musicological disciplines, has affinity to musical analysis, but it is on the other hand also treated with less specific references to individual works. By virtue of this tendency towards overview, it has more affinity to general music philosophy and aesthetics. With the music therapy authors Bruscia, Deuter and Hegi, there is more focusing on individual ones, and especially with Bruscia, this is closely coupled with psychological characterization.

- Parameter analysis is, as the present writer sees it, best suited to describe general properties and their change - to describe outlines and developments, rather than details. ⁽²⁶⁾ To describe melodic, rhythmic, harmonic aspects, more traditional tools are relevant, as Hegi and others also employ. ⁽²⁷⁾ Parameter analysis might, however, put those other characteristics into an expanded perspective.

PARAMETER ANALYSIS APPLIED. CATALOGUING EXAMPLES OF PARAMETER TREATMENT

INTRODUCTORY REMARKS

THE CATALOGUE IN ITS THEORETICAL AND DIDACTICAL CONTEXT

My system is intended as a mapping of large-scale dimensions of the musical universe. On the background of the theory discussed in the last chapter, it seeks to treat the most important parameters in so much detail that a new outlook on the music material could be sensed from it. It does not go into a detailed use and discussion of more traditional concepts. Emphasis has been here on stressing the "macro-level" of musical geography. From this perspective, however, a way of viewing how to combine old and new is proposed.

DESIGN OF THE CATALOGUE

The catalogue seeks to exemplify all the parameters having appeared important till now in my intuitive music classes by references to students' compositions. The properties of each parameter are discussed. For providing information pointing to the didactical perspective, examples of practical exercises are added. For the historical perspective, references to concert music are also included(28).

The selection of compositions here was undertaken from a special point of view originating in the cataloging purpose of this study. It does of course not directly reflect which compositions were the "best" or got the highest notes. However, there has been a view to including interesting compositions that convey the strengths of this composition form. The basis has been the roughly complete archive of examination papers from the first exam in 1985 through 2006. (After 2006, intuitive music teaching became to some extent more centered around the individual student and the main instrument. Materials from the last 2007 examination have not been considered here). In two cases, this has been supplemented with other material in order to have all parameters exemplified.

Because the theoretical context here is parameter treatment, composition technique within our special form has not been commented upon in great detail. Hopefully, examples theirselves will both yield a comparative perspective and demonstrate individual points and subleties in handling the composition form.

BACKGROUND OF STUDENTS' COMPOSITIONS

IMMEDIATE BACKGROUND

During the years 1985-2007 as mentioned above, students have passed an examination of "intuitive music" by presenting small compositions for improvising musicians. This both documents the students' ability to create playing rules and also, in an indirect way, it documents the student's feeling as a musician with this kind of playing situation⁽²⁹⁾.

Even if it may be a requirement when starting composition exercises, it was not a requirement for the final examination that compositions concentrate on one parameter.

THE USE OF "STORIES" AND THE PROGRAM MUSIC TRADITION

Students' liking for "stories" and for illustrating them in a basic, cartoon-like manner seems to have exercised a decisive influence through the years and to have combined in a unique way with the parametric thinking I have proposed!

Program music is a tendency known from music history using suggestive motivic figures and other musical means to hint at objects and actions in the outer world, as well as depicting specified moods. It was especially cultivated in the romantic period, and "Symphonic poems" could specialize in this in detailed ways in late romanticism by composers such as Liszt and Richard Strauss - so to speak film music before the film, as many musical details could connect to the story. "Absolute music" is used as a term for the opposite view of music - that music has its own formal world, that it can not be pinned down to this kind of references which can be said to originate in the listener, not in the notes.

While these issues can only be hinted at theoretically here, they could be of far-reaching interest for further research. A common view among practioners of active music therapy seems to be that therapy music can directly reflect states of mind and mental processes. The obvious background for this view is the necessity in the therapy to interpret what is going on in the client and between client and therapist, psychologically, and the music seems indeed to give strong cues for such interpretation.

From a critical point of view it could be stated that the "truth" of a given interpretation in music therapy is relative and dependent on a dialogic process - not on unchanging properties in the music, and that those who listen have their own personal associations. The study of how interpretations come about and how they may be methodologically secured is known as hermeneutics or phenomenology. The music in question here was not originating from a therapy context, but from free creative work. Nevertheless, going fast from music impression to psychological interpretation is a common way of thinking in our music therapy context. From an artistic, creative point of view it can be said that a one-sided thinking of "illustrating the story" without sufficient consideration to the ways it is done can lead to a cliche-like use of the material. This is of course not pscyhologically effective either. The right way, seen in this perspective, seems to be to consider your musical material with the greatest awareness, putting both hands into it and its combination possibilities and taking it to visionary use (like the serialists did). It's very much how, and how musically illuminating you tell the story that counts, if you so wish.

When the storytelling succeeds in original ways, it seems to have the ability to, on the other hand, to make any kind of musical material alive and fascinating to the reader and listener. The present writer believes that these compositions, with their semi-popular use of advanced musical means, while at the same time being down-to-earth in their way of communicating, possess extraordinary charming qualities that illuminate what the great discoveries of new and experimental music were all about and that this music form could be used with benefit by others, too, within the field of music teaching and training.




Margrete Bach Madsen: Colour wash 60° [Kulørt-vask 60°] (2002). This piece seems to celebrate the programmatic idea in an especially detailed way!

Click on the illustration to see the composition with translations and to listen.

THE TREATMENT OF INDIVIDUAL PARAMETERS IN STUDENT'S COMPOSITIONS

PITCH

Pitch is measurable in an exact way as frequency (cycles per second). In practise, single frequencies hardly exist, as instruments produce spectra of sound and as sounds collect additional frequencies in any environment which has any degree of reverberation, but we may perceive the fundamental tone as a definite pitch.

Jelinek (1952, p.4) points out a special distinction of pitch: in its pure (here=clearly discernible) form, it is specifically musical. It it, for instance, not to be found in spoken language. While Jelinek, as a composer working in the "classic" twelve-tone way of Schoenberg, is arguing to establish pitch as the most important dimension of music, the "signal-like" quality of clear pitches can also be viewed as something notable from a "sonic" view of music connected to electronic music - Danish composer Bent Lorentzen also notes this in Bergstrøm-Nielsen (1979b).

The use of pitch comprises both melodic and other phenomena. Melody was long connected to a harmonic system. However, many simpler uses of one pitch which seems to come up free improvisation again and again, are possible. I thus like to speak of "one-note-tonality", which can have the form of traditional drones and the like. Closely related to this is "interference-tonality", using fluctuations from one (maybe spontaneously agreed upon) note. Both allow for combinations of stasis and change.

Cole (1974) describes with a striking metapher how the emancipation from systems of chord progression, which demanded exact synchronization, lead to a new situation. It became possible to perceive the musical sound more in terms of, for instance, timbre, or, like Cole describes it, more polyphonically:

"It was the necessity of avoiding discord that made exact synchronization into a vital organizing principle. (In the same way - trains have to run to a timetable partly because they must not be allowed to collide. Make trains of soft rubber, and the timetables can be relaxed)" (p.151f)⁽³⁰⁾.

The traditional melody has more than one note and is a microcosmos, a formula of intervals - hence, it is also transposable. There is, however, also a different, "orchestral" use of the pitch space. Virtually all music for symphony orchestra exemplifies this in some way by the very fact that instruments have different ranges and are combined in changing ways. In a context not governed by traditional harmonic rules, the significance of individual intervals has naturally diminished. There can be a different experience of pitches with their vicinities and contrasts, their going together or standing apart. Different registers can stand out in their own right, and one can take the entire audible pitch range into posession⁽³¹⁾. Perla Leifsdóttir illustrates "high" and "low" by little angels and devils descending and arising...

Click on the illustration to see the composition with translations and to listen.

The spreading out into pitch space and narrowing down again is the theme of Arne Kokborg's "Blood circulation" [Blodets kredsløb] (1992):

Click on the illustration to see the composition with translations.

Focusing on one register can have a profound effect in itself, as is the case with deep tones in this excerpt from Mette W. Nielsen "A day and night" [Et døgn], (1999):

- deep tones
- quiet
- SLEEP

Click on the illustration to see the composition with translations.

- and in Karina Fanø (Kristiansen)'s "No title (Four elements)" [u/titel (4 elementer)] (1994):

Click on the illustration to see the composition with translations.

- EARTH
- Firm, heavy rhythm
- Long deep tones

The next example goes further into the alternatives to the welll-known use of pitch in solo melody in a different way: A narrow focus within pitch space could comprise just one slowly moving pitch as a point of reference within a musical universe - as in Bolette Daniels Bech's "Voice improvisation: Tone and rhythm in breathing" [Stemmeimprovisation: tone og rytme i åndedræt] (1990):

For each breathing (expiration), sing a new tone which gradually slides its way to the group's common tone. The common tone is created by listening to each other. It can change [its pitch].

Click on the illustration to see the composition with translations.

One can define general (global) characteristics of melodic movement giving shape to overall structures, as in Anette Mailand: "No title (Noah's Ark)" [u/titel (Noahs ark)] (2001):



- upward stepwise movements /- opadgående trinvise bevægelser
(...)
- downward stepwise movements /- nedadgående trinvise bevægelser

Click on the illustration to see the composition with translations.

Examples from concert music:

Beginnings of Beethoven: 5. Piano Concert and of Grieg: Piano concert in a minor (piano solos comprising the entire range of instrument).

Xenakis, Iannis: Metastasis (1955)

Ligeti, György: orchestral works: Atmospheres (1961), Lontano (1969) and Volumina for organ (1961-62 rev. 1966), Continuum for harpsichord (1968) (use of all registers)

Stockhausen: Telemusik (1966) (electronic music with high pitches)

Wagner: Prelude to second act from Siegfried (focus on deep register with tuba solo)

Exercises:

Recorded exercise:

Please see Listening Page!

DURATION

Predominantly short --- predominantly long.

Durations can be viewed as the durations of individual tones or sounds, or as the statistical distribution of duration in a group of tones or sounds. In much traditional music, durations follow metrical patterns and appear in mixed lengths. Within metrical patterns, the range of note lengths is usually limited. New concert music since 1945 went beyond the range limits in a number of cases, into very short and very long durations - thus making new forms of time-awareness possible. Erhard Karkoshka (1971) wonders at the new universe being opened up here expecially by improvised music:

"...in classical music, perceivable time structures remain restricted to a limited number of models. ... attempts at describing what time in music could be hardly exist, neither do attempts at describing to what extent it can be an immediate musical expression and how we perceive divisions and correspondences of time under given circumstances. Now, my own work which often occupies itself with these questions has found many interesting answers by improvising⁽³²⁾."

It is no coincidence that a large enquete with many answers from improvisors, some of them in great length and touching on weighty philosophical matters, could be made from the question "What happens to time-experience during improvisation" (Riley (1976))

One way in which new time-experience was achieved was by means of pointillistic music in which individual tones could appear in their own right without being part of a continuous melody - this is common to both much American and European experimental music. Here is a characterisation by Henri Pousseur - one can safely say he sees this quality as a positive one:

"es [handelt] sich um das aufmerksame Erfassen eines jeden einzelnen "Hier und Jetzt" in seiner Partikularität, um die wundersame Erfahrung einer hervorschiebenden Zeit ... um den Eintritt in eine Welt, die resulut offengehanten, auf unbestimmte Zeit unvollendet, unaufhörlich im Aufbruch ist [this is about the attentive grasping of every "here and now" with its particular quality, about the wonderful experience of time moving forward ... about entering a world which has been resulutely held open, unfinished for an undetermined time, incessantly breaking up]" (Pousseur (1959)

A different way was by composing long, static structures. Even though this procedure is known from traditional and popular musics with drones, Sabbe's consternation at the existence of notes "which sometimes exceed 8 seconds" in music by Ligeti is interesting because it shows that there is indeed a perceptual difference to the metric rhythms - even if he interprets it as something destructive:

Click on the illustration to see the composition with translations.

Click on the illustration to see the composition with translations.

Click on the illustration to see the composition with translations.

Regular -------- irregular

Furthermore, the metrical system strongly favors ratios of division like 1:2, double or half-length with the exceptions of punctuated rhythm and occasional polythythmic divisions - "Rhythm octaves" are preferred, as Stockhausen (1957) so rightly puts it.

Composers emancipated themselves from this situation by constructing irregular rhythms by means of complicated polythythmic structures, by means of notating in new waysand by means of letting musicians improvise. In jazz, musicians had long improvised irregular rhythms by feeling, not by counting. Non-idiomatic, freely improvising musicians⁽³³⁾

also did so on new grounds, in some, but not all, cases adopting a "pointillistic" practise.

Still one more meaning of "duration" may be mentioned,the duration of the entire piece of music which may also greatly inform time-awareness.

Examples from concert music:

Short durations: Stockhausen Kontra-Punkte (1953) - Bailey/Stevens/Watts: Dynamics of the Impromptu, Entropy CD 004. Recordings from 1973/74 with Derek Bailey, John Stevens and Trevor Watts

Long durations: "Sederunt" and "Viderunt", 4 part organa by Perotin (12th cent.) with drones

Händel: Pifa from Messiah (with drone)

LaMonte Young: Composition 1960 #7 "To be held for a long time".

Eric Satie: Vexations (conceptual piece, very long like LaMonte Young above)

Exercises:

Recorded exercise:

Please see Listening Page!

DYNAMICS

Dynamics are measurable in an exact way by decibel. The most common variety is dB(A) which takes into account the fact that human hearing differs in its sensibility towards different registers of pitch. While 3 dB change means double or half sound pressure physically, perceived double or half level is approx. 6 dB. Within acoustics, dynamics are also called amplitude and can be visualised as the vertical size of the waweform.

Dynamics could seem to be an eminently accessible parameter to vary, including for people with no special musical training. With small children, there is often a direct proportion between intensity of emotion and loudness, and for grown-ups this relation still has a basic importance.

But during music history, the compositional use of prescribed dynamics came only into use at a rather late stage - with Giovanni Gabrieli's Sonata Pian e Forte from around 1600 as a famous early example. Even though Baroque music built on the very basis of affective melody, dynamic change was still practised here in the form of so-called terrace dynamics, with forte and piano strictly juxtaposed.

This nonwithstanding, very different instrumental loudnesses existed. Trumpets and timpani ware used solely by army leaders up to a certain point in history, maybe most often outdoors. A three-manual church organ existed already in the fourteenth century. The clavichord, which is said to have been a favourite instrument of J.S. Bach, on the other hand had a tiny sound, suitable for small rooms. Renaissance and baroque string instruments were more quiet than the modern ones.

Compositional use of both sudden and gradual change of dynamics became common from early classicism and on. By that time, music had become essentially homophonic. Dynamic changes were cultivated further on this basis in romantic music. Only in new music after the second world war we begin to entounter examples of music having individual parts with different dynamic profiles.

If one tries to think in terms of counterpoint again, dynamics could contribute greatly to the differentiation of the parts in the overall sound. This is a different situation from that within the harmonic system where the norm prevails of "balance", that is, parts melting together by being equally loud, except, however, for melody and bass receiving more emphasis than the others. But in a polyphonic context which is a natural state of affairs in freely improvised ensemble music, parts may stand out against each other and interact through dynamic change, polyphonic structures may become highlighted, and there is a perspective of "space", analogous to different distances of sound sources. To achieve such qualities in improvised music, players must have an open ear for the overall sound rather than be absorbed into competetive behaviour.

A peculiar feature of recent developments is the cult of loud music since electric instruments became common in the nineteen-fifthies and sixties as a stimulus in itself in popular music, even at the expense of hearing health - and, as its counterpart, the cult of quiet dynamics found in the Feldman cult of the nineties, and the Swedish "Low Dynamic Orchestra"⁽³⁴⁾

Click on the illustration to see the composition with translations.

Examples from concert music:

Giovanni Gabrieli: sonata pian et forte (two instrumental choirs playing forte when they join together)

Händel: Arie "Ev'ry Valley" from "Messiah" (terrace dynamic changes)

Haydn: Second Movement of "Surprise Symphony" (sudden loud chord)

Ravel: Bolero (very gradually louder)

Sh: Gesang der Jünglinge (1956) (very differentiated / polyphonic dynamics)

György Ligeti: No. 1 from Ten Pieces for Wind Quintet (1968) (polyphonically changing dynamics).

Exercises:

Recorded exercise:

Please see Listening Page!

TIMBRE

Timbre is usually defined as the spectrum of partials belonging to a sounding tone. It could, however, also be understood as the sounding quality or sound colour of composite phenomena, like for instance the timbre of a specific orchestral or ensemble sound. Different vocals sung on the same tone are different exactly because of their different timbres. Just two tones merging into one sound may create an unique timbre, and the concept of timbre thus overlaps with that of harmony, both tonal and atonal varieties. See, however, the citing of Cole (1974) above, in the section about "Pitch", who compares harmonic systems to rigourous train traffic - there is, not least, an important practical difference between a "harmonic" and a "free timbral/polyphonic" structure.

But also for the theoretical consideration timbre can be regarded as a more general phenomenon which includes pitch: “All kinds of sound are characterized by their timbre ... But only certain kinds of sound are characterized by clearly defined pitch height” (Christensen (1996) p.16 - following an observation from Stockhausen (1963b). Likewise, Hegi (1998, p.61) states that "Der Begriff "Klang" wird hier dem musikalischen Begriff "Harmonie" übergeordnet. Harmonie ist dann ein Aspekt des Klanggeschehens, genauso wir "Disharmonie", "Geräusch" oder auch "Lärm"" / "Under the concept of [German 'Klang', meaning both 'overall sound' and 'timbre'], the musical concept "harmony" will be subsumed here. According to this, harmony is an aspect of [Klang] occurrences, just like "disharmony", "noise" or even "racket".

Room and other context acoustics also contribute to the timbral qualities. The importance one can attribute to this parameter can be illustrated by the fact that a cheap violin or other string instrument can play exactly the same tones as one costing several million Euros or pounds or dollars, but the expensive ones are famous for their more interesting timbre!

Physically, all sound consists of vibration patterns. These patterns can be studied by means of oscillograms which depict waweforms, or by means of spectrogrammes which depict pitches. Resonating bodies produce spectra comprising several or many pitches at the same time, whereas pure sine wawes are not found in nature. We humans orient ourselves in the world by hearing spectra as "sound objects", just like we perceive objects in the visual world. When showing oscillograms or spectrograms, the computer acts like a microscope, showing us details which our hearing perception alone cannot discern - "inner microstructures".

Timbre has long been dealt with in intuitive ways. The development of the symphony orchestra and instrumentation for it is a historically important example. While one view of the orchestral instruments saw their "families" basically as individual groups, another view saw the orchestral sound as a whole which could be modeled and transformed by the composer - certainly an influental tendency. Thus, Richard Wagner mentioned the "art of transition" as important for his own music. By this he seemed to mean, among other things, his instrumentation which, as Voss (1970, p. 366) points out, obeyed the formula of "making the contrast as big as necessary and the mediation as detailed as possible". This is close to the definition of serial, parametric thinking proposed by Stockhausen (1958), with its irientation towards polarities and continua. It was cited above under "Parameter concepts in European serialism". There is an overall design with both minute nuances and contrasts, and the design may be different for each composition. Thus, the individual contrasts of a work as well as their modes of differentiation - or, with Wagner's word, "illusions" (cited by Hesselager (2004)), are relative and exchangable seen in the context of several works. But the "art of transition" remains a fundamental prerequisite for realizing this.

The harmonic overtone series is an especially simple and well-known instance of a sound spectrum. Some harmonic systems relate to it, taking the triad as a basic element. Composers and improvisors have sometimes related directly to it in its simple form. One can work with selected parts of the spectrum, in melodic (vertical) and harmonic (horisontal) dimensions and mixtures of both. A number of instruments can produce the tones of such a spectrum by means of flageolets. It can also be done by vocal techniques⁽³⁵⁾

Spectral music, a term which designates a direction in composed new music originating around the French electroacoustic music institute IRCAM in the eighties, went further. Here, instrumental sound can be analysed, emulated and transformed on the basis of scrutinity of its spectra. Such procedures were also at the basis of the commercial development of sampling technology. In spectral music, instrumental compositions of any complexity employing also very complex sounds may be carried out including dimensions of systematic, dynamic change and juxtapositions of spectra.

As the examples of spectral music and the symphony orchestra suggest, timbre has both strong integrative and strong differentiative powers - unity and diversity in a musical process may be determined to a large extent by this parameter and they can have a subtle interaction. On the same line is Reinecke's observation that timbre is that which makes wowels consonants different in Stephan (1969, p.70).

A number of writers recognise the importance of timbre especially for freely improvised music. As Karkoschka (1971/1999) puts it, after having mentioned the "timbral melody" (Klangfarbenmelodie) of Schoenberg as a historical forerunner, as well as the more recent exploration within improvised music of dimensions hitherho repressed by notation: "Compared to earlier we use a listening microscope, as it were... even if we do not at once analyze the formant spectrum as such, we do take in more of its existence than earlier generations did."

Keller (1971) notes an important issue about the timbre parameter being apt for nuanced and spontaneous actions from the players: "Gerade im Bereich des Geräuschs etwa kann ein Spieler weit differenzierter agieren, als sich notieren lässt." / "Exactly in the field of noise, for instance, a player can react in a much more differentiated way as could have been notated"

It should be noted that the classic concept of timbre elaborated on here, though a useful abstraction, has the obvious shortcoming of suggesting something static. Real sounds are not quite so, and for a more complete description, concepts dealing with the changing process of the sound from its start to its end must be considered. Envelope means a curve describing loudness of different constituting components, such as partials, commonly used in synthesizer technology. It has the standard stages attack, body and decay. Grain is an attempt to describe a pattern-like quality of a sound, coined by Trevor Wishart (1985, p.40). This may appear as a special case of what he calls "dynamic morphologies" (p.52)

Establishing continua of timbre, especially exactly definable ones, is not an easy task. Departing from acoustical considerations as well as from common language usage one can, however, propose some:

Tone --- noise

Even though "noise" in the acoustical sense would need to be differentiated from "complex sound" if it were to be treated in a physically exact manner (for instance, to which extent is "colored noise" still noise...), there is no doubt that we have a polarity here. It is possible to describe a given pasage of music according to how relatively "tone-like" or "noise-like" it was.

Light --- dark

Light sounds have a predominance of high partials et vice versa.

"Sunrise" (Solopgang) (1996) by Dida Abrahams maybe speaks for itself:

Click on the illustration to see the composition with translations.

- as does probably also Lone Warncke's untitled piece about "Mother Earth" (1992) with "black sorrow" transforming into many "coloured children":

Click on the illustration to see the composition with translations.

Hard --- soft

This seems a bit more of a psychological matter, even considering strictly timbre, not also dynamics as the important parameter - a quiet tone could also sound hard. But it could seem that the prescence of some strong high partials (which might automatically entail a certain degree of noise-like character) and maybe more (irregular spectrum? less harmonic character of spectrum, i.e. ratio not exactly 1:2:3 etc.?) could contribute to a hard character.

Within one and the same degree in these continua, an infinite number of individual timbres are imagineable.

---

Charlotte Dammeyer Fønsbo contrasts "warm" and "cold" timbres in "Painting the fence" [Male plankeværk] (1992), comparable to colors:

Click on the illustration to see the composition with translations.

In "Fish-Shoals" (1992) Dorthe Bergholt also uses the analogy of color:

<Play the densities and timbres of the fish-shoals>

Click on the illustration to see the composition with translations.

Examples from concert music:

Debussy: various orchestral works

Schönberg: "Farben" from Orchesterstücke op. 16. Illustrates this composer's idea of "timbral melody". (1909)

Per Nørgård Journey (1968) ... 2 Symphony (1970) Canon (1971)

Stockhausen: Kontakte für elektronische Klänge, Klavier und Schlagzeug (1960) (slow change throughout the piece towards lighter timbres)

Stockhausen: Telemusik (1966) (light and transparent timbres predominate)

The Harmonic Choir (dir. by David Hykes) - cassette recording from Danmarks Radio 1984. Overtone singing.

Madam Press: ""Lydlandskab 4" klang". CD MADAM PRESS. Out of the Cage. Carl Nielsen Academy, 2002. Part of a four-movement piece - this movement focuses on changing composite sounds.

Exercise:

make different timbres through varying playing techniques and ways to use the instruments.

Recorded exercise:

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DENSITY

With this parameter, we enter into those that must be operationally defined in some way. This was already the case with the various subdivisions of the concept of timbre for practical, compositional use. Timbre as a dimension, could, however, still in principle be described in an exact way as a physical phenomenon in itself. This is not the case with density - we need to ask, "density of what ?"

It could appear reasonable to take density as both how many sounds per time unit and, at the same time, how "heavy" they are, measured by both their dynamics, timbre and maybe even more. Thus, maximum density would "fill up" completely the perceived musical space. While such efforts could be useful for other purposes, such as individual analysis of works, designing of electronically generated pieces etc., a simple and pragmatic approach is taken here: density as how many musicians are playing within a given time unit. This definition is both manageable for improvised playing within the framework of open compositions, easy to remember and easy to employ in the playing situation. As a measure of perceived thickness it is obviously not very exact, yet it grasps the strategic dimension of how many parts are into play in a polyphonic structure. Note also that of course this definition is relevant only to music produced by a group of persons - not to solo music or electronic music (unless it has specified 'parts').

Density became an important parameter of orchestral music since romantiscism with composers using many and varied sub-divisions of the total ensemble of instruments.

With density, we enter into those dimensions that seem to lie beyond traditional concepts of "basic musical elements". Yet its impact is no less elementary. While loudness could signal intensity of emotion and long durations could signal endurance, increasing density (following the definition here stated) could signal increasing power of group expression, as some of the following examples demonstrate.

Density is a key parameter for group functioning and thus for the flexibility of the music.

Click on the illustration to see the composition with translations and to listen.

"Fish-Shoals" by Dorthe Bergholt which was already quoted under under "Timbre" above is one out of several compositions which uses flocks of animals to illustrate the point.

<Play the densities and timbres of the fish-shoals>

Click on the illustration to see the composition with translations.

"Untitled" (1996) by Anne Kirk Larsen calls for a sudden transition from maximum to lesser density, together with a big change from homophonic to something which is polyphonic in a pointillistic way.

Click on the illustration to see the composition with translations.

Majken Zoffmann's "Migrating Birds (1997) clearly makes the different characters of changing density the main theme of the composition:

Click on the illustration to see the composition with translations.

In Lise Høy Laursen: "A guess at the development of human communication" (2004), the story starts in prehistoric time, moves quickly up to present time with various fast electronic communication and finally describes a future in which intuitive and cosmic thought-reading seems to have replaced the former states. It is interesting to note how the piece in its last two stages contrasts two different kinds of high density, consisting of short and long sounds respectively.

Click on the illustration to see the composition with translations and to listen.

Examples from concert music:

Beethoven: 1. movement from Piano Sonata op. 57, "Apassionata". (During the first 24 measures there are from one to 8 tones sounding simultaneously. Density changes often, this contributing to the dramatic qualities of this music)

Various music for symphony orchestra (alternation between solo/few/many instruments)

Exercise: Attempt to collectively vary the density so that all degrees from zero (no one playing) to maximum (the number of participants) are equally represented. Attempt to let this happen not so much through gradual increases and decreases of density, but through letting spontaneously shifting groups of shifting size play during shifting time-lengths (also solos and general pauses, of course).

This may be very difficult when trying it the first time and require repeated attempts with critical comments in between before it succeeds to some degree. Yet the impact can be a dramatic heightening of the collective awareness of what is happening in the music as a whole and a resulting much greater flexibility of the music - instead of a rather uniform, ever-so-slowly changing common sound the individual potentials of players and their combination can start to show off in endlessly fascinating ways.

Exercise practising to keep density so low that the music remains transparent for both listeners and players - and which at the same time employs a more sophisticated definition of density:

Participants are divided into two groups who play for each other, in turn, using the "Taximeter Principle." This prinicple is that the duration of sound multiplied by the dynamic intensity of sounds equals "consumption" of musical material. From the perspective of the participant: if you play for some time without pausing, if you play loudly or if you do both, it must be balanced by being proportionally quiet at other times. You may imagine that the music offers you a certain amount of space and you are responsible for your own household. And you may imagine a taximeter which is influenced by both duration and by how loud you play.

The listening group points out when the musical process is clear to them and when "over-consumption" occurs, producing a "muddy" sound. This may be done by each member raising a hand, the higher the more overcrowded they think the music becomes. This procedure ensures that ears, not the motoric impulses govern the music and forces the necessary discipline on players from outside - which may open up for a few surprises!

Should some players be clearly dominating at the expense of others, this can and should in many cases be pointed out by the instructor or by a common discussion. If this problem prevails, it can block the flexibility and multitude of the music.

As a part of both exercises mentioned here, it is recommended to listen to recordings of takes which succeed well. Even if an immediate success works in itself to reveal more about what are the real possibilities, listening ensures that it is well memorized, and it expands the experience further.

Recorded exercise:

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PULSE - NO PULSE

So much music in the world has a more or less regular pulse. But experimental music and improvised music has often not. Neither have nature sounds such as those from wind and water in most of their many different forms. Many bird songs and human conversation does not have any clear pulse either.

It could be added that even if there is a pulse in classical music it is not always very marked. If it is polyphonic, the superposition of many parts may also blur individual pulses to a high degree. So-called "New Age" style in music often means that sound is very continous and flowing and a slow tempo contributes to this character. The role of a metre here and even more with much contemporary music may shrink into a purely coordinative device. With contemporary composers and musicologists studying their music it is almost universally regretted that metric notation is no more an adaequate tool⁽³⁶⁾ , still it is also often, paradoxically, considered pragmatically imperative to use, and only some more markedly experimental composers has as of yet taken the step to use other means of notating music. Both for purposes of composition and theory, however, pulse and its opposite may be conceived as a dialectical polarity - they throw each other into relief.

Non-pulsed music may have meditative qualities which pulsed music does not have because pulse strongly acts as a figure throwing itself into the foreground and imposing a certain rationalization, like a ruler, of the perception. Metre makes the figures much easier to grasp and remember, but not to perceive in their utter differentiation.

Working with and without pulse has its special, different delights. In our improvised music, both kinds are common, and so is also conflicts among players, especially beginners, some of who might have the expectation that there must bes a pulse (or who cling to it because they do not know what else to do) while others expect that it should exactly be avoided because it tends to entail a sticking to traditional ways of playing which could be limiting the music.

note It has sometimes been argued that pulsed music is more natural because the earliest human life as a foetus is spent listening to heartbeat sounds. Yet recordings with "uterophones" demonstrate that the sound in the womb is as flowing as it is pulsed, with much rushing and hissing sound⁽³⁷⁾.

If pulse and no pulse are accepted as extremes of a possible continuum, however, this conflict can melt away, and a quite different spontaneous going in and out of pulse along the way, maybe very different each time, can occur.

It must be noted that pulse can be individual or a common one. In the former case there may be no perceivable common pulse. In the compositions quoted below, pulse are generally referred to as common pulse.

Pulse can illustrate a concerted endeavour, which could be both plesant and unpleasant. In several cases, working life is depicted.

Mette W. Nielsen: "A Day and a Night" [Et døgn], 1999, excerpt.
("Gadget" - name of factory, on the chimney)

Click on the illustration to see the composition with translations.

In the following example, the more traditional view of pulse equalling order in a pleasurable way is expressed:

Inge Skougaard: Creative workshop (Kreativt værksted)

Click on the illustration to see the composition with translations.

And this is an example of a slow pulse depicting something outside human activity:

Karina Soon Kristiansen: Water - Earth - Fire - Air (Vand - luft - ild - jord) 1994.

Click on the illustration to see the composition with translations.

In the next example, pulse is the main element constituting "order" (the word appearing in the composition) which undergoes changes through the stages "rigidity" - "eruption" and "freely floating":

Charlotte Zachariassen: "rigidity" - "eruption" and "freely floating" (1999), excerpt

Click on the illustration to see the composition with translations.

In the following example, there is a natural possibility of transition between non-pulsed and pulsed:

Charlotte Lindvang: Water-Music (Vand-Musik) 1995

Click on the illustration to see the composition with translations and to listen.

Examples from concert music:

Alterations Live IRCD 001, 2000 (The music of this English group provides many examples of going in and out of pulse)

Exercise: start with a common pulse (clapping on your legs or in your hands or with drums), make sure it becomes firm and precise. When this is the case, let individual pulses gradually drift away from the common one with rubatos and/or slight accellerandos or ritardandos ... and let this process continue until the pulse is virtually not to be perceived any more. After having reached this stage, go slowly the opposite way until there is again a firm pulse. It is recommended to listen to a recording in order to become fully aware of all the interesting intermediary stages.

After this warming-up, try to improvise freely, going in and out of pulsed sections.

Recorded exercise:

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TEMPO

The existence of this parameter is dependent of a pulse being at least to some degree perceivable or imaginable. Both slow and fast tempos have their own kind of intensity.

In both classical and popular music, assorted degrees of fast and slow are well-known. Changes of tempo are, however, much more unusual - apart from a frequent ritardando practise at endings, from and other slight changes of a rather discreet nature and, admittedly, the changes of tempo found in romantic music.

In Eastern Europe and Russia, there are folk songs having the characteristic feature of a stringendo or accellerando. Indian raga music has a practise of a gradual and slow increase in tempo reaching from very slow to very fast.

In European baroque music, dynamics were bound to "terrace" structures - they were part of the characteristic affect of a piece to be held constant throughout. Whereas dynamics later loosened up, tempos remained mainly fixed - until romantiscism that featured more transitions and even such a speciality as the "rubato" playing associated with Chopin. With modern music later, gradual transitions were not typical any more. So from the still prevailing "terrace" structures in tempo, one could claim that Western classical music still retains a baroque feeling in this respect!


Anette Moltubak employs an accellerando leading to a climax:



Annette Moltubak: "Right time and place" (2005)

Click on the illustration to see the composition with translations and to listen.

Click on the illustration to see the composition with translations.

Click on the illustration to see the composition with translations.

Click on the illustration to see the composition with translations and to listen.

Examples from concert music:

Grieg: piano concerto 1. movement (many tempos and transitions)

Brahms and Dvorak: Slavonic Dances (accellerandos and changes of tempo)

Chopin: various piano works (rubato playing)

Max Reger: Toccata and Fugue op.59. Fantasy over the name BACH (stringendo over long time)

Karlheinz Stockhausen: Kontakte (1960) (- the passage described in "Die Einheit der musikalischen Zeit" in Stockhausen (1963b). It is designated "Moment X" in the score, Stockhausen (1966).)

Various music by Conlon Nancarrow. (This is an experimental composer who since the nineteen eighties became known for a number of compositions focusing on phenomena arising from accellerando and ritardando. They were created for old-fashioned "player piano", having a mechanical device enabling it to be programmed with musical processes, some of which might go beyond the capability of human playing.)

Lou Reed: "Heroin" from LP "Rock'N' Roll Animal" (1974). (Long accellerando is used to depict a drug experience (!))

The Grateful Dead: St. Stephen from LP "Aoxamoxoa" (1969), Warner WS 1970. (Alternation between very slow and normal tempo, with impressive transitions.)

Click on the illustration to see the composition with translations and to listen.

Recorded exercise:

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TONAL - ATONAL

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Click on the illustration to see the composition with translations.

Click on the illustration to see the composition with translations.

Click on the illustration to see the composition with translations.

Click on the illustration to see the composition with translations.

Click on the illustration to see the composition with translations.

Click on the illustration to see the composition with translations.

Click on the illustration to see the composition with translations.

Recorded exercise:

Please see Listening Page!

Click on the illustration to see the composition with translations.

     

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