Example 14:  desiderata mortis  for organ (1984/85) (1986, Edition Gravis, Bad Schwalbach)

                        In the Eighteenth Century, after tempo was discovered as an autonomous element, it could give up its old function: primarily, the articulation of formal models.  The change from the moderately fast minuet to a rapid scherzo in the development of the classical sonata form must have been based on conceptions of tempo:  the formula "moderate-slow-very fast-fast."  In the course of Romanticism, tempo change begins to occur at increasingly smaller stretches.  Here belong also the expressive ritardandi at cadences and half-cadences.  The pinnacle of this trend can be seen in Stockhausen's attempt to give every pitch its duration as a metronome number corresponding to its relative frequency.^[3]  At this point, though, the concept of "tempo" is no longer applicable.  To create tempo, more events are necessary: Stockhausen's single events have just a single duration.

                        This way of thought, originating from Stockhausen, differs fundamentally from earlier practice.  "Tempo" had become also an integral compositional material and is subject now to the personal discretion of the composer, who combines it with other elements in a constructive or destructive relationship.  My own attitude is in line with the above.

                        I am going to describe next, a few exactly notated versions from my works.  The end of Teleologies deals only with elements of folk music from the Philippines (it was a commission from the Cultural Center of the Phillipines).  A very simple melody contained in two 4/4 measures is steadily repeated by high instruments afterward () - as it is common in this music - whereas the locus of its playing moves in a circle (the orchestra seating is unconventional).  Low instruments are playing  the  same  melody,  although  more  slowly  (q =100):  the  location  of  the performance circles in the opposite direction.  One can deduce from the relationship the  polymetric  ratio  of 5:4.^[4]  Another melody in 6/8 is added, where  *=*  of the faster tempo.  Therefore this third tempo is slower ( = ca. 83) than the former at a ratio of 3:2 (Example 15).  Compare also Examples 8 and 9a.  Example 9a shows five various tempi, one on top of the other, at the beginning of Bläsergedichte.  Since all play the same, one hears indeed - even for the first time - a temporary, though not a total chaos.  Other facets of this issue will be elaborated upon shortly.

                                  Example 15:  Teleologies, (ending) rhythmic diagram between the two tempi

                         My beginning compositions with various tempi did not deal with such simple layerings, but involved simultaneous acceleration-deceleration.  In a project for my final dissertation in composition studies, in the "Epilog" of a piece entitled Symphonische Evolutionen für Orchester  (1952/53), it happens three times that a few measures are speeded up in tempo, while some parts are actually slowed down by the introduction of longer note-values (see Example 16). The final outcome results in the simultaneous superimposition of the tempi of the first and second sections:

                            Example 16:  Symphonische Evolutionen, the last tempo acceleration in a rhythmic outline

                        Immediately following the superimposition of the bolero and jazz-rock rhythms in Teleologies  (as sketched out in Example 17) both dances begin to pulsate in contrasting tempi.  Using the notation system of the former example, I am diagramming the following one: the bolero keeps its note-values, the conductor indicates the tempo fluctuations.  The performers of the jazz-rock dance also follow the conductor, but their note-values change in a way that their part slows down as the bolero speeds up, and vice-versa.  For the conductor, in order to reproduce a clearer picture of the music in the score, I stretched out the bar lines as the music slows down.  In effect, this would allow the eye to read the music on the paper at a constant  speed.

                                                            Example 17: Teleologies  as diagram

                        Similar employment of notation with stretched bar lines in individual orchestral parts - without the cross-cuing note-values of the other dance - would take up an unacceptable amount of space on paper.

                        In contrast, at the end of mit/gegen sich selbst  (with/against one's self) for a recorder player (1969) there are no tempo changes; the commas, evenly spaced on top of the staff line, represent seconds (Example 18).  (There are four lines: as the top  line  is  performed  live, it  is  also  tape-recorded  and  is  replayed   with  the performance of the second line.  A similar process continues until the playing of the fourth line, when all four lines will sound simultaneously.)  While in the beginning of the composition different metres and tonalities are combined, the cited last part deals entirely with the same two-part figure which, depending on its tempo, is placed in a high or low register.  In the third run-through, the register and tempo stay the same.  In the rest of the piece, the two parts of this figure stretch out or shrink like a piece of rubber.  The longest version lasts 12 seconds, the shortest, 2 1/2 seconds. The extensions and the contractions are superimposed in a rather distinct manner:  they take over each other or remain behind.^[5]  A rather entertaining whirlwind effect of separate but simultaneous time spans is experienced when one perceives some of the events independently and, at the same time, in conjunction with others.  Before the genuine musical and artistic qualities of this experience "speak" to the person, one has to become familiar with a large gamut of similar phenomena - not just a single piece of music in the genre.  And what is "said" is, of course, beyond verbalization ...

                                                        Example 18:  mit/gegen sich selbst  (Carus Verlag, Stuttgart)

                        Initially, in the Streichersonate  (1954)  ("Sonata for Strings") I notated different tempi played at the same time in an aleatorical manner (see Example 19).

                                             2

                                                                           Example 19:  Streichersonate

Violins I and II, and Violas II stay in the same tempo; the others, led by the conductor, are constantly becoming faster.  When I showed it to a radio orchestra conductor, he refused to consider the piece on the pretext that all members of the orchestra "must hang on to the tip of his baton."  (Thanks to the Nazi era, not a single German musician knew of Charles Ives in the early fifties.)  In this piece the note-values are exactly notated; only the correspondence between the layers is left to chance.  In the organ  piece  desideratio  mortis   the  note-values  of  concurrent pulsation must be estimated from their position on paper.  Since it requires the difficult task of uniform and independent acceleration-deceleration in both hands at once, I spelled this out in a practice score (see Example 20a and b above).

                                                                                                        a) pulsation 

                                b) Practice score

                                                                               Example20:  desideratio mortis

                        Once again those in-between situations are especially attractive and fruitful, as for example, in the combination of exact and aleatoric notations.  In Example 21a (below) from entfalten  all values are exactly notated.  During the part for the soloists (cello and piano, = 60) medium high winds throw in first a quote from the beginning of the piece in the tempo = 96, and when this is played, the high winds repeat the same quote in = 130.

                        Example 21b (below) originates also from entfalten.   To produce flexible tempo changes, the four soloists must assess their own actions and coordinate among themselves independently from the orchestra, which continues to be directed by the conductor in exact rhythms.  (Because of lack of space, only a section of the winds and percussion above, and a section of the strings under the soloists is represented.)  Example 9a can also be viewed in this context.

                        Uncharacteristic timbres help to sustain so-called "pure" temporal qualities.  Just as in Stravinsky, where percussive lines are especially effective because they are realized by wind and string instruments - and not by percussion - so can entire sound constellations highlight temporal events.

                        On the whole, it can be argued that temporal qualities are defined by all elements of the musical texture.  The fact that we hardly often make a point of it can be blamed, in part, on our theoretical tradition that conventionally recognizes counterpoint, harmony, instrumentation and form, but ignores systematic rhythm and, especially, tempo studies.  Although a reservoir of rhythmic models was developed from dances and diverse "figures" (e.g. rhetorical) and eventually expanded - in comparison to the other components of music - rhythm has been hardly formulated historically as a system.  Notwithstanding, one finds in Palestrina-style a dependence on dissonance and other phenomena, like the beginning of an ascending or falling motion to generate "affections" ("Empfindlichkeiten") on note values and influencing also tempo.  In the style of Bach the idea of "motion" ("Bewegung") plays an important role.  In both cases we refer here to phenomena resulting in certain temporal qualities though we avoid dealing explicitly and directly with the role of time.  It appears to me, without overstating the case, that there is a parallel here to the late Middle Ages.  In those times composers did not possess a definition for the triad, and  the notions of inversion and functionality (for example the "dominant") were not yet explicated.  At the same time they have already applied these ideas indirectly  -  at least from a conceptual point of view ("the relationship of the upper voices to the bass").

                                                 Example 21a: entfalten (1984 Edition Gravis, Bad Schwalbach)

 

                   Example 21b: enfalten (copyright 1984 by Edition Gravis, Bad Schwalbach)

 My own work goes seemingly the other way: when I concern myself with temporal attributes, I do not think  "slow" and  "fast," but  in terms  of "expanding"  and "contracting."^[6]  Or, a gradually slowing part appears to me as "observing under a more and more powerful microscope."  In short, in my compositions a frequent key connection to musical time consists in the transformation of the character of the musical object itself.

                         When the idea in Bläsergedichte  ("Windpoems") of working with poetic meter came about, I wondered why it occurred to me only as an adult; even as a schoolboy, when I had to deliver rhythmic recitations of poetry I already made melodies with it. I dug into the subconscious and found that musical objects in our European past had always a single tempo. Though there was a margin of tolerance, nevertheless, composing different fast and slow versions of the same thematic material, transitional passage and instrumentation was unthinkable.^[7]  Today - and more so since Stravinsky - the confrontation of stylistic periods has become inevitably tied to the temporal manipulation of musical objects. To return to the use of poetic meters in my Bläsergedichte : prejudiced by my education, they seemed to me unalterable by using time composition and I needed a conscious idea to overcome this presumed taboo.

                        I was able to implement such character transformations in 1973 at the Studio for Sonology at the University of Utrecht.  They developed there a variable-function generator that allowed one to combine the features of up to two hundred elements and have them run faster and slower by very large orders of magnitudes.  In the electronic composition entitled Bewegungsstrukturen ("Motion structures")(1976) I devised the following strategy:  each burst of a rapid blob of sound was repeatedly stretched to a pattern of several seconds in length (this is analogous to the "increasingly powerful microscope").  In another electronic piece called Zeitmosaik  ("Time Mosaic") (1985) the opposite occurs: a pattern becomes gradually faster.  It is made of segments that initially seem to have nothing to do with the simple rhythm sounding below, at its own tempo - until the segments of the pattern actually fall in place with those rhythms. Accordingly, Thomas Arns created a visual soundscore on slides for synchronous projection with the music.  Example 22 below shows an excerpt from it.

                                                              Example 22:  Zeitmosaik

                        In Klangzeitspektakel,  a piece I am currently working on, I load a computer sequencer with three very different types of music.  In a single overall tempo none of it is comprehensible.  As the sequence is speeded up or slowed down, one of the types becomes comprehensible while the others blur out.  The most difficult and yet unresolved challenge is to create meaningful events  for each phase: a threefold time - counterpoint - or even a multiple one.  Out of the incomprehensibility generated by tempi that are "too slow" and "too fast" for a given type, certain rhythmic and timbral qualities will be produced that will make it function as a whole.

                        I set up for myself similar challenges in possibly my oddest composition, hinter einem marschrhythmus  (behind a marching rhythm) for organ (1971).  The basic idea is simple.  Just as militarism destroys culture, assistants (to the organist) chop up the music by pulling stops to a notated marching rhythm:  we hear only the "filtered" music from behind.  This comments on the music profession:  from Bach to Mozart through jazz, boogie-woogie, to Weisst du wieviel Sternlein stehen  and "Happy birthday to you." In this piece sometimes completely different tempi are superimposed; while the organist keeps his tempo (Example 23a) the marching rhythm speeds up.  In Example 23b the organist has a rather difficult task to perform - some straight polymetric superimpositions at first, then, an accelerando in the right hand, and by the end, a ritardando in the right hand as the left speeds up.  The listener can recognize the events only if they are very simple and known, and lasting at least several seconds.

                                Example 23a: hinter einem marschrhythmus  (Tonos International Music Editions,Darmstadt)

                                    Example 23b: hinter einem marshcrhythmus  (Tonos International Music Editions,Darmstadt)

                        Naturally, the concentration on this aspect of composition has an effect on the large-form concept.  Because of limited space, I laid out only a few pertinent structural elements of my Bläsergedichte  for wind quintet.  The succession of the movements follows the chronological order of meters in history:  "Prologue" (ancient Greek hexameter-pentameter) - "Monopart" (ancient Roman Saturnian verse) and Ode (old German "Nibelungen" strophe) - "Dialogue Toward a Sonnet" (old Italian) - "Scherzettino" (British Limerick) - "Triple-Poem-Fugue" (combinations of various forms of these meters).  The "Prologue" starts simultaneously in various tempi but it converges gradually to a synchrony (Example 9a).  It then continues with a similarly brief, single-voiced "Monopart."  The tempi introduced here stand in a ratio of 3:2 to the slower ones and are systematically listed as in Figure 1:

                  Figure 1: The first column gives the order of appearance in the piece

The "Ode" is connected attacca to this piece.  It alternates tempi between = 144 and  = 108 (= 4:3).  Superimpositions of versions of various length occur here:  one in a 3/4 measure, another in 2/4 and a third partially in 3/4 and 2/4 - as an example for "polymeasured" layering (Example 9b).  In "Dialog Toward a Sonnet," the English and French horns carry out a conversation  in front of a sound backdrop of multiphonics, played by flute, bass-clarinet and bassoon.  The tempo beats are indicated here for all instruments in "soft" notation.  The immediately following  (also attacca ) "Sonnet" represents this poetic form in sound and tempo structure.  The arrows stand for gradual transition from one tempo to another (see Figure 2.)

                                                                                         Figure 2:

                        The limerick represents the classical scherzo.  Its cheerful character is represented by a less elaborate structure with high and low instruments alternating at varying tempi; it ends with a quasi trio using slightly distorted quotes from the traditional form.

                        With the increase of the number of voices in terms of the combined poetic meters, and their polymetric contrasts, the ensuing development sections in the "Triple-poem Fugue" build to a gradual climax.  In this movement, the character transformation of the material derived from the "Nibelungen" strophe is highlighted.  It appears initially in the "Ode" like a "show-off" (Example 9b1,2).  In the Fugue, it takes on first a martial character (Example 9d) and then (after approximately 12 measures), by way of a hesitant, almost anguished version (Example 9e), it turns meditative and elegiac before the end (Example 9h).  Here I see the climactic point of the composition (an "inner" climax):  after it the structure gradually disintegrates and all technical niceties wash out with the weakening breaths of the players.  The work was written for and dedicated to the Camerata Woodwind Quintet of Western Illinois University.

                        Helga de la Motte-Haber  writes in her important essay:  "Man does not have a sense organ to perceive time."  This proposition would have been acceptable with the insertion:  "unmediated - as compared to the other senses of perception."  Also her next definition - "The 'sensation of time' is firmly embedded in systems of Weltanschauung.   It develops in a cultural context" - excludes a domain of other cultures and forms of life and their respective biological time clocks.^[8]

                        Almost everybody who has speculated on time since the ancient Greeks concluded that time exists only as a succession of events.  If one wants to understand time's factual meaning this first question arises:  is a non-event possible?  Even in the state of deepest meditation - as practiced by East Asian masters - heartbeat, breathing, and other bodily functions continue.  In all musical cultures pauses are events, even when they are untimed, leisurely rests.  (A five minute pause between two movements of a suite or symphony...?)  The requirement of a succession of events for perception of time not only serves as a crutch to our supposed, lack of sensation for time - as compared to our unmediated sensitivity for "hot," "red," and "pitch" - it is the very thing itself.  Succession of events and time are two aspects of the same phenomenon (such as, for example, waves and atomic particles are different aspects of light; the latter is even more difficult to conceptualize for us, mere mortals, than time and event successions).  Therefore, our sense of time is there to verify a succession of events - a "meter."  Only on this premise we can use our special capabilities of sensing time and not Stockhausen's, whose duration proportions are based on a false analogy to pitch.  His other erroneous premise was in conceptualizing durational proportions in isolation.  But our sensory discrimination for time can unfold all its possibilities only in longer stretches of time.  Both his misconceptions are based partly on stylistic criteria:  that regular meter and groupings have become antiquated, and that a quasi-scientific idea claiming that duration proportions as the smallest common denominators proves the unity of musical time.  Unfortunately, our senses do not function in such a simplistic manner.  (There is a similarity here to Hindemith's attempt to derive all multiple voicings ("mehrstimmiger Satz") from the overtone structure and combination-tones.)

                        Psychologists distinguish between long- and short-term memory, and lately, ultra-short memory and we musicians should subdivide our memories into further categories. In music, one could define the shortest memory as the time a sound continues to be experienced as it was at the instant of its attack.  But the  time span of the "present" can be significantly longer:  it depends on the events that fill it.  If we establish the theme of the first movement in Beethoven op. 26 at  e  =   92, the beginning double-period lasts a little over half a minute.  The second part of it, being repeated after a ten measure episode enables us to perceive all as an undivided unit although lasting about 70 seconds. In the second movement of Schubert's C Major Quintet D 956, the beginning fifteen-measure phrase units reach the tonic in approximately three minutes.  Is it possible to hear this time span as one "present?"  The answer is an unequivocal yes.  The broadly dispersed, small number of elements allow for an "unmediated present" to last that long - without engaging "recall" or "memory."

                        We arrive here at an important fact with implications beyond the subject matter at hand:  thorough familiarity with a body of music increases substantially the stretches of "present."  Only when we reach through practice the peak of our abilities, can we approach the entirety of wealth and the individuality of mature works between Bach and Brahms. 

                        When listened to in smaller sections, they offer us only a generalized idea about the styles of their time.  We experience without any special effort smaller groupings such as sixteenth, eighth, quarter or 3/8-groups, measure, phrase, period.  With additional practice we can take in more, and longer sections become clearer:  tertiary units (for example, double period, episode, recapitulation), sections of an exposition, the sonata form, and finally, the entire cyclical form.  The ability to integrate simultaneous and interacting orders of temporal magnitude is a specific competence of our temporal sensibility. By the Nineteenth Century this multi-dimensional time experience had vanished as increased doses of discontinuity were introduced with strong, localized and independent harmonic events, and, at the same time, the radius of tonality continued to expand.  Recognizing its disappearance and the historical reasons behind it may help us to reinstate it for the future.  There is a direct, visionary possibility in future music and musical experience: it can lead potentially - under today's fundamentally altered perception of time and form - to the revival and mastering of an expanded, usable temporal space.

                        Incidentally, the significance of long-term memory in relation to the mastering of larger musical forms has not yet been fully explored.  Besides, we know that comparative listening experience of many, and very different works leaves us with specific residues:  and throughout the years, these lasting imprints help to discard the unessentials from our memories.

                        Helga de la Motte describes in the same essay changes in sensation of time, especially in the last one hundred years, and she mentions Einstein's Theory of Relativity.  A number of painters were stimulated by it and the concept was also known to Debussy.  (Einstein's ideas during the lifetime of Debussy were very controversial and therefore little known outside the profession; moreover, Debussy in his later works has returned emphatically to classical principles.  More significant is the closeness of his works from the middle period to the shared consciousness among leading intellects of his generation - a unity of Zeitgeist that never ceases to astonish.  On this account, the Dutch scientist H. A. Lorentz is closer to Debussy because he formulated some foundations of relativity ten years before Einstein.)  Today Einstein's discoveries have become public and were proven to the last detail: they highlight, among other things, the diverging velocities of passing time in particles and systems set in motion against each other.  The individualization of time - depending on velocity, that is itself a product of time and space - removes the old impersonal, unbending rigidity of time itself.  Concurrently, the interaction among all systems will be reinforced (it can be also viewed as a kind of socialization) so that time, by becoming somewhat more active, will take up a new position in our consciousness:  is all this conceivable without repercussions on our musical thought?