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Horizontal Indeterminacy

[Definition] This is often the spark of composition, a metaphorical translation of a natural process or phenomena, 'imitating nature in its manner of operations' as Cage said.

Horizontal indeterminacy involves processes which determine the motion or displacement of vertical material in time. It may be a strict process with a set base unit (clock time or musical/metrical time), or it may be a relative process subject to the performers temporal perception. The level and nature of indeterminacy is subject to two different but related approaches; (1) strict processes designed around repetition with variations below or on the threshold of perception (Feldman's 'hidden variation'), (2) relative processes wherein the indeterminacy arises out of a constantly changing context.

Portfolio

[Whitewater] Bounded improvisation combined with the unpredictable response of the computer: may not be strictly indeterminate but is certainly unpredictable and change from performance to performance.

Computer's rate of harmonic evolution is mapped approximately to the attack rate of the player, so this will alter during the piece: in practice this alteration is largely imperceptible unless the performer makes some extreme gestures or goes through sustained periods of consistently different attack rates.

[Whitewater II] Horizontal indeterminacy arises from the lack of temporal control instructions in the score, which only really specifies that the sound events should be sustained, as well as the nature of the decentralised ensemble playing: events are not co-ordinated, anyone can begin an event and the subsequent inner morphology/continuance of the event is dependent on unco-ordinated decisions made by the players. Of course this is all bounded by the rules of the composition, which keep the possibilities within certain limits, but on a local level, the horizontal features of the piece exhibit a high degree of indeterminacy which contribute to a flexible yet explicit[?] global form for the piece. The specific duration of each sound event is determined by several factors including:

• 1. Duration of note sustain, which relates to how long it is possible to sustain stable notes in different registers. All events have a relatively even distribution of pitches across the register, so the event itself is not a determining factor here.
• 2. Duration of inter-event silence. This is a group choice [literature?]: each player, independent of the group, decides how long this silence is, but any player may break it at any time (notwithstanding those players who may not play in silence, so about half of them depending on pre-performance strategy choices)

[Marx] This piece is limited in its application of horizontal indeterminacy, this is only evident in the synthesiser part [and occasionally in the viola d'amore or voice parts when durations are tied to breath/bow lengths ?]. Marx is constructed as a whole made of three interlocking parts. In any given event, the viola and voice parts are sustained dyads which generate the synthesiser's pitches, the viola (or sometimes the voice) also acts as the event's transient, the gesture which signals the beginning of an event. Because these parts are the transient and sustaining elements of the event, the synthesiser part is the only element which can use horizontal indeterminacy, which takes the form of a time-space notation where stemless pitches are specified but their metrical durations are not: durations are to be read as a function of the position in the bar and whether or not they are long notes (open noteheads), normal (closed noteheads) or short (cue-sized noteheads), any of which may also be tied. These subjective durations are a function of the synthesiser's ADSR envelope (A – 2”; D – 1”; S – 2”; R – 4”).

At the next structural level, event durations exhibit an example of Feldman's 'hidden variation', in that there is a perceptual ambiguity over how long each event is. Or more importantly/succinctly/exactly[?], two factors limit the observer's ability to judge whether or not successive events are increasing or decreasing in duration and whether or not there is a pattern;

• 1. Event durations are similar but never the same, disorienting the listener's ability to judge difference from event to event, thus problematising the formation of structure in the listener's mental map of the piece – occasionally there is an especially short or long event which acts as a formal marker to re-orient the listener, providing a (relatively...) clear 'difference' and resetting/re-initialising expectation:
• 2. Lack of metrical time within events. Most events have no attacks or structural markers other than the initial transient, a form of stasis with an inner motion of overlapping pitches (which are again temporally irresolute[hard to resolve]).

At the same time there is no consistent event length or pattern to deviate from to cause tension, ultimately, the lack of a clear tension generating device is in itself a source of tension/anxiety.
[need literature on expectation, predictability, information theory: see also the article on Feldman/hidden-variation to clarify terms and refs]

[Primes] As with Whitewater, the bounded improvisation means that control of temporal parameters rests largely with the performer, who is operating within the possibilities prescribed in the score, and the computer's sound output lacks strong attacks with which to articulate the form: in contrast to Whitewater, this function is also left up to the performer, with no significant input from the computer.

[Nano] [send this to commentaries and cut down for this particular chapter]
The text score describes a simple formula for events consisting of a descending pattern of sub-semitonal intervals at a steady tempo, until the end a breath or an unnaceptably large interval being reached. Horizontal indeterminacy arises from both pitch and temporal aspects.

• 1. The score requires that a new tempo be chosen for each successive event (an event may only last the length of a non-circular breath): the text may be interpreted here to mean 'new' as in 'different to the last', or 'new' meaning 'not used previously', I have no preference, but the latter seems almost impossible to achieve in performance except in a very short performance.
• 2. Pitch material must be organised into descending scales whose largest interval must be smaller than the semitone. As the performance's duration increases, the possibilities for differentiation between events tends to zero: the possible sets of allowable material generated within the piece's defining limits (or register and breath duration) are extremely high, but differentiation between events becomes more difficult as the piece progresses.

Indeterminacy can be mitigated against by choosing to perform highly differentiated events, and the possibility for this certainly exists in the score through the careful zoning/parsing of the material which can be generated within the pitch and tempo limits (defined as mechanical limits of sequential fingering/lip possibilities and breath duration). But this possibility tends to zero as the performance's duration increases. Apart from the simple elegance of the score, this piece is written as text because it should encourage the player to think outside of the confines of notation and instead embrace the infinite continuum of pitch and durational possibilities, which are only truly limited by the player's ability [and the listener's perception/concentration?].

[Bifurcations] Horizontal indeterminacy is here absent from the time aspect of the score, the piece is notated metrically strict: the only possibilities for indeterminacy are that dal niente attacks will never be on-the-beat. The indeterminacy is more present in the perception of the horizontal pitch aspect. The lack of distinct attacks (other than the bifurcatory ensemble stabs referred to in the piece's title) within sections and the sustained motion of the pitches[?] means that there is little in the way of temporal markers to orient the listener.

It is intended that by the time the first section ends, the listener's attention should have shifted away from time by to the gradual transformation of the single chord into two separate streams: separated only by pitch elements, the increasing gap between clars 1 & 2 and clars 3 & 4 should become more apparent as the two groups form separate beating patterns when their pitches become less than a semitone apart.

There is of course a slight temporal marker in the wave motion of the instruments fading in and out, difficult to mask with only four players. I have attempted to mitigate against temporal pattern-forming here by constantly altering the note lengths, but it is hard to avoid this becoming rhythmic pattern for listeners to attach to, especially as there is no other time pattern to observe.