The patch contains:
– 4 3F synthesis banks (1s3f, 2s3f, 3s3F, and 4s3f); notated as 3f(1), 3f(2), 3f(3), and 3f(4) in the score.
– 4 Markov path generators (1smer, 2smer, 3smert and 4smer)
– 4 Synful synthesis banks (synful, Bsynful, Csynful and Dsynful)
– 1 leslie (or rotation of the sound on itself)
– 1 frequency-shifter
– 2 samplers (or samplers)
– 1 reverb
– 1 spatializer.
3F synthesis (developed by Miller Puckette) creates inharmonic sounds with control over 3 basic frequencies.
Markovian paths generates melodic movements according to certain probabilities of succession between notes. Here, they are mainly used to control the movements of one of the three frequencies of 3F synthesis.
Synful synthesis (developed by Eric Lindemann) creates instrumental sounds. In this piece, only string pizzicatos are used.
The Leslie is a system that rotates sound around itself, with the speed measured in revolutions per second. This system is inspired by old Hammond organs, in which a device consisting of three speakers rotated on a pivot.
The frequency shifter is a modulator that transforms a sound (in this case, that of a piano) by introducing inharmonicity. It has two outputs: positive (by adding frequencies) and negative (by subtracting frequencies). When the two outputs are used at the same level, this transformation is called ring modulation.
The sampler plays and transposes a recorded sound.
The reverb simulates a virtual space in which a sound will be projected.
The spatializer simulates distance and make a sound travel in a real (or virtual) space around the audience.
Depending on the acoustics of the venue, the solo piano may or may not be amplified. For example, during Daniel Barenboim’s premiere at the BoulezSaal in Berlin, the piano, located in the middle of the audience, did not need to be amplified.
Evt 1:
If the piece begins the concert or the second half of the concert:
- Start event 1 (regular chords) as the audience enters.
- Begin at a “p” dynamic and gradually increase the volume.
- Reach the “ff” dynamic when the lights dim (blackout and spotlight on the piano).
- The pianist seats and plays the piece.
If the piece is played after another piece:
- Start event 1 during the applause
- Start at a “mf” dynamic and gradually increase the volume.
- Reach the “ff” dynamic when the pianist arrives on stage.
- The pianist seats and plays the piece.
This first part is based on chords played by 3F synthesis voices: 3f(2), 3f(3)] and 3f(4). The first two voices [3f(1) and 3f(2)] will frequently move from low to high, while the last two [3f(3) and 3f(4)] will remain in the low register and at a steady rhythm.
Throughout this first section, dotted rhythms (30nd notes) should be tight and of more or less equal value, even when they occur in triplets. This is a convention that comes from the dotted rhythms in French-style openings from the Baroque era, in which the dotted 8th note/16th tend to be played as a double dotted 8th/32nd. The piano must be synchronized with the regular chords of the electronic music. This dotted rhythm is a foreshadowing of what will be the second theme of the sonata that follows.
The piano is transformed with a Leslie effect, which produces variable rotations of the sound on itself. The level of the transformations must be lower than that of the acoustic piano.
Evt 2:
The first synthesis voice 3F [3f(1)] produces a very fast random texture (spatialized to the northwest).
Evt 3:
The second 3F synthesis voice [3f(2)] rises towards the high register, accelerating until it produces a random texture similar to that of event 2.
The climax preceding the piano entry should be around 5 ». However, the pianist may begin as soon as they hear the onset of this progression towards the high register.
The piano is treated here with a frequency shifter. It develops a contrapuntal progression in three voices that accompanies that of the electronic music as it progresses towards the extreme high register.
Evt 4:
Transposition of the spatialized 3f(1) texture to the southwest.
The piano, still processed by a frequency shifter, colors the electronic texture. The regular succession of these 16th note sextuplets anticipates what will become theme 1 of the Sonata.
Evt 5:
Effect of spatial distancing (at 5 meters) of the high textures of the electronic music.
The piano is processed with a leslie.
Evt 6:
The texture of 3f(2) gradually transposes toward the high register until it overlaps that of 3f(1). Throughout this process, the two textures rotate around the audience. 3f(1), rotating counterclockwise, accelerates to a moderate rotation, while remaining fairly distant, while 3f(2) accelerates in the opposite direction to a very fast rotation speed, resulting in a high-pitched “A.” During this acceleration, the distance of this voice is reduced to 1 meter.
The piano is not transformed here. It develops a new progression towards the extreme high register, but here in four voices.
Evt 7:
3f(1) completes its acceleration here and joins the high “A” of 3f(2) while moving closer (1 meter). The two textures, tuned to the same note, rotate in opposite directions, now at very high speed around the audience.
The piano sums up the situation by hammering the high note and rolling out a bass line covering the entire range.
Evt 8:
The two textures [3f(1) and 3f(2)] descend in rotations that slow down until they become indistinguishable from each other in the extreme low register. From this point on, the rhythms of 3f(3) and 3f(4), which had been regular until then, become more complex and intertwine. They nevertheless remain in the low register.
The piano, again processed by a frequency shifter, takes up the sextuplet figure from event 4, accompanying the electronic music as it descends towards the low register.
Evt 9:
First piano development on the spectra generated by the 3F synthesis.
The piano is still processed by a frequency shifter.
Evt 10:
New progressions towards the high register of 3f(1) and 3f(2), accompanied by the piano in sextuplets.
Evt 11:
Descents similar to those in event 8 but shorter, leading to a new tuning of the four voices of 3F synthesis.
Evt 12:
Second piano development on the spectra generated by the 3F synthesis.
Evt 13:
Beginning of the dissolution of the low voices: 3f(1) rises rapidly towards the extreme high register.
The piano must wait approximately 2 seconds after the end of this rise before continuing with the next figure.
Evt 14:
3f(2) rises rapidly towards the extreme high register.
Evt 15:
3f(3) rises rapidly towards the extreme high register.
Evt 16:
3f(4) rises rapidly to the extreme high register. The low spectra have now completely disappeared.
Evt 17:
Duplication of the same harmonic structure on the piano and synthesized music to prepare for another (in)harmonic situation.
Evt 18:
Third piano development on the spectra generated by the 3F synthesis.
The piano is processed by a frequency shifter, with positive and negative outputs (ring modulator).
The phrase is composed of a pole of harmonic stability and a descending chord sequence.
Evt 19:
Fourth piano development on the spectra generated by 3F synthesis.
The phrase follows the same structure as before.
Evt 20 to 24:
Fifth piano development on the spectra generated by 3F synthesis.
The phrase follows the same structure as before.
Evt 25:
Descending phrase made up of alternating 3f(3) and 3f(4).
Wait until the motif on F#/A is “pp” and very slow before continuing with event 26.
Evt 26:
Introduction to Interlude 1.
3f(1) and 3f(2) unfold an extremely calm and slow structure. This will serve as a canvas for Interlude 1.
INTERLUDE 1
During this interlude, the piano is treated with a frequency shifter whose resulting frequencies are approximated in the score above.
The pianist should play “at the limit” of the sound. The transformed sound should largely dominate the acoustic sound of the piano, even if the overall nuance is very soft. If the piano is amplified, the amplification should be turned off here.
Evt 26.5:
The processing on the piano stops here.
Evt 27: SONATA 1
Introductory chord sequence to the Sonata.
There is no processing or electronic synthesis in this phrase. Only the acoustic piano.
Evt 28: Theme 1 of the Exposure
Here we enter the rigorous phase of this piece. After the “free fantasy” of the beginning, the form here will be structured like a Beethoven-style sonata. The first theme is an ostinato on “E flat” consisting of three superimposed sources:
- A spectral sweep of 3f(1) on inharmonic sounds
- A repetition of “E flat” by pizzicati played by Synful
- A sequence of piano chords distributed randomly on certain “E flat” notes played by the Sampler. Each of these chords chooses its own random location in space by means of a random draw in a 360° space.
The pianist must wait approximately 15 seconds before continuing with the next sequence. This sequence must be synchronized with the tempo of the electronic music. The characteristic of theme 1 can be reduced to a succession of notes in a regular and rather lively tempo (toccata or ostinato), as well as scattered chords attached to it.
Evt 29:
Markovian distribution of phrases with an upward trend and ending on “E flat.”
3f(3) reacts to 1.5% of the notes played by 3f(1) by varying the spectra on E flat.
The pianist must observe a pause of approximately 4 seconds before continuing with the next sequence.
Evt 30:
The Markov distributions become more complex in their contours. The phrases are more uneven and do not rise systematically as before.
The piano chord sequence that follows (after a pause of approximately 6 seconds) should be very rhythmic. In the following phrase, clearly mark the accented notes to give the phrase a more chaotic and less regular feel.
Evt 31:
Continuation of the previous sequence but with Synful and the Sampler. The 3f(1) stops.
Evt 32:
Evolution of the Markov sequence with the introduction of new higher frequencies. 3f(1) and 3f(2) join the discourse.
Evt 33:
The Markov sequence evolves towards the medium register.
Evt 34:
Diminuendo of the sequence.
Evt 35:
Fade out of theme 1 (Markov sequence) and preparation of theme II. Theme II consists of two short notes which are introduced here in the rhythmic domain. Two spectra, one played by 3f(3) and the other by 3f(4), are slightly out of sync. But it is always theme 1 that controls the events. Thus, theme II arises from a pairing probability that is based on the ostinato of the Markov sequence. For each note produced by the Markov matrix, a probability is drawn. The value “$proba_bell1 := 2” means that in 2% of cases, the delay between 3f(3) and 3f(4) (Theme 2) will be heard. This is a kind of musical metaphor for dark energy: we cannot perceive it, but we can perceive the influence it exerts on other objects. Here, we no longer perceive Theme 1, but it is Theme 1, through its regular rhythm, that causes all these probabilities, some of which will make the rhythm of Theme 2 heard.
Evt 36: Sonata 2: Theme 2 of the Exposure
Theme 2 enters. It consists only of an ascending minor third (A/C) played with the characteristic rhythm introduced in the previous event. This third is played by voices 3 and 4 of Synful (Csyn and Dsyn, respectively) reacting to 3f(3) and 3f(4). Of course, it is impossible to know when this third will occur. However, the density of its irregular appearance is higher than that of the two spectra in the previous event (9.5%).
Evt 36.5:
The piano plays the other element of theme 2: a trill introduced by a sixth interval. The attacks here must be hard and aggressive, while the trills must be played, with a few exceptions, in the “p” dynamic.
The probability of the minor third appearing in the electronic music drops back to 5.5%.
Evt 37: Coda of the exposition.
This is the end of the exposition, during which the two themes are superimposed. The first (ostinato in the high register) occurs at the limit of audibility. The pianist must begin playing the chords (second theme) as soon as they begin to perceive the first motif in the high register.
Evt 38:
The first theme appears with itself in the electronic music. First in its original rising form in triple-sixteenth notes (played jointly by 3f(1) and Syn), then in double diminution in double-sixteenth notes (3f(2) and Bsyn). As soon as the pianist hears this sixteenth-note motif, they should follow along, synchronizing with its tempo.
The remaining voices (3f(3), 3f(4), Csyn, and Dsyn) continue to develop the dotted rhythm of the second theme.
Evt 39:
This event follows on from the previous one, the main difference being a change in the Markov paths (markov7.txt and markov8.txt instead of markov5.txt and markov6.txt). The piano develops the chords of theme 1 (see event 30).
Evt 40: Sonata 4: Development
This development begins with theme 2, which takes on a more exaggerated character. Here, the diffusion of the electronic music can reach quite a high intensity.
The piano alternates between trills and dotted rhythms before evoking the first theme in 32nd notes.
Evt 41:
Continuation of the development on theme 2.
Evt 42:
The piano takes up theme 1 again, but with control of the synthesis. Each note of the piano will drive one of the three frequencies of the 3f(2) synthesis, which will produce an inharmonic doubling of the piano part by the synthesis.
Evt 43:
This event initiates a process, still based on the ostinato of theme 1, during which the system observes the pitches played by the Markov process and, if certain specific pitches are played, the sampler produces a particular crotales sound. Here is how this process is described in Antescofo:
case $watch_3fcB == 90: @SMP1(“bell.15_fa#5”,12) means “if the pitch is MIDI 90, then the sampler plays the sample ”bell.15_fa#“
@st1(@rand(360),1,40) means ”the sampler chooses a particular location for spatialization (between 0° and 360° »
case $watch_3fcB == 89: @SMP2(“bell.14_fa5”,12) means “if the pitch is MIDI 89, then the sampler plays the sample ”bell.14_fa »
@st2(@rand(360),1,40) means “the sampler chooses another specific location for spatialization (between 0° and 360°)”
Etc./
This stream is spatialized to the northeast.
Evt 44:
Spatialization to the southeast.
Evt 45:
Spatialization to the northwest.
Evt 46:
Spatialization northeast.
Evt 47:
Spatialization southwest.
Evt 48:
New development event. Themes 1 and 2 are superimposed in the electronics while the piano alternates between them before intertwining them.
Evt 49:
Theme 1 spins around itself with the same control over the sampled crotales as in event 43, while the second theme intervenes randomly, always according to a probability of appearance that depends on the first theme.
The piano sequences that follow once again control a voice of the 3F synthesis.
Evt 50:
Long diminuendo of theme 1
Evt 51:
Fade out of theme 1, leaving the processes that still depend on it to resonate: crotale sounds and the dotted rhythm of theme 2.
Evts 52.1 to 52.4: Interlude 2.
In this second Interlude, the piano is again processed by a frequency shifter. Here, the electronic events must be synchronized with the piano notes.
Evt 53:
Here begins a process in which several sound objects appear, always according to the same probability process linked to the development of theme 1 (which cannot be heard here). These objects are: 4 bell sounds and a mokubio roll. This process overlaps with the previous one, which allows the sounds of rattles and echoes of theme 2 to be heard.
Evts 54.1 to 54.4:
Modification of the rhythmic values of the Markovian procedures. Theme 1 is derived from the unfolding of a Markovian process whose “ostinato” variable is set to 100. This means that all note durations are reduced to an equal value determined by a tempo value. By lowering the “ostinato” variable to 0, we return to the irregular rhythmic values that were determined for each note of the Markov process. The result is a rhythmic construction with unequal durations but which sometimes tend to repeat themselves over similar durations. We are therefore in between themes 1 (regular) and 2 (irregular).
The piano, still processed, produces figures inspired by the rhythmic behavior of electronic music. During the descending “pp” chords in measure 238, push the piano transformation (frequency-shifter) so that it is slightly above the acoustic sound (amplified or not).
Evt 55:
New process inspired by that of event 53. Here, nine figures are distributed, again randomly, following the course of theme 1 (which is always hidden). Once again, the musical metaphor of dark energy is at work here. These figures are as follows: 1 crotales sound, 1 bell sound, a dotted figure (theme 2), a mokubio roll, and 5 occurrences of log drum sounds inspired by theme 1 (rapid and regular succession of sounds). These five occurrences are distributed according to the Fibonacci sequence: 1 sound, 2 sounds, 3 sounds, 5 sounds, and 8 sounds. When the “log drums” situation is chosen, another random draw selects which of the five occurrences will be played.
But here the performer will enter into musical contact with this process. They have 18 short sequences at their disposal, each of which echoes one of the electronic sequences played here. For example, sequences 1 and 2 echo the sounds of bells, sequence 3 (a succession of 5 triple-sixteenth notes) echoes the log-drum sequences. The very high-pitched sound that follows is reminiscent of the sound of a crotales, while the rapid repetitions on the same high note are similar to the roll of a mokubio. This allows the pianist to react to an electronic figure as they wish, choosing a sequence that suits them, or deciding to respond only to a specific figure. There are no rules. These sequences can be repeated as many times as desired, the idea being that too long a duration would risk becoming a little tedious. I therefore leave it to the performer’s discretion to decide the duration of this section. The piano is not transformed here.
Evt 56
Last section of this Interlude, during which the piano is transformed again and plays a slow, free-form sequence over an inharmonic 3F synthesis texture. The last three measures (on a low E-flat-B-flat pedal) will be quoted in Interlude 4.
Evt 57, 58, 59 and 60: Sonata 5: Reexposure
Theme 1, the secret architect of the entire development, reappears, accompanied by its double on the piano, which exposes fragments of it, still following Fibonacci proportions (13, 21, 5, 13, 8, 3…).
The piano must play in the tempo given by the electronic music.
Evt 61: Interlude 3
Entries of 2 synthesized voices 3F: 3f(1) on theme 1 and 3f(2) on an irregular and slow rhythm.
Evt 61.1:
Entrance of the 3f(3) synthesizer voice on an irregular, slow rhythm.
Evt 61.2:
Entrance of the 3f(4) synthesizer voice on an irregular, slow rhythm.
Evt 61.3:
Set up the system for controlling the synthesis by the piano. This is the most interactive section of the piece. The four independent synthesized voices will be transposed according to the pitches played by the piano. In other words, the piano’s registration will also apply to the synthesis, but the notes played will permeate the electronic musical structures. There is therefore, on the one hand, an automatic and independent system that generates its own musical structures, but these are “distorted” by the pianist’s playing. The order of the piano sequences is completely free. As noted in the score, you must start with sequence “a” and end with “j.” Sequences “a, d, e, f, and h” can be played twice.
Evt 62:
The interaction between the piano and the four electronic voices stops here. The piano responds with fragments of theme 1, which it exchanges with 3f(1).
Evt 63:
Theme 1 at 3f(1)
Evt 64:
Theme 1 on the piano
Evt 65:
Theme 1 at 3f(1)
Evt 66:
Theme 1 on the piano
Evt 67:
Theme 1 3f(1)
Evt 68:
3f(4) stops
Evt 69:
3f(3) stops
Evt 70:
3f(2) stops
Evt 71:
Stop of 3f(1)
Quasi una cadenza (Reexposure of theme 2)
This is a cadenza for solo piano without electronics or transformation. It is constructed on elements of theme 2, into which fragments of theme 1 (sixteenth note sextuplets) are inserted.
Evt 72:
This is a kind of “climax” that takes place here on theme 2. The electronic music should be played at a fairly high volume here. The dominant spectral frequencies are C#/G.
Evt 73:
Continuation of the same process. The dominant spectral frequencies are E/G.
Evt 74:
Continuation of the same process. The dominant spectral frequencies are A-flat/G
Evt 75:
Continuation of the same process. The dominant spectral frequencies are C/G
Evt 76
Conclusion of this recapitulation with a “liquidation” of theme 1. While the second theme gradually fades away in the electronic music, the piano evokes the first theme (a succession of rapid, regular notes) in several fragments that fade away “in tatters,” separated by numerous silences.
Evt 77:
Entrance of the frequency shifter (on B flat: MIDI 70) for the transformation of the piano.
Interlude 4
During the last of these Interludes, the balance between the piano and the electronics must be the same as in the first, i.e. the sound level of the transformation must be higher than that of the acoustic piano (amplified or not). If amplification is used, it must be turned off here. This Interlude is a kind of synthesis of the previous interludes: here, the same formula is repeated in the left hand in the extreme low register (see Interlude 1, measures 108 to 115), while the “Morse code” repetitions in measures 322, 324, 328, and 331 refer back to measures 233 to 236 (Interlude 2).
Evt 78:
Modification of the shifting frequency: E flat (mid 75)
Evt 78.1:
Here, the frequency shifter outputs equally on its two negative and positive outputs, making it equivalent to a ring modulator. The scalar descents of the piano evoke measures 115 and 116 of the first Interlude, with the difference that, depending on the harmonic relationships between the notes played and the shifting frequency, the sounds resulting from this melodic descent will give an ascending shape, thus moving in the opposite direction to what is played on the keyboard.
Evt 78.2:
Glissando of the shifting frequency from E-flat (75) to B-flat (70). As this glissando is spread over 7 seconds, the notes repeated on the piano on F-sharp must be inserted in this proportion.
The following measures (on the E flat/B flat fifth) are a quotation from the end of the second interlude (see measures 255 to 258). During the ensuing rise, try to maintain a certain rhythmic continuity between the slow tempo at the beginning and the extreme speed of the final trill.
Evt 79:
Entry of the synthesis in unison with the piano trill notes (A/Bb).
Evt 80: Coda
We are now in the coda of the sonata (and of the entire work), which will unfold in two parts. The first part is a final evocation of theme 1. Here, the succession of rapid, regular notes is doubled in an even faster tempo. But above all, the piano goes through a whole system of leslie and transpositions that multiply its figures in the high register.
Evt 81:
Synthesized glissando leading to a first spectral harmony. The irregular nature of the repetitions of this sound is due to a random variation in intensity for each new occurrence.
Evt 82:
Piano sound with attack and resonance in time stretching (digital time stretching). The sound perforation and granulation effect is due to the stretching (approximately 60 times longer) of an aggressive attack on a high note sustained by the pedal.
Evt 83:
Second spectral harmony.
Evt 84:
Piano sound with attack and resonance in time stretching and third spectral harmony.
Evt 85:
Synthesized glissando.
Evt 86:
Glissando of the second spectral harmony towards a unison (E-flat). The discontinuous and irregular intensities become regular here.
Evt 87:
The intensities become irregular again. The piano joins the electronics in a rise towards the high register (reminiscent of Beethoven’s Opus 111 No. 2).
Evt 89:
Second part of the coda. The second theme makes a final appearance here, exactly under the same conditions as when it appeared in event 36.
Evt 90:
Long fade out of the high “E flat” repeated with irregular intensities.
Evt 91:
Piano sound with attack and resonance in time stretching on a high B flat.
Evt 92:
Piano sound with attack and resonance in time stretching on an F sharp.
Evt 93:
Stop of theme 2. The command “1smer walk 0” is the reason for this. Theme 2 only appeared according to a probability linked to the unfolding of a Markovian path (theme 1). When this unfolding is stopped, as is the case here with this instruction, there is no more random selection, so there is no more possibility of hearing theme 2.
Evt 94:
Last occurrence of the minor third of theme 2, immersed in a long reverberation.