This piece is for me a spectral harmony study, as well as an attempt to push the extension in time of a limited material to its limit. The main advantages of using audio-scores for this performance was to place performers at a considerable distance from one another, and to allow the string quartet to play in just intonation very accurately.
7.3.1 Harmony
The piano’s harmonic language is quite free and intuitive, while the string quartet almost exclusively uses the harmonic series of a low F.
Figure 58: the 17 first partials of the harmonic series of a low F
In order to obtain a greater variety of combinations, I allowed few transformations to this theoretical model. More precisely partial No11 (low B) and No13 (low D), have often been transposed an octave lower. These two partials present quartertones: No 11 is 49 cents lower than tempered B, so exactly a quartertone for the human perception. No 13 is 59 cents lower than D, so slightly closer to D flat than D natural, but still differs clearly from the equal temperament. An octave lower, these two notes get more weight, and contribute to the ‘micro-tonal consonance’ I was looking for. The idea of transposing some partials down an octave actually comes from Gerard Griseys’s Partiels (1975), where similar types of transformations allow a gradual progression towards inharmonicity.
The partial number equals the multiple of the fundamental frequency (a low F), and lowering a note by an octave means dividing its frequency by two, which is why partials 11 or 13 heard in the register of middle C are notated with ratio 11/2 or 13/2 in the following example. This extract displays the strings part of the beginning of the piece. Above each note, the corresponding partial number is indicated in a circle.
Figure 59: Piano Quintet, score extract (1)
In the first four bars, the octave between violin and viola amplifies the 13th harmonic. It exemplifies the attempt to achieve microtonal consonant harmony. For me the main difficulty of working with harmonic spectra is to find ways of avoiding a dominant seventh chord impression. I found out that avoiding the major third can help (A, 5th or 10th harmonic), which is why the note A rarely appears as a sustained note in this extract (although it is still present in bars 5, 6 and 8). The presence of this note in many cases makes the chord identifiable in terms of classical harmony: it becomes an ‘accord classé’. With this same ‘dominant seventh’ concern in mind, I often grounded chords on a C (3rd harmonic) rather than on the fundamental (F) for example in bars 1-4 and 12-15 of the same extract.
Nearly the entire piece is grounded on a low F, though in few sections, when the piano has a more prominent role, the string quartet freezes on a breathe-like gesture. The fundamental needs to change in these passages, in order to obtain a more contrasting chord, like in the second and fourth bar of the extract below, where the fundamental of the strings’ chord alternates between F sharp and F natural.
Figure 60: Piano Quintet, score extract (2)
Bars 33-37 are displayed above, though the alternating gesture goes on for twenty bars. In an interview with Charles Shere, (Shere, 1967) Feldman, while discussing one of his pieces for three pianos, associates this kind of repetitive alternation with the classical cadential gesture V-I-V-I. This gesture appears four times in the piece: bars 25-45, 128-146, 332-336, 422-427. It occupies a substantial amount of time in its first two appearances (around 20 bars), but it is only briefly evoked when it returns towards the end, only as reminiscence.
Unlike in the Trio, we managed to have many rehearsals with the string quartet, and I was able to hear an improvement in each rehearsal, especially in terms of stabilisation of intonation. During the first run-throughs, the string players constantly adjusted to the pitch sent to their ear, which resulted in very small glissandi throughout the piece. After the third rehearsal, the players had already memorised most of the finger positions of microtones, and consequently could find their pitch straightaway.
7.3.2 Placement of the performers and sonic spatialisation
Figure 61: Piano Quintet, placement of the performers and technical setup
Again in this piece, a computer conducts the five performers. It sends individual pitches through a soundcard to each of the musicians independently, with a common click track for all. The movement of sound in space is very important here. The following is an explanation of how I discovered this parameter in a musicological article, which will show how the diagrams employed in this paper have inspired a ‘choreography of sound’ used in the string quartet, though in a very different musical context.
A book of collected writings about the Portuguese composer Emmanuel Nuñes has been of central importance for my understanding of spatialisation during the first years of my composition studies. This book contained an extensive analysis of the piece Lichtung I, for ensemble and electronics (Nuñes, 1988-91), which displayed very detailed diagrams representing the itinerary of the sound processed in the electronics. Each of the eight loudspeakers was assigned a number. These itineraries, (or trajectories of the sound) were described as a suite of numbers, and represented as arrows on a diagram. (cf thesis)
The trajectory above represents a sound beginning on loudspeaker 0, travelling through different stations across the room and finishing on loudspeaker 1. During the realisation of the piece Lichtung I, it would have been described as the list (0 3 5 6 1) by the composer and his co-workers electronic music designers (RIM: Réalisateurs en Informatique Musicale) at IRCAM.
Although I never incorporated this level of complexity in my music, I was influenced by these notions of trajectory, and tried them on various occasions with both electronics and instruments. I will now show how the movement of sound occurs in my Piano Quintet. The performers primarily play one after the other rather than being homorhythmic. This allows the circulation, as exemplified in the three passages extracted from the strings parts below: (cf thesis)
7.3.3 Rhythmic organisation and tempo modulations
The rhythmic structure of this piece often deals with slightly different periodicities, which is a material I have often worked with. In the opening of the piece for instance (figure 50), Violin I and Cello are slightly slower than Violin II and Viola. In these cases, an effort was made to find the simplest placement of bars and beats possible, so that the players can just stay in phase with the general tempo. The piece was first composed assembling sustained string samples on a sequencer , assigning each sample to a certain pitch, and the rhythmic notation came afterwards, with the placement of bars and beats, using metronome marks between 33 and 75. I found out that in extremely slow tempi (33-40), the click track allowed for a great flexibility: I was able to move each impulse with a great amount of rubato without disturbing the understanding of meter, and this allowed for a great simplification of the rhythmic notation. The tempo changes were made intuitively, so there is no specific ratio between two consecutive tempi, as can be found for instance in the Renaissance use of proportions or in Elliot Carter’s ‘metric modulation’. Most passages were written independently and then ‘concatenated’ in seven short movements; a tempo change within one movement often reflects a change in the musical material, thus revealing how different passages have been assembled.
Jonathan Bell 
This piece is for me a spectral harmony study, as well as an attempt to push the extension in time of a limited material to its limit. The main advantages of using audio-scores for this performance was to place performers at a considerable distance from one another, and to allow the string quartet to play in just intonation very accurately.
7.3.1 Harmony
The piano’s harmonic language is quite free and intuitive, while the string quartet almost exclusively uses the harmonic series of a low F.
Figure 58: the 17 first partials of the harmonic series of a low F
In order to obtain a greater variety of combinations, I allowed few transformations to this theoretical model. More precisely partial No11 (low B) and No13 (low D), have often been transposed an octave lower. These two partials present quartertones: No 11 is 49 cents lower than tempered B, so exactly a quartertone for the human perception. No 13 is 59 cents lower than D, so slightly closer to D flat than D natural, but still differs clearly from the equal temperament. An octave lower, these two notes get more weight, and contribute to the ‘micro-tonal consonance’ I was looking for. The idea of transposing some partials down an octave actually comes from Gerard Griseys’s Partiels (1975), where similar types of transformations allow a gradual progression towards inharmonicity.
The partial number equals the multiple of the fundamental frequency (a low F), and lowering a note by an octave means dividing its frequency by two, which is why partials 11 or 13 heard in the register of middle C are notated with ratio 11/2 or 13/2 in the following example. This extract displays the strings part of the beginning of the piece. Above each note, the corresponding partial number is indicated in a circle.
Figure 59: Piano Quintet, score extract (1)
In the first four bars, the octave between violin and viola amplifies the 13th harmonic. It exemplifies the attempt to achieve microtonal consonant harmony. For me the main difficulty of working with harmonic spectra is to find ways of avoiding a dominant seventh chord impression. I found out that avoiding the major third can help (A, 5th or 10th harmonic), which is why the note A rarely appears as a sustained note in this extract (although it is still present in bars 5, 6 and 8). The presence of this note in many cases makes the chord identifiable in terms of classical harmony: it becomes an ‘accord classé’. With this same ‘dominant seventh’ concern in mind, I often grounded chords on a C (3rd harmonic) rather than on the fundamental (F) for example in bars 1-4 and 12-15 of the same extract.
Nearly the entire piece is grounded on a low F, though in few sections, when the piano has a more prominent role, the string quartet freezes on a breathe-like gesture. The fundamental needs to change in these passages, in order to obtain a more contrasting chord, like in the second and fourth bar of the extract below, where the fundamental of the strings’ chord alternates between F sharp and F natural.
Figure 60: Piano Quintet, score extract (2)
Bars 33-37 are displayed above, though the alternating gesture goes on for twenty bars. In an interview with Charles Shere, (Shere, 1967) Feldman, while discussing one of his pieces for three pianos, associates this kind of repetitive alternation with the classical cadential gesture V-I-V-I. This gesture appears four times in the piece: bars 25-45, 128-146, 332-336, 422-427. It occupies a substantial amount of time in its first two appearances (around 20 bars), but it is only briefly evoked when it returns towards the end, only as reminiscence.
Unlike in the Trio, we managed to have many rehearsals with the string quartet, and I was able to hear an improvement in each rehearsal, especially in terms of stabilisation of intonation. During the first run-throughs, the string players constantly adjusted to the pitch sent to their ear, which resulted in very small glissandi throughout the piece. After the third rehearsal, the players had already memorised most of the finger positions of microtones, and consequently could find their pitch straightaway.
7.3.2 Placement of the performers and sonic spatialisation
Figure 61: Piano Quintet, placement of the performers and technical setup
Again in this piece, a computer conducts the five performers. It sends individual pitches through a soundcard to each of the musicians independently, with a common click track for all. The movement of sound in space is very important here. The following is an explanation of how I discovered this parameter in a musicological article, which will show how the diagrams employed in this paper have inspired a ‘choreography of sound’ used in the string quartet, though in a very different musical context.
A book of collected writings about the Portuguese composer Emmanuel Nuñes has been of central importance for my understanding of spatialisation during the first years of my composition studies. This book contained an extensive analysis of the piece Lichtung I, for ensemble and electronics (Nuñes, 1988-91), which displayed very detailed diagrams representing the itinerary of the sound processed in the electronics. Each of the eight loudspeakers was assigned a number. These itineraries, (or trajectories of the sound) were described as a suite of numbers, and represented as arrows on a diagram. (cf thesis)
The trajectory above represents a sound beginning on loudspeaker 0, travelling through different stations across the room and finishing on loudspeaker 1. During the realisation of the piece Lichtung I, it would have been described as the list (0 3 5 6 1) by the composer and his co-workers electronic music designers (RIM: Réalisateurs en Informatique Musicale) at IRCAM.
Although I never incorporated this level of complexity in my music, I was influenced by these notions of trajectory, and tried them on various occasions with both electronics and instruments. I will now show how the movement of sound occurs in my Piano Quintet. The performers primarily play one after the other rather than being homorhythmic. This allows the circulation, as exemplified in the three passages extracted from the strings parts below: (cf thesis)
7.3.3 Rhythmic organisation and tempo modulations
The rhythmic structure of this piece often deals with slightly different periodicities, which is a material I have often worked with. In the opening of the piece for instance (figure 50), Violin I and Cello are slightly slower than Violin II and Viola. In these cases, an effort was made to find the simplest placement of bars and beats possible, so that the players can just stay in phase with the general tempo. The piece was first composed assembling sustained string samples on a sequencer , assigning each sample to a certain pitch, and the rhythmic notation came afterwards, with the placement of bars and beats, using metronome marks between 33 and 75. I found out that in extremely slow tempi (33-40), the click track allowed for a great flexibility: I was able to move each impulse with a great amount of rubato without disturbing the understanding of meter, and this allowed for a great simplification of the rhythmic notation. The tempo changes were made intuitively, so there is no specific ratio between two consecutive tempi, as can be found for instance in the Renaissance use of proportions or in Elliot Carter’s ‘metric modulation’. Most passages were written independently and then ‘concatenated’ in seven short movements; a tempo change within one movement often reflects a change in the musical material, thus revealing how different passages have been assembled.
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