David A. Jaffe (2007, revised 2017)
ABSTRACT: This paper describes the techniques, mappings and algorithms used in the author’s composition “Underground Economy – frameworks for improvisation,” written for the Durán/Schloss/Mitri trio in 2006. A video of the work can be found at www.davidajaffe.com/music/underground-economy
Introduction
The goal of the work “Underground Economy” was to create a structured improvisation, in which all three instruments: the piano, the violin and the RadioDrum, are sending data to the computer. The computer then combines these inputs into an electronic audio response. The title of the piece stems from the notion of passing information “under the table” to the computer.
The piano is fitted with a physical sensor (Moog “Piano Bar”) that reports the pitches and velocities of the pianist via MIDI. The violin has a simple contact mike that is used for amplitude and pitch tracking. The RadioDrum features two sticks that act as radio transmitters and a drum pad that serves as a set of four antennas. The software uses the relative strength of the antennas to derive continuous X, Y and Z information for each stick independently, as well as to detect surface strikes.
From a compositional standpoint, perhaps the most interesting aspect of the piece was the challenge of writing a fully-improvised piece that has a distinct composer-specified identity, yet leaves a great deal to the musical personalities of the performers. This goal was accomplished by a combination of custom software that describes a series of interactive “schemes” and a score that dictates general directions to the players, such as style, range, dynamics and key center. Thus, the music has an “economy of specification,” another meaning of the title.
This paper describes some of the more novel interactive scenarios that were unique to this work. In addition, the piece builds on Radio Drum solo idioms developed using the Max software environment by Andrew Schloss in his continuing work as a RadioDrum soloist (Schloss, 1990).
Timbre Rhythms
The simplest interactive scheme, but one that is surprisingly effective, has the RadioDrum performer controlling which of a set of unison doublings is applied to the piano part. The RadioDrum, with the software doing rapid continuous polling of the stick positions, can perform cross rhythms (or “timbre rhythms”) with respect to the rhythm of the piano. This effect is first applied to the piano as a whole, then split into two separate ranges, each controlled by one hand of the RadioDrum performer. Later in the piece, a similar technique is applied, with the exception that the RadioDrum is trigging samples by striking the surface. Thus the doublings are not simultaneous, but rather are performed by the RadioDrummer himself. This allows interesting cross-rhythmic echoes of what the pianist has just played.
Passing the Baton
Another basic but effective mapping has the pianist and RadioDrum performer alternating fast, scale-like material. The sampled sound automatically plays when the pianist plays two notes followed by a rest at the same tempo as the pianist used. The sampled sound uses a timbre determined by the RadioDrum by continuous polling of the stick positions. It repeats the last 32 notes that the pianist has played, either backwards or forwards, with the direction settable by the RadioDrum performer. The X location of the stick determines the phase offset of the cycling sequence. As a refinement, the pianist may interject individual notes or slow material without interrupting the sampled sound, providing that no two notes are within 250 milliseconds. This scheme creates an effect similar to the rapid alternation of orchestral instruments in Richard Strauss’ Rosenkavalier.
A different type of inverse relationship is produced in a duo between the violin and the RadioDrum. Here an envelope follower samples the violin amplitude, which plays intense tremolo, unisons and glissandi from unisons to semitones and quarter-tones. The RadioDrum performs a tremolo whose amplitude is the inverse of that of the violin. Thus the violin controls the “crossfade” between the acoustic violin and the electronic sampled sound. In addition, the RadioDrum controls the pitch of two independent timbres (one for each stick) and can do micro-tonal pitch bend using the Z dimension of the instrument.
Free Canons, Converging and Diverging
While the canon is one of the most constrained musical constructs, its use in “Underground Economy” has a sense of freedom and flexibility. A canonic effect is created in which the pianist performs a canon melody, which the RadioDrum performer can then imitate an octave above, two octaves above, and three octaves above. This is accomplished by mapping the RadioDrum Y axis to canonic instance. Each strike of the Drum causes the next note in the canon to be played. By specifying in the score the start and end notes of the canon, and insisting that the canon start on the lowest note of the melody and end on the highest note of the melody, a “divergence/convergence” effect is created. For contrast, the piano plays staccato in the low register, while the sampled sound uses a sustained harp timbre. The effect is a free texture that nonetheless seems to be heading in a general direction, like a flock of birds. This approach was explored in a somewhat different manner in the second movement of “The Seven Wonders of the Ancient World” (Jaffe, 1994) and before that in “Silicon Valley Breakdown” (Jaffe, 1982). It has also been explored in instrumental contexts in a number of pieces such as “Wanting the Impossible” (Jaffe, 1985) and was first suggested to the composer by Henry Brant.
Conversely, the violin and RadioDrum perform a canon in which the violin is sustained, while the sampled sound is a staccato xylophone. In this section, the RadioDrum part is in the upper register and is quite dense. This is accomplished by having the violin perform its canonic melody mostly via glissandi and having the pitch of the violin sampled at 200 millisecond intervals. Pitch bend is then used to get micro-tonal fluctuations in pitch, including vibrato. Finally, the piano/harp and violin/xylophone canons are performed simultaneously (in reverse direction), producing a complex but comprehensible divergence/convergence result. (Note: due to difficulties with the violin pitch detection, for the premiere, a pre-recorded violin sequence was used; it is hoped that this restriction will be removed for future performances.)
Another form of convergence/divergence is used in a brief section in which all instruments play tremolo on the same sequence of pitches, separated by free material. The Y axis of the RadioDrum is mapped to “divergence.” As the Y values are decreased, there is a random divergence from the pitch specified in the score.
15th century jazz
Automatic generation of accompanying material is used in a pseudo-Afro- Cuban section as follows: The violin plays a series of pizzicato notes on the G string. These are doubled an octave below (not necessarily the same pitches) by string bass pizzicato. Then, when the other instruments enter, the timing and amplitude of the violin is used as a repeating sequence, while the pitch material of the violin serves as a set that is traversed using an approximation to a 1/f noise function. The effect is of an improvisational iso-rhythmic bass line that recalls 15 th century medieval music. A similar technique generates a high xylophone/piccolo solo.
Feedback delay networks, string physical models, timpani and gongs (oh my!)
Perhaps the most complex mapping builds on earlier work exploiting the similarities between string physical models and reverberation algorithms. This was originally done in works such as Silicon Valley Breakdown (1982), where a bank of Karplus/Strong/Jaffe/Smith waveguide-based pluck strings are switched dynamically between string identity and reverberation identity, and strings were cross-coupled to produce sympathetic vibrations. Both of these techniques (and many others) are described by Jaffe/Smith, 1983.
In Underground Economy, this process is taken further by substituting a “feedback delay network” (FDN) for the bank of strings. The network is similar to that proposed by Stautner and Puckette in 1982, which in turn can be seen as a generalization of the Michael Gerzon reverberation algorithm, published in the journal Studio Sound in 1971.
The key element in these designs is the use of a unitary matrix for cross-coupling. The innovations in the Underground Economy implementation versus these earlier versions include the shortening of delay lengths to the range of audible pitch-periods, the RadioDrum control context, and the limiting method.
The network used consists of four delays, conceptually in a “square”, with coupling between neighboring delays. Each delay is augmented with a low-pass filter and an optional passive non-linear element (VanDuyne/Pierce, 1997). This network is then used with both percussive and sustained excitation samples.
The RadioDrum performer has control over a variety of parameters, including the trigger of the excitation, which is performed by the software sampler, as well as the length of the four delay lines (using the four surface dimensions of the Drum), the gain of the coupling, the pitch bend of the excitation, the low-pass filter coefficients, etc. The excitation was chosen as a set of timpani samples. Since an actual timpani is quite reverberant and supports glissandi, the effects of the simulation bare a striking resemblance to an actual timpani. Note that there are two ways that the RadioDrum performer can modify pitch: by modifying the excitation and by modifying the resonance frequencies (delay lengths). In addition, both can be modified at the same time, leading to a variety of unusual effects. In addition to the timpani sounds, a variety of gongs and percussion instrument samples may be enabled via a foot pedal. In addition, in transition sections, mallet percussion samples are used. These produce strong resonances when their pitches coincide with the poles of the network.
The signals modifying the delay length are low-pass filtered at 5 Hz. This allows the RadioDrum performer to execute vibrato-like motions, while shielding the feedback delay network from unnecessary jitter noise.
Since modifying the delay lengths is such a pronounced effect, foot-pedals are used to enable/disable the effect. When the pedal is released, the delay lines retain the values they had at the point of release. This allows the RadioDrum performer to find interesting delay line values and freeze the network at these values, then improvise with these values for an extended period. It also helps with the inherent limitation of the RadioDrum Z values, in that X and Y do not remain constant as Z varies, thus each strike of the RadioDrum tends to produce a glissando when the delay variation is enabled.
Yet another mode of the mapping, which is triggered by a high-velocity pedal (“stomp”), allows setting all four delay lines to the same value with a single stick and performing a glissando of these values using a single dimension of the RadioDrum. This allows a much more correlated and strongly-pitched effect and frees up the other three surface dimensions for other controls, such as excitation pitch bend.
An effective mapping allows the RadioDrum performer to control the wet/dry mix, i.e. the output of the network versus its input. This is used in the coda of the piece. When the performer has one stick in the full wet position and the other in the full dry position, an interesting alternation occurs, as if a percussion instrument were being struck alternately with that same instrument striking a string.
A novel technique for avoiding overflow distortion was employed: A limiter detector is placed within the network, but the limiting value is applied not within the loop, but directly to the input. Thus, the input is “ducked” when the network starts to saturate. This is precisely what is needed for the RadioDrum performance situation, where the player is modifying both excitation and resonance pitch in complex ways and can’t necessarily predict when large resonances will suddenly occur. The limiter used is done in the dB space, derived from that used in Analog Devices’ VisualAudio package (Jaffe et. al. 2005).
Note that the delay lines use linear interpolation for fractional delays, which tends to introduce some additional loop loss, except at DC and when the delay happens to be an integer. This is a limitation of Max MSP’s delay (TapRead/TapWrite) module. An alternative would be to use a technique such as the all-pass crossfade method described in VanDuyne/Jaffe/Scandalis/Stilson, 1996 (patent US5742532.)
Another extension that has not yet been fully exploited, but would be a logical extension to this method is to allow the RadioDrum performer to dynamically control the degree of coupling between the delays, and to generalize to a network in which each delay feeds all others, as described by Jot (1991). This approach was suggested by Sean Costello (personal communications.) As long as the unitary nature of the matrix is preserved, the network will remain well-behaved. Of course, additions such as this run up against the challenge of choosing what not to control, as the RadioDrum has only 4 truly independent dimensions (the addition of Z causes degredation of the other dimensions.)
Summary
“Underground Economy” offered the unique opportunity to write interactive computer music for accomplished improvisers working in a distinctive style. The melding of experimental ensemble interactions with the strong musical quality of Afro-Cuban jazz improvisation proved a fruitful combination.