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The Sequencial Drum

Max V. Mathews

Rapport Ircam 27/80, 1980
Copyright © Ircam - Centre Georges-Pompidou 1998

I Introduction

The sequential drum is a device to demonstrate a new method to play "intelligent instruments" such as a computer controlled synthesizer. The method demonstrates a different relationship between the musician, the score, and the instrument.

As shown in Fig.1, with traditional instruments, all the information in the score pass trough the musician who communicates the information to the instrument by physical gestures. The musician has absolute and fast control over the sound, but he must be able to read the score rapidly and make complex gestures quickly and accurately. Some scores make great demands on his virtuosity.

A second possible relationship between score, musician and instrument is shown in Fig. 2. This relationship is used by pure digital synthesis programs such as MUSIC V and MUSIC 10. The musician first prepares the score in a machine readable form. It is then read and performed by the instrument without further intervention by the musician. No real time demands are made on the musician. He can take as much time as he wants to prepare or revise the score. But he cannot perform the score in a way that resembles traditional instrumental performance.

A third relationship is shown in Fig. 3. Here, the score and the musician both send information directly to the instrument. The score is a sequence of partial descriptions of musical events. In general the sequence is ordered by time. The information not contained in the score is supplied by the musician in real time during the performance. In general, the aspects of the performance which are to be interpreted are supplied by the musician. The aspects which are not subject to interpretation are supplied by the score.

In many cases, the timing (tempo, attacks, etc... ) of the music is one of the most important quantities to be interpreted. If so, the events in the score can specify sounds which are concentrated in time or which start at definite times. The musician can "trigger" the starting times of these events.

II Sequential drum

Figure 4 is a schematic diagram of the sequential drum. The drum itself is a rectangular surface which is hit with the hand or a stick. Hitting the surface does not produce the music directly. Instead four electrical signals are sent to the computer-synthesizer. The music is produced by the synthesizer using these signals along with a score which is in the computer memory. The four signals are :

A trigger pulse occurring when the drum is hit.
An amplitude signal which is proportional to how hard the drum is hit.
and 4. X and Y signals which encode the position of the stroke.

The signals can be used in any desired way by the computer-synthesizer. Typically the trigger is used to start the next event in the score. The amplitude signal is used to control the loudness of the event. X and Y signals are used to control the timbre. However many interesting alternative uses of the signals are appearant. X and Y might control the physical location of the sound (assuming the synthesizer has multichannel outputs). Interesting accent patterns can be performed by using X or Y to control loudness. If an event is a group of notes rather than a single note, then one signal can control the tempo at which the group is played.

III Monophonic pitch sequences

For much traditional music it is useful to make the score be the pitches of the sequence of notes to be played, each event being the pitch of one note. Each time the performer strikes the drum, he automatically gets the next pitch in the sequence. Thus the computer plays the melodic line automatically. The performer controls all the other parameters - the tempos and times of occurrence ot the notes, the accents and dynamics, and the timber.

Why is this mode of control interesting ? Because, in traditional music, the performer has almost no freedom in interpreting pitch. If he changes the pitch from what the composer has written, it is almost always considered to be a performance error. By contrast, he has much greater freedom in choosing tempos, making slight changes in attack times for phrasing, making accents and choosing loudnesses.

Figure 5 shows a fragment of a monophonic score taken from a Bach violin sonata. The musical staff and the corresponding list of pitch events are shown.

The events are written in the 4 C E D language developed by Curtis Abbott to run on the PDP 11/34 with the 4C sound synthesizer at IRCAM. This language is very well adapted to the sequential drum. The rest of the 4 C E D instructions needed to make the sounds are shown on Fig. 6

The four signals from the drum are connected to replace the first four potentiometers on the Cockerell Box (trigger Pot 1, amplitude Pot 2, X Pot 3, Y Pot 4). To adapt to the drum, Abbott has made a modification to the 4 C E D program so that a trigger signal (the Z trigger) is generated by Pot 1 increasing to above a threshold.

Three identical instruments are used to generate the single voice. Successive notes are rotated amongst the three instruments so that the "tails" of the decays on a note can overlap with the beginnings of the next two notes.

In addition to the trigger signal, the amplitude signal from the drum is used to control the loudness of the sound. The X and Y signals are not used.

The performer should have freedom to ornament the pitch, for example to use vibrato. The drum is probably not an appropriate control device for vibrato, but other inputs such as knobs or footpedals can also be attached to the computer to control these more continuous quantities.

IV Polyphonic sequences

There is no problem in generalizing the score to encode a sequence of polyphonic events. Almost any traditional score with any number of voices can be mapped onto a single time line which gives the time order of events in the score. An example of a more complex Bach sonata is shown in Fig. 7 and 8. In this interpretation the first ten chords are encoded as single events that are triggered by a single drum stroke. In the third measure, the C sharp and sixteenth note G are triggered together by a single stroke. The C sharp sustains and the next three sixteenth notes are triggered by the next three strokes.

V Sequencial piano and multiple input devices

One can easily generalize the concepts of the sequential drum to multiple drums or to other percusive devices. Multiple drums might be played by a single player or by several players.

A sequential piano is an intriguing idea. The piano would have only ten keys, one for each finger of the player. Conceptually the task of the computer can be thought of as moving the right key from the 88 normal piano keys and placing it under the finger of the performer at the right instant so that when he depresses his finger, the right note will be played.

VI Physical piano and multiple input devices

Many ways exist to measure the four signals generated by the drum. We have chosen a very straightforward method in which the strength of the stroke is measured by the size of the signal from contact microphones and the X and Y position information is measured by grounding wires from grids of wires which run in the X and Y directions. Figure 9 shows a sketch of the mechanical construction of the drum surface. It consists of six layers :

The drum head, made of plastic coated fabric.
A grid of 29 X sensing wires which run perpendicular to the x axis at a spacing of 3/4 inch. Hence the spacial resolution is 3/4 inch.
Several x grounding wires parallel to the X axis. When the drum is hit, one of the X sensing wires touches an X grounding wire, thus setting an output voltage level.
A layer of insulating cloth.
A grid of 17 Y sensing wires which run perpendicular to the Y axis at a spacing of 3/4 inch. Hence the Y resolution is 3/4 inch.
A 1/4 inch thick aluminium backplate which serves as mechanical support and as the Y sensor grounding plate. The contact microphones are attached to the backplate.

Figure 10 shows the resister network attached to the X and Y sensing wires. The sizes of the resisters are chosen so that the X and Y sensor output voltages are linear functions of the X and Y positions of the stroke.

The right end of the X network is grounded so the steady state X voltage with no stroke is one unit more positive than the voltage when the right hand wire is grounded (approximately 7,5 V).

The lower end of the Y network is ungrounded. Thus if no Y wire is grounded the Y sensor output is + 15 V. The large voltage step (15 V to 7,5 V or less) produced by any drum stroke is used to generate the event trigger.

VII Description of circuit

The electronics are mounted on two cards underneath the drum. One of the cards contains a

15 volt power supply and a + 5 V regulator. The other card contains the electronics.

Figure 11 shows a schematic of the electronics.

It operates as follows :

In the upper chain of electronics, signals from two contact microphones are processed. The signals are amplified and summed by amplifiers 1 and 2. The summed signal is half-wave rectified by dioded DI. The resulting signal is integrated by R₁₁ and C₁. The voltage on C₁ is amplified and sampled at d₂ time by switch S₁₂₃. The output is held on C₇ and buffered by amplifier 4' to create the AMP output. The value of AMP goes from 0 to + 5 V.
The X sensor and Y sensor signals are processed in similar ways by the circuitry associated with amplifiers 3 and 3'. At d₄ time, the voltage on holding capacitors C₁₁ and _C12 is set approximately to 10 V by switches S_{9 10 11} and S_{14 15 16}.
The 10 volts is greater than the maximum signal which can be produced by the X or Y sensors.
After d₄ time, the holding capacitors C₁₁ and C₁₂ will discharge and hold at the minimum voltage occurring on the sensor lines. Thus the holding capacitors will measure the voltage obtained when one of the sensor wires is grounded. The X and Y output voltages range from 0 to 5 volts.
Triggering is done by chain of one shots D 0 through D 4 and associated circuitry. The initial trigger is gotten from the transition in the Y sensor from + 15 V to some value less than 7,5 V. The Y sensor voltage is sharpened by amplifier 5 and formed into an appropriate trigger by amplifier 4 and associated circuitry. A timing diagram of the trigger pulses is shown :
1. D₀ determines the minimum retriggering interval. This is the minimum interval between successive strokes.
2. D₁ is trigged on the leading edge of D₀ and provides a time delay during which the microphone signal is integrated.
3. D₂ is triggered on the trailing edge of D₁ and samples the amplitude signal.
4. D₃ is triggered on the trailing edge of D₂ and is amplified to produce the note trigger. The duration of D₃ depends on the computer circuit which is to be triggered. The present Cockerell Box requires a 50 ms trigger for reliable operation.
5. D₄ is triggered by the leading edge of D₀ and is used to reset the X and Y signals. D₄ must be completed before the X and Y sensors have ungrounded in order to read correctly.