The digital Trautonium

Jörg Spix
Bloherfelder Str. 72
D-26129 Oldenburg
Germany

e-mail:

Joerg.Spix@arbi.informatik.uni-oldenburg.de

Abstract

The digital Trautonium is the first replica of the Mixture-Trautonium in digital technique, from the whole range of data acquisition at the performance interface up to sound synthesis. Some smaller modifications were made due to the current technology and also some extensions to the instrument which seemed to be suitable. The instrument is not fixed in the actual version but should be seen as a starting point for future enhancements and experiments.

Introduction

The digital Trautonium was build after the original instrument, invented by Friedrich Trautwein in the thirties in Berlin, Germany, with enhancements made by Oskar Sala in the fifties which led to the well known Mixture-Trautonium.

Three variants of the instrument are planned:

  1. An "expensive" realtime version with the simulation of the original sound synthesis of the Trautonium on an IRCAM Signal Processing Workstation,

  2. a "cheap" realtime version, using a commercial MIDI synthesizer, with the drawback of lacking some aspects of the original sound,

  3. a Csound program for the realization of the original sound synthesis from standard MIDI files, which could be recorded during a performance with one of the realtime-versions.

From these three variants, the two realtime versions have been completed.

First the structure of the classical instruments will be shown, then the structure, user interface and sound synthesis of the digital instrument will be explained. The ISPW version will be explained first, followed by a discussion of the requirements for the MIDI synthesizer. At least, known results will be presented and possible enhancements will be discussed.

The classical Trautonium

The classical Trautonium in the form of the Telefunken-Trautonium has one manual, one pedal and some switches and dials.
The manual of the Trautonium was made after the "Bandmanual" of the Hellertion, invented by Hellberger and Lertes, but used a resistive wire resp. a nonconductive string covered by a resistive wire. The point of contact of the string with the contact strip below determines the voltage resp. the resistance of the right part of the string controlling the frequency of a sawtooth-like generator about a range of three octaves.
The manual is mounted movable. So the pressure could be converted to electrical signals by a carbon microphone mounted below the manual to control the volume of the tone.
The signal of the frequency generator was fed into two parallel resonant filters, realized by two electrical resonant circuits. The footpedal controlled the volume ratio of the output of the two filters. The resulting signal was weighted by the pressure sensor and further fed into a power amplifier connected to a speaker.

In the Mixture-Trautonium two manuals and two pedals exist. Each of the manuals, which are approximately 70 cm (28 inches) long having a range of four octaves, controls four tone generators, whose frequencies will be subharmonics, a quotient of the master frequency and a natural whole number, of the controlling frequency of the master oscillator. The selection of the subharmonics for the four oscillators is made by rotary switches. The pressure sensor is a liquid resistor.
The pedals of the Mixture-Trautonium are completed by two switches which are controlled by lateral movement selecting a different set of subharmonics. The volume ratio between the oscillators is fixed for each of the three lateral pedal positions.
The sum of the subharmonic signals will be feed to the two parallel resonant filters.

The structure of the digital Trautonium

The digital Trautonium consists of the manuals, the pedals and a user interface, forming, together with an Atari ST computer and a multichannel 12 bit a/d-converter, the Trautonium controller. The controller measures the continuous values and the switch states and puts these values into the MIDI protocol which will be send out of the MIDI interface. The conversion of the finger pressure is made by a pressure sensor strip, placed between the manual base and the flexible contact strip for the string, at the whole length of the manual. The string is made of a single nylon cord covered by a preoxyded resistive wire. At the surface of the resulting string the oxyd is carefully removed to be able to contact the string without shortening the spiral coverage.


fig.1: Crosscut of the manual

The analog voltages produced by the string position, the manual pressure and the pedal angle are mesured by an eight channel 12 bit a/d-converter connected to the ROM port of the Atari ST and then the data is transmitted as pitch bend, volume controller and controller no. 31 in 14 bit resolution. The pedal switches are connected to the joystick port of the Atart ST. The two alpha-dials for the selection of the parameter and the modification of the value of this parameter as well as the two locking switches above the wheels are connected to the mouse port of the Atari. The three remaining switches of the user interface box, used for "next preset", "previous preset" and "store parameters into the actual preset" are connected to three unused data lines at the address of the a/d-converter.


fig.2: The user interface

The MIDI data produced by the MIDI controller is received by the program MAX on a Apple Macintosh computer whose task is the management of parameters (values of the subharmonics for each pedal position, filter settings) and presets. Depending on the version the program will send the actual data of the manuals, pedals, subharmonics and filters to the sound generator. The MAX patches differ a bit for each of the two versions.


fig.3: The structure of the digital Trautonium

The sound synthesis in the ISPW uses four freely running oscillators, which are synchronized only when one or more of the subharmonics change. They should be synchronized also when the string is pressed down to the contact strip, but this is currently not implemented. This very simple form of synchronization works well because of the high phase stability of oscillators in the ISPW (20 minutes without perceivable aberration). The waveform of the oscillators is shaped after the charging curve of a capacitor. The resonant filters (ISPW wahwah-object) are digital filters with feedback (two pole IIR filters), vibrating on their resonant frequency after being stimulated by a sharp edge in the signal. The computational load of the NeXT-ISPW is 50% of the first processor (75% with a reverb patch added). The second processor is not used.


fig.4: Block diagram of the sound synthesis

Special requirements will be set on the synthesizer, which are satisfied by very few commercially available equipment. The synthesizer should have a pitch bend range of at least +/- two octaves (three octaves or more preferred) and the resolution in this pitchbend range should be smaller than one cent. Combinations (layering) of multiple sounds should be possible with four or more sounds with a transposition range of four and a half octaves minimum and a resolution of one cent maximum. If layering is not implemented, it should be possible to control each oscillator on a seperate MIDI channel. Because of the serial transmission of MIDI messages it would definately not be possible to synchronize the oscillators.
It is further necessary to control the volume of each of the MIDI channels seperately with a resolution of at least 10 bit if possible.
For the use of subharmonics and two manuals, the synthesizer should have the MIDI multimode, being able to receive on up to eight channels simultaneously.
For the generation of the sound range of the original instrument, the oscillators of the synthesizer should be able to produce sawtooth- and square-like waveforms. Ideally the module contains two pairs of (or four separate) parallel resonant filters, which should be independently assignable to a MIDI channel. As a substitute, external MIDI controllable resonant filters could be used. In this case, separate audio outputs are needed at the synthesizer for the two manuals or two separate synthesizers must be used.
The synthesizer actually used is a Hohner HS-2/E expander (identical to the Casio VZ-10M resp. the Casio VZ-1 / Hohner HS-2 for the keyboard version) which has a maximum pitchbend range of +/- 4 octaves with a resolution of 14 bit. So at the maximum range the resolution is approximately 0.3 cent. Unfortunately the resolution in the "Combination"-modus (layering of sounds) is not fine enough, so separate MIDI channels are used for the transmission of the oscillator pitches. Phase synchronization is not possible. Only one parameter of the sound generation, volume or timbre, could be controlled. The controller for master volume (controller no. 7) influences the total volume of the whole module, so it is not possible to control volume and timbre of the two manuals independently. The actual version of the MAX patch is able to control two manuals without the variation of timbre control. The use of external filters at the separate audio outputs of the synthesizer is possible. A sawtooth-like waveform could be choosen for the oscillators. The reaction time of the synthesizer to a sharp volume attack is very slow, so only soft attacks will be heared.

Results

In an auditive comparison of the ISPW version and LP/CD recordings of the classical Mixture-Trautonium no remarkable difference could be discovered with the exception of the typical problems in digital audio processing (aliasing, characteristics of digital filters).
The two-manual MIDI-synthesizer version could not control timbre due to restrictions of the synthesizer module. A single manual version could influence timbre through the control of the modulation of a phase modulation operator by moving the pedal. Alternatively two complete sets of oscillators could be interpolated in volume. By connecting external MIDI controllable resonant filters and using a sawtooth-shaped waveform for the oscillators the most important aspects of the sound generation of the Mixture-Trautonium could be realized with consumer equipment.

Prospect

With the ISPW version of the digital Trautonium a new generation of the instrument exists which could replace the old generation of analog instruments. The advantage of the digital technique lies in the portability of the algorithms to new computer generations. It is no longer needed to completely reengineer the whole instrument. Only the MIDI controller of the Trautonium might change, dependant on the actual sensor technology. An enhancement might be the integration of the position measurement into the pressure sensor strip. The current pressure/position sensors show a pressure weighted position of all points of pressure which has a negative impact on the playing technique of the instrument (i.e. playing a trill). The separation of the two measurements should result in a robust and wear-resistant manual which could be used by children and adolescents.

Acknowledgements

I would like to thank all the people who helped me during this project, namely "GIMIK: Initiative Musik und Informatik Köln" for the usage of the ISPW, Miller Puckette for his friendly help regarding problems with the ISPW, the "Institut für Musikforschung Berlin" as well as the communal library of Cologne and the institute of musicology at the university of Cologne for their support of providing literature and sound examples. Special thanks also to Oskar Sala for the demonstration of his instrument and Jörg Schwanke who takes care of my thesis and was very helpful at any time showing a lot of interest for my work.

References

(Books and articles)

Sala, Oskar:
Experimentelle und theoretische Grundlagen des Trautoniums - Erster Teil, in: Frequenz 2, No. 12, 1948, p. 315-322

Sala, Oskar:
Experimentelle und theoretische Grundlagen des Trautoniums - Zweiter Teil, in: Frequenz 3, No. 1, 1949, p. 13-19

Sala, Oskar:
Subharmonische elektrische Klangsynthesen, in: Klangstruktur der Musik, ed. Fr. Winckel, Berlin 1955, p. 89-108

Trautwein, Fr.:
Elektrische Musik, Veröffentlichungen der Rundfunkversuchsstelle bei der Staatl. akademischen Hochschule für Musik - Band 1, Berlin 1930

Sala, Oskar:
Trautonium-Schule, Mainz, Schott, 1933

Lertes: P.:
Elektrische Musik, Dresden & Leipzig 1933, p. 171-184

(Recordings)

Sala, Oskar:
My fascinating instrument, Hamburg, Erdenklang Musikverlag, 1990, CD + Booklet

Hindemith, Paul:
Langsames Stück und Rondo, in: Die dreißiger Jahre, Thorofon CTH 2044, 1989, CD

Genzmer, Harald:
Trautonium-Konzerte, Mainz, Wergo Schallpl., 1986, LP 30 cm, 33 rpm, stereo


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