Overtone Tracking in Music and Performance Systems
Overtone Tracking in Music and Performance Systems
Demonstration 2: Inharmonic Vibration with Time-Varying Overtone Amplitudes
Continuing, the NRI patent-pending technology [1] provides for real-time amplitude measurements of the fundamental and portions of the overtone series of a pitched audio-frequency electrical signal and the use of these measurements to create real-time control signals for controlling of audio synthesis processes. This demonstration page illustrates some exemplary audio synthesis arrangements employing measured real-time overtone amplitude control signals. The harmonic example providing the first five harmonics, depicted in an earlier demonstration page, is used as the control signal generator.
A potential application that may occur immediately to those familiar with classical audio synthesis as pioneered by Robert Moog and recorded by W. Carlos is in a vocoder arrangement. In adapting to such a setting, the overtone amplitude tracking technology functions as a type of pitch tracking filter bank with filters tuned in ratios of integers rather than with exponential spacings. Rather than elaborating, attention will be directed instead to a number of other illustrative non-classical applications which give rise to new types of responsive time-varying sound timbres.
As a simple first class of examplary applications, amplitudes of the first five harmonics of an audio signal (as may be generated by the measured vibrations of an electric guitar string) are used to control the pulse width of five oscillators (DCOs or VCOs) as shown in the animation below. The five oscillators (depicted in the animation as VCOs) may be tuned to nearly the same frequency (so as to give an evolving drone effect), may be tuned in a series of octaves, or vary in other manners. In the pulse waveforms depicted, two periods are shown although implicitly not scaled to depict any particular frequency relationship. The oscillator frequencies may track the audio source providing the signal whose overtones are measured, or may be fixed, or may be controlled in other ways (for example by a keyboard, etc.).
As a variation of this example, the pulse-width modulators may be replaced with controlled filters (DCFs or VCFs) applied to harmonically-rich waveforms created by the oscillators. In both this and the PWM example above, the overtone-tracking control signals are used to control spectral-modifying processors.
As second examplary class of applications, the five overtone-tracking control signals may be used to control the levels of five VCAs. This could be viewed as a variation on a vocoder wherein the processed audio filter bank is replaced by other sound sources. As a first example of this class, the audio signals whose amplitudes are varied responsive to the overtone-tracking control signals may be the outputs of a frequency divider or frequency multiplier chain driven by a single VCO. The animation below depicts the results applied to the outputs of a square wave frequency-divider chain, such as a string of toggle flip-flops.
Alternatively, a triangle-wave frequency-divider chain or algebraic frequency-multiplying chain may be used in lieu of the square wave frequency-divider chain may be used. For a more sophisticated sound, the cross-product outputs of a frequency-divider cross product chain [2]-[5] may be used instead of a simple frequency-divider / frequency-multiplying chain.
As third examplary class of applications, the five overtone-tracking control signals may be used to control the levels of modulation applied to other signal processing modules. As a first example, the five overtone-tracking control signals may be used to control the levels of low-frequency oscillator (LFO) modulation applied to controllable audio-frequency oscillators (DCOs or VCOs) to create separately varying decaying vibrato effects. In one implementation of this, each of the controllable audio-frequency oscillators are tuned in an overtone series, resulting in separately varying decaying vibrato effects for each individual synthesized harmonic. In another implementation the controllable audio-frequency oscillators may be tuned in near unison so as to create a crazed ensemble vibrato that settled down as individual overtone-tracking control signals converge to zero.
All the examples thus far have had a heterogeneous organization, but individual overtone-tracking control signals may be used to control various unrelated processes. One example is shown below. Here a stereo sound is produced by means of two controllable audio-frequency oscillators (DCOs or VCOs, depicted as VCO). The values of the five control signals are summed to produce a summed control signal that controls the overall stereo volume. Additionally, the detected amplitude of the fundamental controls the cross-panning of the stereo signals. The detected amplitude of the first overtone (second harmonic) additionally controls the amplitude of an oscillatory frequency-modulation signal complementarally applied to the two controllable audio-frequency oscillators. The detected amplitude of the second overtone (third harmonic) additionally controls the frequency of a controllable low-frequency oscillator used to modulation the frequency of two controllable audio-frequency oscillators. The detected amplitude of the third overtone (fourth harmonic) additionally controls the parameter of a continuous waveshaper operation as well as a controllable filter associated with the first controllable audio-frequency oscillator. The detected amplitude of the fourth overtone (fifth harmonic) additionally controls the parameter of a pulse-width modulation operation as well as a controllable filter associated with the second controllable audio-frequency oscillator. Many other various are of course possible.
REFERENCES
[1] U.S. Patent Application 10/676,926, published April 15, 2004 as Pub. No. 2004/0069128
[2] U.S. Patent 6,849,795 "Controllable Frequency-Reducing Cross-Product Chain," February 11, 2005
[3] L. Ludwig, "A Square-Wave Frequency-Division Sub-Octave Cross-Product Module," Electronotes, Vol. 11, No.98, February 1980, pp. 9-15.
[4] Synthesis Technology, "MOTM-120 Sub-Octave Multiplexer Module," product description, http://www.synthtech.com/motm120.html.
[5] NRI Whitepaper, "Controllable Frequency-Reducing Cross-Product Chain,"