Spectral Interpolation

An analysis/synthesis technique in which a musical tone is modelled as a set of harmonics with slowly varying amplitudes. As long as amplitudes vary relatively slowly, linear interpolation between wavetables provides an efficient synthesis technique.

To date, we have worked on reproducing sounds from prerecorded examples. Current work uses tables to store representative spectra (or waveforms) as a function of pitch and loudness (and perhaps other parameters in the future). This idea is mentioned in our early papers but not fully realized until the work by Istvan Derenyi.

Sound examples are available.


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Dannenberg, Serra, and Rubine, ``Comprehensive study of analysis and synthesis of tones by spectral interpolation,'' Journal of the Acoustical Society of America, Supplement 1, Vol 82 (Fall 1987).

This is a short paper on the spectral interpolation technique, documenting a conference presentation.


Serra, Rubine, and Dannenberg, ``Analysis and Synthesis of Tones by Spectral Interpolation,'' Journal of the Audio Engineering Society, 38(3) (March 1990), pp. 111-128.

A fairly complete presentation of our work and probably the best paper to cite for a general reference.


Serra, Rubine, and Dannenberg, ``The Analysis and Resynthesis of Tones via Spectral Interpolation,'' in Proceedings of the International Computer Music Conference, Computer Music Association, (September 1988), pp. 322-332.

An article for the computer music community. The JAES article is probably easier to come by and more complete.


Serra, Rubine, and Dannenberg, ``A Comprehensive Study of the Analysis and Synthesis of Tones by Spectral Interpolation,'' CMU Technical Report CMU-CS-88-146, June 1988.

This is the most comprehensive presentation of our work on analysis and synthesis. I still have copies; if you would like one, send me email.


Dannenberg, Pellerin, and Derenyi. ``A Study of Trumpet Envelopes,'' in Proceedings of the International Computer Music Conference. San Francisco: International Computer Music Association (1998) pp 57-61.

This paper is the first I know of that reports on envelopes of trumpet tones played in a musical context. "Real" trumpet envelopes exhibit features never seen in the classic studies. We also show statistical relationships between melodic shape and envelope shape, confirming Clynes' general idea, but contradicting some specific details of the Clynes model. This paper is really a companion to Derenyi and Dannenberg 1998 (below).

[Acrobat (PDF) version] [HTML version]


Istvan Derenyi and Roger B. Dannenberg. "Synthesizing Trumpet Performances," in Proceedings of the International Computer Music Conference. San Francisco: International Computer Music Association (1998) pp 490-496.

This paper puts into practice what we described as early as 1987 and what we've been aiming for all along: the idea that we can generate envelope information and use it to drive a spectral interpolation synthesizer. Interesting results here include some studies of the validity of the assumption that the spectrum is really a function of amplitude and frequency, and that there is not enough "history" in the system to matter. This paper is really a companion to Dannenberg, Pellerin, and Derenyi 1998 (above).

[Acrobat (PDF) version] [HTML version]


Dannenberg and Derenyi, ''Combining Instrument and Performance Models for High-Quality Music Synthesis,'' Journal of New Music Research, 27(3), (September 1998), pp. 211-238.

This is a full-length journal article which partially overlaps the two ICMC articles listed above. The abstract follows:

Convincing synthesis of wind instruments requires more than the reproduction of individual tones Since the player exerts continuous control over amplitude, frequency, and other parameters, it is not adequate to store simple templates for individual tones and string them together to make phrases. Transitions are important, and the details of a tone are affected by context. To address these problems, we present an approach to music synthesis that relies on a performance model to generate musical control signals and an instrument model to generate appropriate time-varying spectra. This approach is carefully designed to facilitate model construction from recorded examples of acoustic performances. We report on our experience developing a system to synthesize trumpet performances from a symbolic score input.

[Acrobat (PDF) preprint version]


Dannenberg and Matsunaga, ''Automatic Capture for Spectrum-Based Instrument Models,'' in Proceedings of the 1999 International Computer Music Conference, San Francisco: International Computer Music Association, (1999), pp. 145-148.

This paper reports on initial work to automate the capture of Spectral Interpolation models. The abstract follows:

Our goal is to automate the analysis of recorded acoustic performances in order to study the relationship between scores and performance. An automated system segments a recorded performance into individual notes. These are then analyzed to determine pitch and amplitude envelopes. Spectral data is also measured. The technique consists of two stages. First, a rough estimation stage performs pitch detection based on MQ analysis. Second, an accurate estimation stage uses period-synchronous analysis. The data will ultimately be used by a machine learning process to build instrument and performance models. Experiments with trumpet tones are described.

[Acrobat (PDF) version]