I'm trying to find a list of Fourier Coefficients (frequencies/amplitudes, ie, spectral data) to simulate different musical instruments using additive synthesis. Are these data published somewhere? This is for a Math class: I just would like to add more frequencies and listen how the sound generated compares with the real sound.


  • I'll migrate this over to sound design - be aware that your additive model doesn't take into account attack, decay etc.
    – Rory Alsop
    May 12, 2015 at 21:27

4 Answers 4


I think the Sandell Harmonic Archive (SHARC) will help you out: http://www.timbre.ws/sharc/index.php

Click on the browser link at the top of that page and then select the instrument and the note. You won't get actual coefficients but you can pick a coefficient of 1 or 10 for the fundamental and you should be able to scale the rest based on that.


Or, you could find audio recordings of instruments, e.g. Philharmonia, and open them using SPEAR to see both the component frequencies/amplitudes as well as how they change over time. This is how I've managed to create the best synthesis models of real instruments I've ever achieved.


For a math class, as you are asking, a good option is the software Mathematica from Wolfram Research, because it has included the recording of several instruments and the commands to analyze them with Fourier analysis and reproduce them with Fourier synthesis. I have created an activity for doing exactly that with my students, showing them step-by-step how to do it with an oboe recording included in Mathematica, then asking them to do it with another recording. You can also import your own recording, please see the PDF document in this link: http://matecmaticaacustica.weebly.com/fourier-synthesis.html I hope that helps.


Welsh's Synthesizer Cookbook, Vol 2: Harmonic Catalog contains the frequency response plots showing the harmonic components of common orchestral instruments. Obviously these are just snapshots and will not show you how the harmonics change over time, but it will give you a good starting point for recreating a basic timbre.

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