minipost

Let your spectrum analyzer listen to middle C on a piano and take a look at what comes out. (guess what? your smartphone can do it) Most of the acoustic energy, assuming the piano is tuned to a 440 A is concentrated at a tad below 262 hertz (cycles per second), but other things are going on. Bursts of energy at multiples of the 262 Hz fundamental frequency paint the spectrum along with a few other bursts. The integer multiples of the fundamental frequency are called partial harmonics and the others are inharmonic partials. Together they form a large part of why a piano sounds like a piano - in fact why a specific piano sounds like that particular instrument - it's timbre.

The time development of a note can be very complex with the distribution of energy in the various harmonics changing as the note decays. A really nice way to study this is with Fourier analysis. I gave a crude non-mathematical introduction earlier, but I just came across another beautiful illustration.

Enter Anna-Maria Hefele . She's a remarkable singer who has mastered the art of overtone singing. Thanks to Richard Feynman's life-long fascination with Tuva you're probably aware of Tuvan throat singing. Her singing is much richer. Let's start with her voice as an instrument in this lovely version of H.I.F. Biber's Rosary Sonata 1.

and now a graphical look into the flexibility she has .. simply wonderful! Such a fine way to show off the overtones.