Wired harmonic spectra of percussion - the unique timbre

 I discussed the harmonic pattern of bells in the previous article. Spectra of percussion instruments are often irregular, that is the reason why the timbre of each percussion instrument is special. For percussion containing wood or metal bars with free ends, the sequence of harmonic partials is irregular.

Sethares (2010) calculated the pattern of the first 6 partials as:

        f, 2.76f, 5.41f, 8.94f, 13.35f, and 18.65f

It is assumpted that the bar is perfect even thickness and density. The resonators under the bars also tune back the partials to adjust closer to the harmonic series. Marimba, vibraphone, and xylophone have resonators underneath. The examples below show the first several partials are adjusted, not quite fitting Setheres's calculation.

This is a spectrum of marimba, as roughly follows the sequence above.

Marimba on note A3

This is a spectrum of vibraphone, it partly follows the traditional harmonic series at the beginning, but the second partial is missing and the partials beyond partials the fourth partial in the higher register are hard to line up with a sequence.

Vibraphone on note A3

This is a spectrum of a Xylophone. Although the note is played is on the A4=440Hz, the harmonic series is based on the fundamental on A3=220Hz, the combination tones let our brain also hear the A3 as well. 2860/220=13. 4620/220=21.
Xylophone on note A4
This is a video to demonstrate this acoustic effect as well.

To conclude the patterns of the percussion examples above, their harmonic spectra are either irregular ratios between each partial, missing partials in the harmonic series, or the false fundamental of the series.

Sethares, W. A. (2010) Tuning, timbre, spectrum, scale. 2nd ed. London: Springer.

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