August 11, 2006
The Spectrum of a Dead Tine

Someone recently sent me a kalimba with some dead tines. Actually, the "A" note was the worst. I am trying to understand the "dead tine syndrome", which occurs in rather old kalimbas. He bought his kalimba on eBay, and I guess his kalimba is about 30 years old, judging by the text style on the sticker on the back.

To study this kalimba, I recorded the sound it makes and analyzed that sound mathematically.

I played a glissando (i.e., stroked my thumb over several tines to make a chord), playing the upper four notes on the left side, or D, F#, A, and C. I then made a spectrum using the sound from 0.0 - 0.1s, from 0.1 - 0.2s, on through to 0.4 - 0.5s.

By the way, a spectrum is generated by Fourier transforming the wave's time series, and it shows us how much energy is in the different vibrational frequencies. If we actually want to look at the different notes in the spectrum, it makes sense to use a logarithmic display on the frequency axis. If you're a stranger to Fourier transforms, check out this book that provides a really clear explanation: Who Is Fourier? A Mathematical Adventure.

In the first 0.1 second after all the notes have been played, we see similar amounts of energy in all four notes, but the A is actually a bit louder than the others (this is significant, we'll come back to that another day). The four notes we strummed appear as peaks at the appropriate frequencies. There is a lot of other "noise" in the spectrum, much of it is high frequency stuff left over from the attack.

Between 0.1 and 0.2 s, the high frequency attack noise has mostly gone away, the D, F#, and C have gone down by about 5dB, and the A has gone down by 20dB, which means that the A note has only about 1% of the energy it had just 0.1 s ago!

Between 0.2 and 0.3 s, the D and F# have gone down very little, the C has gone down a bit more, and the A has gone down again by almost 20dB, so the energy loss is again about 99% in 0.1s. No wonder the tine sounds so dead!

The energy loss in the A note continues its precipitous decline. The high C is down 10dB since the last spectrum.

And further down.

What is causing the catastrophic decline in the A note on this kalimba? What do modern kalimbas do? What can we do to fix this? I will try to answer these questions in the coming weeks.