July 7, 2006
Anatomy of a Kalimba Note
Since posting this tip, I discovered that the SONAR plots show 30 frames per second (not 29!). I have made the necessary corrections and highlighted them in gold below.

The different notes on the kalimba have very different characteristics. We start with the note A (A440, actually), the colored tine in the middle of the right side of the Alto kalimba. This note is usually the loudest note on the kalimba because it is the resonant frequency of the box. This makes this note particularly odd in a few respects.

We explore the waveform of the note A as plotted with the SONAR recording program. Most recording software shows you similar displays, so you can probably do your own exploration.

The above plot shows the envelope of the note. The x axis is time (in Hour:Minute:Second:Frame format--a "Frame" is 1/30 of a second, or 0.0333 second), and the y axis is the intensity of the vibration. At first (i.e., on the far left), there is no note. Then as you move to the right, there is a soft attack (i.e., the initial rise in intensity), followed by a decrease in intensity and then an oscillation in intensity (up and down) for about a third of a second, or about 10 frames. After that, the intensity decreases more or less exponentially (i.e., very smoothly and taking a long time to die out completely).

Now this second plot shows a blowup of the previous note. The sampling of the computer screen is now sufficient to see the actual vibration of the wave, but the "argyle" pattern is an artifact of the interaction between the screen's sampling and the exact vibrational frequency; this artifact is due to something called "aliasing". Pretty, even if it isn't what is really happening.

In this third plot, we are zooming in further. The aliasing makes for other interesting patterns. We can really see that the attack is very smooth, and takes about 6 cycles of the fundamental vibrational frequency.

In this fourth plot, we are now zoomed in enough so that aliasing is not a major problem for the fundamental frequency. The fundamental vibrational frequency can actually be calculated by counting the number of vibration cycles within a certain amount of time (the software has a bug, and the second 00:00:00:03 should be 00:00:00:04); within 2 frames, or 0.067 seconds, there are about 30 complete vibrational cycles: hence, in a full second, there will be 30/0.067 ==> 448 vibrations per second. Of course, the number is supposed to come out to be A 440.

If you look at the attack of the note in this final plot (i.e., where the vibrations begin), you will see something very interesting: at first, there is a lot of hair on the vibration. That hair is actually higher frequency vibrations called "transients" because they don't stick around for very long. At first, all of the energy is in these higher frequency vibrations, but that energy is quickly transferred into the lower frequency vibrations of the fundamental frequency. Also, as the amplitude of the fundamental vibration comes up after four or five cycles, the magnitude of the hair (ie, the high frequency vibrations) drops off. The "hair" will be at many different frequencies, but in the second downward half of the fundamental cycle, the super high frequency part of the hair is dying down, and we can count about 6 or 7 cycles of "hair" within that half cycle of the fundamental. That means that a transient tone at about 6.5 * 2 times higher frequency than the fundamental is ringing briefly. This would be about 6000 Hz, a very high pitch indeed (this is about half an octave higher than the highest note on a piano).

Next week, we'll look at the anatomy of a different kalimba note and we'll see just how different the notes can be. The diversity of notes on the kalimba is fundamental to the way the instrument sounds.