July 14, 2006
Anatomy of a Kalimba Note: One Octave Lower
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.

Last week, we looked at the middle A note, which was A 440 (i.e., 440 Hz, or 440 vibrations per second). And we really DID look at those vibrations. Today, we look at the low A note on the ALTO kalimba. This SHOULD be A 220. To make a note that is one octave lower, the frequency should be half. One octave higher requires the frequency to double. A question for you: what do you do to the frequency to make it a whole step higher?

OK, we've got very similar plots of the low A note, so you should be able to compare them fairly well with the middle A note (try to open two different browser windows to do this).

This plot shows the first second of the low A note. This note actually goes on for about 4 seconds, much longer than the middle A. However, this note isn't as loud as the middle A. This is important: not as loud, but lasts longer; the other one was louder and didn't last as long. Why?

This note has a sharper initial attack, apparently no oscillation in amplitude, and then a smooth exponential decay.

Zooming in, this second plot actually reveals a bit of amplitude oscillation. This amplitude oscillation is coming in at about 26 Hz, which is exactly the "beat note" between this low A and the low B (i.e., the next note). We'll study beat notes in a month or two. They are very cool.

Zooming in again, we can see there is a lot of "high frequency hair" on this note, espcially at the beginning. This note is far from the resonant frequency of the kalimba box. Remember, the middle A from last week was right at the resonant frequency of the box, and that note very quickly transferred the energy in the high frequency vibrations into the middle A vibrations. In this note though, those high frequency vibrations don't fade out nearly so quickly.

The SONAR display has a bug, and the 00:00:00:03 (i.e., 3 frames, a frame is 1/30 of a second -- this is leftover from movie work, which has 30 frames per second) should say 00:00:00:04. From this plot, we can calculate the fundamental frequency of this vibration. Between the line just to the left of 02 frames to the line just left of 08 frames (i.e., in 6 frames, or 6/30 of a second, which is 0.2 seconds), I count about 44 vibrations. To convert to Hertz (i.e., vibrations per second), divide 44 by 0.2 s, and we get 220 Hz.

Zooming in yet again, we can see that the high frequency hair on the attack of the note (i.e., the far left) actually quickly changes into the fundamental vibration plus a harmonic of a particular frequency (you can see this about a third of the way to the right). I count about 7 of those shorter wavelength, higher frequency vibrations on each of the fundamental vibrations. As the fundamental vibration is 220 Hz, this harmonic is about 7 times higher frequency, or about 1540 Hz. If you know about harmonics, you will see that this note does not harmonize with the fundamental (i.e., they don't sound good together). Fortunately, the high harmonic is disappears from the note when you get to the far right side of this plot (which is about 1/10 of a second, long enough to hear, but not long enough to annoy you).

Zooming in one last time. You can very clearly see the transition from the high frequency transient vibrations at the left of the plot, to the fundamental low frequency vibration and the high frequency harmonic at the right of the plot. If you looked at the vibration about 1s further to the right, you would see that the vibration amplitude was much lower (i.e., the note is softer), and the vibration would be very smooth looking, without any of the hair. This means it would be very nearly just the fundamental frequency.