December 22, 2006
Anharmonic Overtones Die Out Quickly

The overtones of a kalimba are supposed to be an-harmonic, i.e., they don't sound good with the fundamental vibrational tone. But look here! The overtones are fairly weak, and they die out much faster than the fundamental.

db, or decibel, is a relative measure of power. The fundamental of the F# goes down about 3 db every 0.2 second, i.e., it decreases in power by half every 0.2 seconds. However, the 6.6 X overtone decreases by 15 db, or down by 97%, every 0.2 s. The 2 X overtone (i.e., the octave) starts out weaker, but does not die so quickly. So, one of the reasons why the kalimba sounds so beautiful even though the overtones ARE an-harmonic is that those anharmonic overtones die out very, very quickly, leaving us with a simple fundamental tone.

F# / 369Hz:

Time (s)	Fundamental (db)	6.6X Overtone (db)	2X Overtone (db)
0.1	-3	-20	-44
0.3	-5	-35	-52
0.5	-8	-48	-58
0.7	-11	-63	-64

C / 525Hz:

Time (s)	Fundamental (db)	6.6X Overtone (db)	2X Overtone (db)
0.1	-0	-26	-35
0.3	-5	-66	-44
0.5	-9	-97	-53
0.7	-14	gone!	-61