Making Cents of Hertz
The exact pitch of a Crystal Tones bowl is indicated with a note name (letter) plus a number. The number refers to “cents,” a linear unit of measurement that divides every semi-tone (our smallest interval on the piano) into 100 equal parts. Thus the number on a Crystal Tones bowl ranges from 5 to 50 or -5 to -50, indicating how far above or below a “true tone” pitch the bowl sounds. Octaves (the distance from one note to the next note of the same name, i.e ‘A’ to ‘A’ or ‘B’ to ‘B’) are comprised of 12 semi-tones of 100 cents each, totaling 1200 cents.
It’s important to note that cents and Hz do not correlate, as Hz are what we pay attention to for creating binaural beats. Unlike cents, Hz are not a linear measurement, but an exponential one (geometric, to be exact), as every octave doubles the frequency of the previous one. Thus A440 becomes A880 an octave up, followed by A1760, A3520, etc. An octave on the low end of the piano may span 65HZ while one at the top may span over 2000! And since each of these octaves are divided into 1200 cents, you can see that not all cents are created equal, in terms of Hz! The upshot is that we will use a smaller differentiation of cents in bowls at a higher pitch than we will with lower ones to create the exact same Hz difference.