Fun With Octaves

I sit here at campsite 17 in an undisclosed location in northern Minnesota, listening to the August screams of children treating the national forest campground as if it’s a Wisconsin Dells water park. Pity the mergansers, cedar waxwings, the confusing fall warblers, shallow-watered guppies, and campers who are here to get away from these very sounds. They are so distracting that I keep reading the same lines repeatedly in David Foster Wallace’s “Infinite Jest” that I have finally, at roughly a quarter of the way through, started to make some sense of. It is admittedly quite a ride, even if I am unable to hang on at all times. But I digress.

Since many, if not most of the readers of this blog are bassists and/or bass players (unsure what the difference is, truth be told), it’s abundantly clear that octaves resonate with each other. To demonstrate, one only needs to play the low G on the E string to visually witness that the open G string sympathetically resonates with it. Other overtones can be heard as well, but for the purposes here only octaves will be considered. Based on the assumption that octaves resonate with each other, and that this resonance means something if only sheer consonance, I wish to expound upon certain theories based upon simple “math”.

OK, the term “math” scares a lot of people. The brain shuts off. “Oh my, I just don’t DO math”. And so on. My special brand of math involves only two things: multiplying by two, and dividing by two. Calculators are OK, too.

Sound frequencies are measured in “Hertz”, a term synonymous with “cycles per second” or “waves per second”. The shorthand for Hertz is “Hz”.

To obtain the frequency of the next higher octave of any given pitch, simply double the base frequency. To illustrate, the next-higher octave of 440 Hz (“A-440”) is 880 Hz. Doubling the frequency again results in an A of 1760 Hz, and so on. The human ear can hear upwards of about 20,000 Hz.

Conversely, dividing a frequency in half results in the next-lower octave. The octave below 440 Hz is 220. Going lower still, the frequencies of 110, 55, and 27.5 Hz are octaves of A-440. The open A string of a bass is 55 Hz. The human ear can hear down to around 20 Hz.

That’s all for octaves. For right now. In the next article, I’ll discuss a few books that influenced me and some very low tones below the human threshold of hearing.