Study Hall

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Whistle While You Work: Using Your Body As An Ultra-Low-Tech Test & Measurement Instrument

A guide to your "on-board kit" and how it can make your work a little quicker and easier...

First, find your lowest note. This may take a little practice, and a decent analyzer or phone app, so you can identify your fundamental (read lowest) whistle tone. Be sure to push out very little air to get as low as possible.

What I found really interesting is my lowest pitch didn’t change from day to day, or month to month. When I figured that out, I knew I was on to something useful. From that moment on I had a mid-band sine wave generator that’s available anywhere and anytime needed.

Plus, having good relative pitch allows me to easily whistle, or imagine – I can’t whistle much above 2 kHz, and nothing below 500 Hz, so everything else has to be imagined – the various intervals above and below my fundamental.

For quick reference, based on a tuning reference of A = 440 Hz: C0 is 16.35 Hz, and C9 is 8,372.02 Hz. C4, which is also known as middle C, is 261.63 Hz. The notes of a 1-octave, ascending C major scale are C, D, E, F, G, A, B, C. The intervals between those notes have a percentage relationship too, regardless of octave, based on their position above the fundamental C.

The major 3rd above any C is E, which is roughly 25 percent higher. The major fifth above any C is G, which is about 50 percent higher, and the A above any C is about 75 percent higher. These percentages are the key to finding other frequencies. If we translate these concepts into their corresponding frequencies, using 500 Hz for mathematical simplicity, we get these frequencies over two octaves:

C5 [fundamental] = 500 Hz (actual C5 is 523 Hz) I’ve rounded everything for simplification.
E5 [a major 3rd above 500 Hz] x 1.25 = 625 Hz (actual E5 is 659 Hz)
G5 [a major 5th above 500 Hz] x 1.50 = 750 Hz (actual G5 is 784 Hz)
A5 [a major 6th above 500 Hz] x 1.75 = 875 Hz (actual A5 is 880 Hz)
C6 [1 octave above 500 Hz] x 2 = 1,000 Hz (actual C6 is 1,047 Hz)
E6 [a major 3rd above 1,000 Hz] x 1.25 = 1,250 Hz (actual E6 is 1,319 Hz)
G6 [a major 5th above 1,000 Hz] x 1.50 = 1,500 Hz (actual G6 is 1,568 Hz)
A6 [a major 6th above 1,000 Hz] x 1.75 = 1,750 Hz (actual A6 is 1,760 Hz)
C7 [1 octave above 1,000 Hz] x 2 = 2,000 Hz (actual C7 is 2,093 Hz)

Table 1 (directly below) provides a precise translation between musical notes and their corresponding frequencies. Hopefully, you can see the repetitive patterns. I’ll leave it to you to figure out the other interval percentages if you like. Use your favorite spectrum analyzer phone app to find your lowest tone, then practice with the basic intervals outlined above.

Table 1. (Credit: sengpielaudio.com)

Every frequency you can hear, whistle or imaging follows these patterns. All you need to do is learn how to transpose the concept into your fundamental whistle tone. It’s the percentage above your lowest whistle frequency that’s the important point of this whole exercise. Don’t make the mistake of thinking that C5 or C6 are important or problematic frequencies; they’re not. They were picked because of my fundamental note, which was also a convenient way to explain the intervals in mathematical terms.

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