[doki_pen]

Get a list of tone frequencies and do math with them. You will see patterns, called harmonics by musicians. Doubling the frequency (octave) can be thought of as the same tone playing twice, with an even offset. Our brains can pick up on that and notice that 440Hz is the same as 880Hz (only and "octave" higher)

Interesting fact: The tones of the scale aren't exactly evenly spaced, because of math. Some instruments use true tones and are made specifically for a certain key. Other instruments that can play in any key (like guitar) are never truly in tune.

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To generate a list of tone frequencies, start with A=440Hz and multiply by 2^(1/12) to get the frequency of the next higher tone or divide by 2^(1/12) to go down to the next lower tone in the chromatic scale. Notice that the octave is 12 of these intervals away, making it's frequency (2^(1/12))^12 = 2 times the initial frequency.