Music is related to math. For each octave raised, the frequency is doubled. For each octave lowered, the frequency is cut in half. Each half step is a difference of the 12th root of 2 or the 12th root of ½.
The standard for tuning instruments is A above middle C at 440 Hz. MIDI calls that note A3. Here are some known facts based on the calculations.
Middle C (aka C3) is 261.6 Hz.
Piano range: A at 27.5 Hz to C at 4,186 Hz.
Pipe organ range, also MIDI C-2 to G8: 8.18 Hz to 12,544 Hz.
Range of standard 6-string guitar with 24 frets: E at 82.4 Hz to E at 1,319 Hz.
Range of standard 4-string bass guitar with 24 frets: E at 41.2 Hz to G at 392 Hz.
I own a 7-string bass with 24 frets, tuned low F sharp to C. The range: 23.1 Hz to 523 Hz.
I also own a custom 8-string guitar with 31 frets, tuned low B to high A. The range: 61.7 Hz to 2,637 Hz.
Average human hearing range: 20 Hz (E flat) to 20 kHz (E flat).
60 Hz "buzz" on power lines is between B flat and B.
Given the above facts, here is an interesting bit of information. The 2005 Guinness World Records lists the lowest note detected in the universe, generated by a large black hole in the center of the Perseus cluster of galaxies 250 million light years away, as a B flat 57 octaves below middle C. It does not list the frequency, but my calculations show it to be 1.62 femtohertz (fHz). For those not familiar with the prefix "femto" it is micro times micro times milli, or 10-15. At that frequency, the wave completes one cycle in about 618 trillion seconds, or about 19.6 million years. And you thought rush hour traffic was slow!
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Page created 13 Sep 2006 by G.R. Van