Double bassist Doug Johnson (www.myspace.com/douglasjohnson) has written a series of fascinating blog posts on the relationship between pitch cycles per second and how these translate to beats per minute. This is heady and fascinating stuff! Doug writes:
….pitches in music are measured in frequencies, or more specifically "Hertz" (Hz), which are cycles per second. Most western music is tuned to A-440, which means that the pich "A" above middle C is 440 Hz. This will be my reference for the pitch to tempi table below.
When a frequency is doubled, it sounds exactly one "octave" higher. So if 440 Hz is an A, then 880 Hz will be an A one octave higher, as in the first and last do in do-re-mi-fa-so-la-ti-do. Halving A-440 will result in A-220, which is an A one octave lower.
Now, since octaves "resonate" with each other, and if you play the bass you know what I mean, tempi can also resonate with pitches. Tempi are measured in beats per minute (bpm), so converting a pitch to its tempo is done by halving the pitch frequency several times and then multiplying by 60 to turn cycles per second to cycles, or beats, per minute.
Read the complete post here. Doug has also provided a table listing all of these aforementioned relationships.
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