[78-L] 45 to 78 in semi-tones - help! I need a math major!

[Jeff Lichtman]

The formula for the number of semi-tones between two different speeds 
is actually pretty simple if you have a calculator (and everyone with 
a computer has one):

semitones = 12 * (log(speed1 / speed2) / log(2))

That is, the number of semitones is 12 times the logarithm of the 
ratio of the two speeds divided by the logarithm of 2. The base of 
the logarithm doesn't matter as long as it's the same in both cases.

For example, the number of semitones between 45 RPM and 78.26 RPM is 
12 times log(78.26 / 45) divided by log(2), which comes to about 9.58 
(which is actually closer to 9.6 than to 9.5).

To get the number of cents, multiply by 1200 instead of 12. In this 
case you would get 958 cents, which is 9 semitones plus 58 cents.


                        -        Jeff Lichtman
                                 jeff at swazoo.com
                                 Check out Swazoo Koolak's Web Jukebox at
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