>>Yes, exponential.
>>
>>http://www.math.ucdavis.edu/~kouba/Math21BThomasDIRECTORY/Expo
>nential.p
>>df
>>
>>Pipes arranged in a decreasing series of half tone steps do not 
>>increase in length by a constant amount (which would make the profile 
>>of their ends a straight line.) The difference in their lengths gets 
>>larger and larger and so makes a curved profile - an 
>exponential curve.
>
>OK, my math-starved brain can follow that reasoning, but do 
>they not increase in length by a constant PERCENTAGE (as 
>opposed to a constant LENGTH)?  


Yes, that's right. And so the amount of increase increases at every step.

>I thought exponential dealt 
>with powers of 10 or some such thing.  (My daughter is the 
>math whiz in the family; she certainly didn't get it from ME!)

It does have to do with powers but not of 10. Each half tone increases by
the twelfth root of 2, which is 2 to the 0.08333 power, which is 1.0594.

Multiply 1.0594 times itself 12 times (for 12 steps in the octave) and you
get 2  (i.e. twice the frequency, or one octave).

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