>>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). _______________________________________________ Finale mailing list Finale@shsu.edu http://lists.shsu.edu/mailman/listinfo/finale
