---------- > From: Robert Scott <rscott@wwnet.com> > To: pianotech@byu.edu > Subject: Re: The math behind perfect 5th tuning > Date: Tuesday, February 04, 1997 12:32 PM > > Richard Moody asks: > > > r^12 = 2 or r = the twelth root of 2 > > > >Is this right ??? > > Robert Scot replies > Yes, that's where it comes from. ALLRIGHT!!. Where were you when it took me a 1.5 years to get through math 104? Robert writes In case you're wondering how to use > a hand calculator to solve this for r, just take the logarithm of both sides: then use the inverse log button to get r. > Richard replies Hmm I forgot about logs, and my W95 Calculator (Start, programs, accessories, calculator) doesn't have inverse log. But considering the nth root of a number in computer terms is x^1/n to find the twelth root of 2 using W95 calculator ( go to view and choose scientific) press [2] then [*] then[x^y] then [12] then [1/x] finally [=] and you should get 1.059463094359 To check its validity, hit [ms] then [*] then [27.5] [=] and the reslut is the frequency of A# (key number 2). If you do this 12 times you should get the octave or 55. or A of key # 13. On the calculator it goes [27.5] [*] [MR] [x^y] [12] [=] 55 ( [MR] is the stored value of twelth root of 2) Using the number 48 in place of 12 you get 440 Voila Now for a brain tickler, if you multiply 27.5 times 1.059463094359 88 times what note do you get ?? Hint 27.5 is the freq of the first (lowest) note (A) on the piano. Gee Math sure is fun with a calculator especially when you don't have to sweat a grade. Next the results of a 1.5 fifth in 7 steps compared to 12 fifths in 7 octaves. Richard Heflunkedslideruleinninthgrade Moody
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