The math behind perfect 5th tuning

[Richard Moody]

----------
> 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