Two to the one twelth power

[Bruce D. Rempe]

When I ask excel to take it to 30 places after the decimal.  I get
1.059463094359300000000000000000

So, it seem to end at the 3.  If you take this to the 12th power, you get
exactly 2 (at least excel does).

-bruce
 

> -----Original Message-----
> From: pianotech-bounces at ptg.org 
> [mailto:pianotech-bounces at ptg.org] On Behalf Of John Delacour
> Sent: Saturday, September 30, 2006 11:35 AM
> To: Pianotech List
> Subject: Re: Two to the one twelth power
> 
> At 4:42 am -0400 30/9/06, KeyKat88 at aol.com wrote:
> 
> >Greetings,
> >
> >        Punching 2 to the 1/12 power into my calculator, it gives me 
> >1.05946285.
> 
> You must have a bad calculator. The figure to 8 decimal places is
> 
>    1.05946309
> 
> or to 13 places
> 
>    1.0594630943593
> 
> But it's no use using a level of precision your calculator 
> doesn't understand.
> 
> >   How far does this number go on? Is it a number like Pi 
> that goes on and on?
> 
> Probably not, but it doesn't matter.
> 
> >  What sort of software will let me see how far it can go?  If I am 
> >doing harmony calculations, how far is it practical to go? 
> What is the 
> >norm?
> 
> As with all sorts of measurement you need to decide what 
> degree of error is acceptable.
> 
> If you raise 1.05946309435929526 to the 96th power, you will 
> get 2560.00000000001 instead of 2560
> 
> 
> If you use 1.05946309 you will get 2559.99991665553
> 
> Using 2^(1/12) in your formula will give you the maximum 
> precision available, but whatever you use will be quite 
> accurate enough for your needs given the frequency range of 
> audible sound.
> 
> JD
> 
> 
> 
>