Re: [tuning] Re: ¿ cents value for 1048576/531441? (short&2t.pt)

> From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Friday, May 02, 2003 10:10 PM
> Subject: [tuning] Re: � cents value for 1048576/531441? (short&2t.pt)
>
>
> --- In tuning@yahoogroups.com, czhang23@a... wrote:
> >
> > Quick quick what is the cents value for
> > 1048576/531441? I can't find it anywhere in my
> > books, my calculator sux beyond a certain point,
> > and no website that I know of has it listed...
> >
> > Thanx.
>
> if you know that the pythagorean comma is 23.5 cents,
> then you can see this is just 1200 - 23.5 = 1176.5 cents.

Micosoft Excel gives me this:

1048576/531441 = (2^20)*(3^-12) = ~1176.53999 cents.

you could pretty much say that it's 1176.54 cents.

Excel often truncates long strings of decimal
places to 7 or 8 decimal places, but here it
only rounds to 5.

to explain what paul said:

(2^-19)*(3^12) is the prime-factorization of
the Pythagorean comma, very nearly 23.46 cents.

inverting the signs of the exponents,
(2^19)*(3^-12) is a "negative Pythagorean comma",
approximately -23.46 cents.

adding an "8ve" (1200 cents) to this,
-23.46 + 1200 = 1176.54 cents.

algebraically, -23.46 + 1200 simplifies to
1200 - 23.46, which is basically what paul wrote.

-monz