> From: monz <joemonz@yahoo.com>

> To: <tuning-math@yahoogroups.com>

> Sent: Saturday, February 02, 2002 11:44 AM

> Subject: Re: [tuning-math] simple math question

>

>

> there are some very good low-integer-ratio approximations to

> the log_10 of the lowest primes

>

>

> Examples:

>

> log_10 ~fractional value

> of: of logarithm

>

> more accurate less accurate

>

> 2 3/10

> 3 10/21 = ~1/2

> 5 7/10

> 7 11/13 = ~5/6

> 11 25/24

> 13 39/35 = ~10/9

> 17 16/13 = ~11/9

> 19 23/18 = ~14/11 = ~5/4

in fact, i observed before that 3/10 showed up in a sumerian

calculation which i think relates to tuning -- see the middle of

http://www.ixpres.com/interval/monzo/sumerian/sumeriantuning.htm

i had a hunch there that this had something to do with tempering,

and now i realize why i had that hunch

3/10 is so close to the log_10(2) that it would serve just fine

as an approximation in doing calculations by hand

hmmm ....

-monz

_________________________________________________________

Do You Yahoo!?

Get your free @yahoo.com address at http://mail.yahoo.com