rational approximations to logarithms (was: simple math question)

> 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

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