Re: [tuning] raintree's scale

> From: monz <joemonz@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, December 16, 2001 6:06 AM
> Subject: [tuning] raintree's scale (was: (unknown))
>
>
> When you write "this fifth is almost perfectly circular", what
> you mean is that 16384:10935 is only a skhisma (~2 cents) lower
> than the typical Pythagorean "5th" with ratio 3:2, so that it
> very closely resembles the "5th" of 700 cents found in 12-EDO,
> which is a closed system.

2^(168/12) * 3^-7 * 5^-1
- 2^(7/12) * 3^0 * 5^0
--------------------------
2^(161/12) * 3^-7 * 5^-1 = ~0.001280077 cent = ~ 1/781 cent

A very tiny discrepancy indeed.

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

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--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > From: monz <joemonz@y...>
> > To: <tuning@y...>
> > Sent: Sunday, December 16, 2001 6:06 AM
> > Subject: [tuning] raintree's scale (was: (unknown))
> >
> >
> > When you write "this fifth is almost perfectly circular", what
> > you mean is that 16384:10935 is only a skhisma (~2 cents) lower
> > than the typical Pythagorean "5th" with ratio 3:2, so that it
> > very closely resembles the "5th" of 700 cents found in 12-EDO,
> > which is a closed system.
>
>
>
> 2^(168/12) * 3^-7 * 5^-1
> - 2^(7/12) * 3^0 * 5^0
> --------------------------
> 2^(161/12) * 3^-7 * 5^-1 = ~0.001280077 cent = ~ 1/781 cent
>
>
> A very tiny discrepancy indeed.

Margo Schulter brought this up before -- I think Kirnberger proposed
this a method for tuning 12-tET -- of course the process would be
very cumbersome, as one would have to tune about 100 just pitches
just to get the 12 notes you want.