Re : Re : [tuning] Re: temperament equal(new?)

genewardsmith@juno.com

> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>> --- In tuning@y..., "Wim Hoogewerf" <wim.hoogewerf@f...> wrote:
>
>> > After the equal division of the octave and the equal division of
>> the fifth,
>> > the next step could be the equal division of the major third into
> 4
>> steps
>> > (4th root of 1.25) and simply forget about the octave as an
> imposing
>> > interval.
>
>> Watch out -- the octaves in this system would be 41 cents flat!
> Ouch!
>
> I think it would make much more sense to take 5^(1/28) as basic; then
> 3/2 ~ 5^(1/4) is 5.4 cents flat and 2 ~ 5^(3/7) is 5.9 cents flat.
>
> If we are seeking after the bizarre, we could tune to intervals
> derived from zeros of the Riemann Zeta function on the critical line
> in the hope that this might represent some condition of maximum
> perversity. The tunings nearest the 12-et are 11.8226, 18 cents
> sharp, and 12.2485, 25 cents flat.

I simply mentioned this possibility as a sort of answer to Mr. Dimitrov.
It's pure phantasy/theory. First the octave, then the fifth, next comes the
major third. Right?

-Wim Hoogewerf

--- Wim Hoogewerf <wim.hoogewerf@fnac.net> a �crit�:
> genewardsmith@juno.com
>
> > --- In tuning@y..., "Paul Erlich" <paul@s...>
> wrote:
> >> --- In tuning@y..., "Wim Hoogewerf"
> <wim.hoogewerf@f...> wrote:
> >
> >> > After the equal division of the octave and the
> equal division of
> >> the fifth,
> >> > the next step could be the equal division of
> the major third into
> > 4
> >> steps
> >> > (4th root of 1.25) and simply forget about the
> octave as an
> > imposing
> >> > interval.
> >
> >> Watch out -- the octaves in this system would be
> 41 cents flat!
> > Ouch!
> >
> > I think it would make much more sense to take
> 5^(1/28) as basic; then
> > 3/2 ~ 5^(1/4) is 5.4 cents flat and 2 ~ 5^(3/7) is
> 5.9 cents flat.
> >
> > If we are seeking after the bizarre, we could tune
> to intervals
> > derived from zeros of the Riemann Zeta function on
> the critical line
> > in the hope that this might represent some
> condition of maximum
> > perversity. The tunings nearest the 12-et are
> 11.8226, 18 cents
> > sharp, and 12.2485, 25 cents flat.
>
> I simply mentioned this possibility as a sort of
> answer to Mr. Dimitrov.
> It's pure phantasy/theory. First the octave, then
> the fifth, next comes the
> major third. Right?
>
> -Wim Hoogewerf
Not :)) Because this order is very similar to the
order of...harmonics !!! Fyrst harmonic=octave,
second=octave+fifth and the 3th ? Octave+octave and
not the major third...

Mr Dimitrov

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