Fwd: [tuning] Re: phi and pi connection - 600 cents???

Thanks Cameron;

After 44 steps of fourths or fifths LucyTuning arrives at approx. +/-
1.7¢ from 600 cents.

i.e from A by fifths at (B6#) B followed by six sharps = 601.6905 cents.

A by fourths at (D6b)D followed by six flats = 598.3095 cents

I can see no reason why it should ever arrive at exactly 600¢.

Hence LucyTuning can be approximated by 88 edo.

It gets even closer with 1420 edo, so check what happens at 710 steps;-)

Charles Lucy lucy@lucytune.com

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Begin forwarded message:

> From: "Cameron Bobro" <misterbobro@yahoo.com>
> Date: 25 September 2007 20:33:18 BDT
> To: tuning@yahoogroups.com
> Subject: [tuning] Re: phi and pi connection
> Reply-To: tuning@yahoogroups.com
>
> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >
> > Thanks for clarifying that Keenan;
> >
> > I'll play with the numbers;-)
> >
> > As a matter of mathematical interest, in the mid 1970's, the
> > mathematical connection between pi and phi was found.
> >
> > Details here:
> >
> > http://www.lucytune.com/academic/pi_phi.html
>
> I don't see the most obvious pi/circle connection,
> 2cos(Pi/5), which is especially odd since, if I'm not
> mistaken, 600 cents is used in Lucy Tuning and 600 cents
> can be found exactly the same way (from equal division of
> Pi): 2cos(Pi/4).
>
> -Cameron Bobro
>
>
>

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:

> I can see no reason why it should ever arrive at exactly 600¢.

It cannot ever arrive at 600 cents. That would require that there be
integers a and b such that 1200a + 600b + 300b/pi = 600. Since pi is
irrational, this is impossible.