Fwd: Re: 41 "miracle" and 43 tone scales

--- In tuning-math@y..., graham@m... wrote:
In-Reply-To: <9h8hfa+ki4n@e...>
Dave Keenan wrote:

> > In that case, you'd expect the result to look
> something like
> > a 41-note MOS of a good 11-limit temperament. The scale he ends
up
> with does
> > fit schismic better than Miracle.
>
> Please give details. How many holes in a chain that encompasses it.
> How big are the errors? Are there any overloads? Maybe on the other
> list.

The 43 notes become a 41 note schismic MOS, with duplicates exactly
where
you expect them. Wilson showed this. You get the same 41 note MOS
with
either the Exposition of Monophony or Genesis 43 note scales.

Graham
--- End forwarded message ---

Dave, your response?

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> The 43 notes become a 41 note schismic MOS, with duplicates exactly
> where
> you expect them. Wilson showed this. You get the same 41 note MOS
> with
> either the Exposition of Monophony or Genesis 43 note scales.
>
>
> Graham
> --- End forwarded message ---
>
> Dave, your response?

I've responded to thi sin responding to an earlier message. In
summary:

There are actually two schismic mappings from Wilson. One has two
overloads (-2 holes or 2 free electrons), the other has 20 holes.
Miracle-45 has 2 holes. I find overloads unacceptable and 20 holes is
too many.

-- Dave Keenan

--- In tuning@y..., "Dave Keenan"
<D.KEENAN@U...> wrote:

> There are actually two schismic mappings from Wilson. One has two
> overloads (-2 holes or 2 free electrons), the other has 20 holes.
> Miracle-45 has 2 holes. I find overloads unacceptable and 20 holes is
> too many.

Why do you find overloads
unacceptable?

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., "Dave Keenan"
> <D.KEENAN@U...> wrote:
>
> > There are actually two schismic mappings from Wilson. One has two
> > overloads (-2 holes or 2 free electrons), the other has 20 holes.
> > Miracle-45 has 2 holes. I find overloads unacceptable and 20 holes
is
> > too many.
>
> Why do you find overloads
> unacceptable?

Well if Partch really wanted those two notes to be separate, who are
we to say they have to share a key. Or else one of them ends up
somewhere else such that it doesn't fit the standard chord patterns
for the keyboard mapping.