RE: [tuning] Re: well-temperament wazoo

Monz,

I don't know how you're getting that from the numbers I posted! You must be
misintepreting in some way, but I can't see how. Can you show your reasoning
with an example or two?

-Paul

> [Paul Erlich, http://www.egroups.com/message/tuning/11858]
>
> Monz,
>
> I don't know how you're getting that from the numbers I posted!
> You must be misintepreting in some way, but I can't see how.
> Can you show your reasoning with an example or two?
>

Go to:
http://www.egroups.com/files/tuning/monz/HE-minimizer/he-wts.htm

I've made a webpage table out of the numbers for the first
16 scales you posted which show signification deviation from
12-tET, with a chart graphing those deviations.

The numbers along the x-axis refer to the place in the cycle
where the '5ths' fall; for example, '1' means C:G, '2' means G:D,
etc.

It's easy to see on the graph what I wrote about here:
http://www.egroups.com/message/tuning/11857

-monz
http://www.ixpres.com/interval/monzo/homepage.html

Hey Monz,

I see what you mean now, and I hadn't noticed that before! But you're not
right to assume that each circle starts at C. As I mentioned before, all
modes are equivalent, so to use these well-temperaments in their traditional
manner, you'd transpose them so that the widest fifth is always at G#-Eb.

After doing that, see if you can see a subtle feature in the structure of
all of the ones that differ significantly from 12-tET.

-Paul

> [Paul Erlich]
> http://www.egroups.com/message/tuning/11862
>
> Hey Monz,
>
> I see what you mean now, and I hadn't noticed that before!
> But you're not right to assume that each circle starts at C.

My bad.

> As I mentioned before, all modes are equivalent, so to use these
> well-temperaments in their traditional manner, you'd transpose
> them so that the widest fifth is always at G#-Eb.
>
> After doing that, see if you can see a subtle feature in the
> structure of all of the ones that differ significantly from
> 12-tET.

OK, I did do that now, and the only significant pattern I can
see is that the first six '5ths' (C:G:D:A:E:B:F#) are always
pretty close to 700 cents, and the latter six (F#:C#:G#:Eb:Bb:F:C)
deviate more widely.

(Unfortunately - ooh I LOOOOOVE Windows! - Excel crashed before
I had saved this version of my spreadsheet. I'm not going to
go thru all that work again... so I had to just summarize what
I remember seeing...)

Is that what you were talking about?

-monz
http://www.ixpres.com/interval/monzo/homepage.html

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:

> OK, I did do that now, and the only significant pattern I can
> see is that the first six '5ths' (C:G:D:A:E:B:F#) are always
> pretty close to 700 cents, and the latter six (F#:C#:G#:Eb:Bb:F:C)
> deviate more widely.

> Is that what you were talking about?

No, that's the same pattern that others already mentioned, and is
pretty much true of all historical well-temperaments. But there is a
subtler feature common to those, of the ones my optimizer got stuck
on, which differed significantly from 12-tET. Can you spot it?