Re: superparticular subdivision of 3^12:2^19 for Bachs 1723 WTC tuning instruction

--- In tuning-math@yahoogroups.com, "a_sparschuh" <a_sparschuh@y...>
wrote:

> All the tempered 5ths beat equal synchronous at same
> frequency of just one single Hz

I'm surprised Gene hasn't remarked on this, considering his extensive
posts here on synchronized-beating temperaments like two years ago. It
would be interesting to know how this strategy compares with other
synchronized-beating circulating temperaments such as Robert Wendell's
and the ones Gene derived from polynomial equations.

Of course, I don't want to distract Gene from answering my Kees tuning
posts, assuming he hasn't forgotten about those . . .

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:

> Of course, I don't want to distract Gene from answering my Kees tuning
> posts, assuming he hasn't forgotten about those . . .

No one responded to my Kees tuning web page, so I thought we'd wrapped
that topic up for now. It seems you can't prove Kees tuning is
stretched TOP tuning, because sometimes it is, and sometimes it isn't.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
>
> > Of course, I don't want to distract Gene from answering my Kees
tuning
> > posts, assuming he hasn't forgotten about those . . .
>
> No one responded to my Kees tuning web page, so I thought we'd wrapped
> that topic up for now.

You have an odd way of communicating with people, Gene. When you post
something on a *discussion* list and someone asks you what you meant by
that (for example 'the constraint' you referred to), or asks you
specific questions about what you posted (as I did for some
calculations and other symbols), ignoring the questions doesn't
tend "wrap up the topic" in other people's eyes. It is almost as if the
only person's understanding that matters anything to you is your own.
This is a very poor strategy in any kind of collaborative endeavor.
Instead, one should aim for the opposite -- constantly work to remain
and keep others cognizant of:

1) Your understanding of the material;
2) Others' understanding of the material;
3) What you understand about the understanding of others;
4) What others understand about your understanding.

> It seems you can't prove Kees tuning is
> stretched TOP tuning, because sometimes it is, and sometimes it isn't.

But it seems that when it isn't, the TOP tuning you started with was
only one of several possible, equally optimal choices. And another one
of those choices would have led to the Kees tuning. Right or wrong?

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:

> But it seems that when it isn't, the TOP tuning you started with was
> only one of several possible, equally optimal choices. And another one
> of those choices would have led to the Kees tuning. Right or wrong?

I guess you could argue that for the 5-limit, but the whole thing is
going to break down anyway as you go uplimit. Why not simply address
Kees tuning on its own terms, and keep stretched TOP tuning in mind
also as an interesting tuning option?

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
>
> > But it seems that when it isn't, the TOP tuning you started with
was
> > only one of several possible, equally optimal choices. And
another one
> > of those choices would have led to the Kees tuning. Right or
wrong?
>
> I guess you could argue that for the 5-limit, but the whole thing is
> going to break down anyway as you go uplimit.

Are you sure? How do you know that? I could imagine rhombic
dodecahedra replacing the hexagons in the 7-limit, and I'd be really
surprised if suddenly things broke down there.

> Why not simply address
> Kees tuning on its own terms, and keep stretched TOP tuning in mind
> also as an interesting tuning option?

I'd like to do that but even addressing it in it own terms with you,
you fell silent.

But the deep connection that my plot points out that interests me.
And that the whole "metastructure" of

tonespace - projective tonespace - duality - projective tuningspace -
tuningspace

seems to relate to Kees tuning in a fundamental way interests me.

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
> --- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:

> > I guess you could argue that for the 5-limit, but the whole thing is
> > going to break down anyway as you go uplimit.
>
> Are you sure? How do you know that? I could imagine rhombic
> dodecahedra replacing the hexagons in the 7-limit, and I'd be really
> surprised if suddenly things broke down there.

The Tenney metric unit ball has 2^n corners in n space, whereas the
Kees unit ball has 2n(n-1) corners, so they can't very well correspond.

> I'd like to do that but even addressing it in it own terms with you,
> you fell silent.

I didn't. I posted a web page, and got no comments in return.

> But the deep connection that my plot points out that interests me.
> And that the whole "metastructure" of
>
> tonespace - projective tonespace - duality - projective tuningspace -
> tuningspace

Lots to be said there, I suppose. There's also projective space stuff
going on with regular temperaments in general, connected with
Grassmann varieties, but I've been avoiding wading into that much.
>
> seems to relate to Kees tuning in a fundamental way interests me.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
> > --- In tuning-math@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...>
> > wrote:
>
> > > I guess you could argue that for the 5-limit, but the whole
thing is
> > > going to break down anyway as you go uplimit.
> >
> > Are you sure? How do you know that? I could imagine rhombic
> > dodecahedra replacing the hexagons in the 7-limit, and I'd be
really
> > surprised if suddenly things broke down there.
>
> The Tenney metric unit ball has 2^n corners in n space, whereas the
> Kees unit ball has 2n(n-1) corners, so they can't very well
>correspond.

Why is this not a problem in the 5-limit, then? The Kees unit ball
there has 6 corners, which is clearly not a power of 2, and yet it
all seems to work out there.

And if you're so sure, why don't you give a specific counterexample?

> > I'd like to do that but even addressing it in it own terms with
you,
> > you fell silent.
>
> I didn't. I posted a web page, and got no comments in return.

OK, I owe you some comments. So can I expect to see some sort of
answers to all my questions when I view the webpage? If so, I had no
idea.

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:

> Why is this not a problem in the 5-limit, then? The Kees unit ball
> there has 6 corners, which is clearly not a power of 2, and yet it
> all seems to work out there.

The six corners lead to three lines from the center. The eight corners
for Tenney lead to four lines, but one of the lines isn't relevant,
since it corresponds with the zero "temperament". So in this case they
correspond, but even so the Kees and IOP tunings are not the same for
one of the lines.

> And if you're so sure, why don't you give a specific counterexample?

A seven-limit temperament where the Kees tuning is not a stretched TOP
tuning, or what?

> OK, I owe you some comments. So can I expect to see some sort of
> answers to all my questions when I view the webpage? If so, I had no
> idea.

Actually, I was under the impression I did answer them.

>> And if you're so sure, why don't you give a specific counterexample?
>
>A seven-limit temperament where the Kees tuning is not a stretched TOP
>tuning, or what?

I think that's what he meant.

Is "stretched TOP" the same as NOT?

-Carl

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

> A seven-limit temperament where the Kees tuning is not a stretched TOP
> tuning, or what?

Yes, that would do it.

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> Is "stretched TOP" the same as NOT?

NOT!

>> Is "stretched TOP" the same as NOT?
>
>NOT!

Thanks.

Say, 'dyou ever putthis back up?

http://66.98.148.43/~xenharmo/meanwil.html

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> Is "stretched TOP" the same as NOT?
> >
> >NOT!
>
> Thanks.
>
> Say, 'dyou ever putthis back up?
>
> http://66.98.148.43/~xenharmo/meanwil.html

Where does it link from?

>> >> Is "stretched TOP" the same as NOT?
>> >
>> >NOT!
>>
>> Thanks.
>>
>> Say, 'dyou ever putthis back up?
>>
>> http://66.98.148.43/~xenharmo/meanwil.html
>
>Where does it link from?

Your brats page.

-Carl

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
>
> > Why is this not a problem in the 5-limit, then? The Kees unit
ball
> > there has 6 corners, which is clearly not a power of 2, and yet
it
> > all seems to work out there.
>
> The six corners lead to three lines from the center. The eight
corners
> for Tenney lead to four lines, but one of the lines isn't relevant,
> since it corresponds with the zero "temperament". So in this case
they
> correspond, but even so the Kees and IOP tunings are not the same
for
> one of the lines.
>
> > And if you're so sure, why don't you give a specific
counterexample?
>
> A seven-limit temperament where the Kees tuning is not a stretched
TOP
> tuning, or what?
>
> > OK, I owe you some comments. So can I expect to see some sort of
> > answers to all my questions when I view the webpage? If so, I had
no
> > idea.
>
> Actually, I was under the impression I did answer them.

Where?

Here:

http://66.98.148.43/~xenharmo/kees.htm

or in actual posts?