updated "positive" and "negative" definitions

OK, have a look now:

http://www.ixpres.com/interval/dict/negative.htm
http://www.ixpres.com/interval/dict/positive.htm

But I'm confused about one thing: on the "negative" page,
I have 53- and 65-EDO listed as negative temperaments,
and they do indeed have negatively-tempered "5ths", but
they both have p = +1. ?????

-monz

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Well I wouldn't object to still calling a schismic
temperament "meantone", but you should make the distinction
between negative systems and negative temperaments
and positive systems and positive temperaments clear to
avoid this confusion.

Manuel

monz wrote:

> But I'm confused about one thing: on the "negative" page,
> I have 53- and 65-EDO listed as negative temperaments,
> and they do indeed have negatively-tempered "5ths", but
> they both have p = +1. ?????

Hasn't this been answered? It seems to be the first question coming round
again. 53-EDO has fifths larger than 700 cents, but smaller than a 3:2
ratio.

One use for the terminology that I haven't seen mentioned is that it tells
you whether pitch will rise or fall as you go up one column of the
Bosanquet keyboard. The 12-centricity is because Bosanquet's keyboard did
have 12 columns. Wilson's layout can have 7 or 5 columns if you hold it
the right way up, hence he generalized the terminology to be 5- or
7-centric as well.

I have other stuff about this at
<http://x31eq.com/notakey.htm>. That's somewhat out of date,
but mostly holds. The & notation, for which I'm using an & again, is the
most successful.

Graham

> From: <graham@microtonal.co.uk>
> To: <tuning-math@yahoogroups.com>
> Sent: Saturday, January 12, 2002 3:28 AM
> Subject: [tuning-math] Re: updated "positive" and "negative" definitions
>
>
> monz wrote:
>
> > But I'm confused about one thing: on the "negative" page,
> > I have 53- and 65-EDO listed as negative temperaments,
> > and they do indeed have negatively-tempered "5ths", but
> > they both have p = +1. ?????
>
> Hasn't this been answered? It seems to be the first question coming round
> again. 53-EDO has fifths larger than 700 cents, but smaller than a 3:2
> ratio.

Duh! Thanks, Graham. That's pretty obvious, isn't it?
So I was really confused over this 12-EDO/Pythagorean question.

> One use for the terminology that I haven't seen mentioned is that it tells
> you whether pitch will rise or fall as you go up one column of the
> Bosanquet keyboard. The 12-centricity is because Bosanquet's keyboard did
> have 12 columns. Wilson's layout can have 7 or 5 columns if you hold it
> the right way up, hence he generalized the terminology to be 5- or
> 7-centric as well.
>
> I have other stuff about this at
> <http://x31eq.com/notakey.htm>. That's somewhat out of date,
> but mostly holds. The & notation, for which I'm using an & again, is the
> most successful.

Cool, thanks!

-monz

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