real equal beating not almost

Meta meantone if seeded with whole number integers will produce whole number beating . whether it is a whole number fraction of a comma seem insignificant.
it is the sound one wants. also metameantone allows for an infinite number of tones to be added.
It also allows each person to seed it how they wish , depending on the application all with the same property. in a sense it is a whole family of scales just like meta slendro or pelog.
there are an infinite number of them
what is gained by sticking with a whole number fraction in this case anyway? which is nothing more than an equal division of a just ratio. not what one would call a very consistent method to work with.
Conceptionally, if you look at it, the very idea is rather awkward. take the opposite- just ratios fractions of equal divisions or of an equal generator that leave some remainder.
talk about mixing apples and oranges.
And if you are interested in equal beating what is gained by having one that is 'almost' equal beating?

>
>Message: 1 > Date: Tue, 30 Aug 2005 00:19:47 -0000
> From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
>Subject: Re: Digest Number 3639
>
>I'm not sure if this is directly related, Kraig (but I'm willing to be >proved wrong!) -- I believe what George was talking about was much more >along the lines of this very recent post from Gene:
>
>/tuning/topicId_59904.html#59904
>
>In other words, for quite a number of simple n/d-comma meantones (such >as 1/7-comma, 2/11-comma, 1/5-comma, 3/11-comma, etc), the beat rate >ratios are *almost* (to quite a few digits!), but not quite, simple-
>integer ratios (2, 5/2, 3, and -3, respectively, for these examples). >Metameantone is not precisely a simple n/d-comma meantone and hence its >*exact* beat rate ratio of 1:1 is not a counterexample to this pattern. >There is, however, a simple n/d-comma meantone which has a beat rate >ratio of *almost* exactly 1:1 and hence follows this pattern, while of >course being an extremely close approximation to metameantone. I won't >spoil the answer for you Kraig should you decide to look into this >yourself.
>
>
> >
> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

Kraig, you missed the point and turned this into a value debate when
it never was one. If it sits better with you 'politically', you could
turn my statement around and have it say that meantone tunings with
*exact* simple-integer beat rate ratios happen to *almost* be simple-
ratio n/d-comma meantones, and it would be all the same to me. I was
simply trying to expand on George's observation in a friendly,
participatory manner.

> whether it is a whole number fraction of a comma seem
> insignificant.

I agree completely but this is what George started with so I jumped
off from there.

> also metameantone allows for an infinite
> number of tones to be added.

So does Lucy tuning, or 1/4-comma meantone, or just about anything.
What's the point?

> what is gained by sticking with a whole number fraction in this
>case
> anyway?

Absolutely nothing and you misread me if you think I think otherwise.

> Conceptionally, if you look at it, the very idea is rather
awkward.
> take the opposite- just ratios fractions of equal divisions or of
an
> equal generator that leave some remainder.
> talk about mixing apples and oranges.

Not sure what you mean here.

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> Meta meantone if seeded with whole number integers will produce
whole
> number beating . whether it is a whole number fraction of a comma
seem
> insignificant.
> it is the sound one wants. also metameantone allows for an
infinite
> number of tones to be added.
> It also allows each person to seed it how they wish , depending on
the
> application all with the same property. in a sense it is a whole
family
> of scales just like meta slendro or pelog.
> there are an infinite number of them
> what is gained by sticking with a whole number fraction in this
case
> anyway? which is nothing more than an equal division of a just
ratio.
> not what one would call a very consistent method to work with.
> Conceptionally, if you look at it, the very idea is rather
awkward.
> take the opposite- just ratios fractions of equal divisions or of
an
> equal generator that leave some remainder.
> talk about mixing apples and oranges.
> And if you are interested in equal beating what is gained by
having one
> that is 'almost' equal beating?
>
>
>
> >
> >Message: 1
> > Date: Tue, 30 Aug 2005 00:19:47 -0000
> > From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
> >Subject: Re: Digest Number 3639
> >
> >I'm not sure if this is directly related, Kraig (but I'm willing
to be
> >proved wrong!) -- I believe what George was talking about was much
more
> >along the lines of this very recent post from Gene:
> >
> >/tuning/topicId_59904.html#59904
> >
> >In other words, for quite a number of simple n/d-comma meantones
(such
> >as 1/7-comma, 2/11-comma, 1/5-comma, 3/11-comma, etc), the beat
rate
> >ratios are *almost* (to quite a few digits!), but not quite,
simple-
> >integer ratios (2, 5/2, 3, and -3, respectively, for these
examples).
> >Metameantone is not precisely a simple n/d-comma meantone and
hence its
> >*exact* beat rate ratio of 1:1 is not a counterexample to this
pattern.
> >There is, however, a simple n/d-comma meantone which has a beat
rate
> >ratio of *almost* exactly 1:1 and hence follows this pattern,
while of
> >course being an extremely close approximation to metameantone. I
won't
> >spoil the answer for you Kraig should you decide to look into this
> >yourself.
> >
> >
> >
> >
> >
> >
>
> --
> Kraig Grady
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
> The Wandering Medicine Show
> KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

Anyway, since it appears you're more interested in finding imagined
points of philosophical disagreement than in the mathematical
curiosity at hand, I'll just give the answer:

The fifth of metameantone is 695.6304 cents.

The fifth of 5/17-comma meantone is 695.6296 cents.

A difference of less than a thousandth of a cent.

To do better with a n/d-comma meantone, you have to go all the way to
452/1537-comma meantone!

You may rightly ask, who cares? Maybe only Joe Monzo does, since he's
attached to a particular way of drawing lattices of n/d-comma
meantones that doesn't extend to meantones more generally. But George
Secor brought up the observation (broadly speaking) and I thought it
would make an interesting point of discussion, a way to bring one of
the curiosities from tuning-math over here. I guess I'll know better
next time.

So just to clarify my position: There's absolutely no musical reason
I know of why anyone would prefer 5/17-comma meantone over true
metameantone. It's just an example of a curious mathematical
phenomenon that the two are very, very, very close.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> Kraig, you missed the point and turned this into a value debate
when
> it never was one. If it sits better with you 'politically', you
could
> turn my statement around and have it say that meantone tunings with
> *exact* simple-integer beat rate ratios happen to *almost* be
simple-
> ratio n/d-comma meantones, and it would be all the same to me. I
was
> simply trying to expand on George's observation in a friendly,
> participatory manner.
>
> > whether it is a whole number fraction of a comma seem
> > insignificant.
>
> I agree completely but this is what George started with so I jumped
> off from there.
>
> > also metameantone allows for an infinite
> > number of tones to be added.
>
> So does Lucy tuning, or 1/4-comma meantone, or just about anything.
> What's the point?
>
> > what is gained by sticking with a whole number fraction in this
> >case
> > anyway?
>
> Absolutely nothing and you misread me if you think I think
otherwise.
>
> > Conceptionally, if you look at it, the very idea is rather
> awkward.
> > take the opposite- just ratios fractions of equal divisions or of
> an
> > equal generator that leave some remainder.
> > talk about mixing apples and oranges.
>
> Not sure what you mean here.
>
>
>
> --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> > Meta meantone if seeded with whole number integers will produce
> whole
> > number beating . whether it is a whole number fraction of a comma
> seem
> > insignificant.
> > it is the sound one wants. also metameantone allows for an
> infinite
> > number of tones to be added.
> > It also allows each person to seed it how they wish , depending
on
> the
> > application all with the same property. in a sense it is a whole
> family
> > of scales just like meta slendro or pelog.
> > there are an infinite number of them
> > what is gained by sticking with a whole number fraction in this
> case
> > anyway? which is nothing more than an equal division of a just
> ratio.
> > not what one would call a very consistent method to work with.
> > Conceptionally, if you look at it, the very idea is rather
> awkward.
> > take the opposite- just ratios fractions of equal divisions or of
> an
> > equal generator that leave some remainder.
> > talk about mixing apples and oranges.
> > And if you are interested in equal beating what is gained by
> having one
> > that is 'almost' equal beating?
> >
> >
> >
> > >
> > >Message: 1
> > > Date: Tue, 30 Aug 2005 00:19:47 -0000
> > > From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
> > >Subject: Re: Digest Number 3639
> > >
> > >I'm not sure if this is directly related, Kraig (but I'm willing
> to be
> > >proved wrong!) -- I believe what George was talking about was
much
> more
> > >along the lines of this very recent post from Gene:
> > >
> > >/tuning/topicId_59904.html#59904
> > >
> > >In other words, for quite a number of simple n/d-comma meantones
> (such
> > >as 1/7-comma, 2/11-comma, 1/5-comma, 3/11-comma, etc), the beat
> rate
> > >ratios are *almost* (to quite a few digits!), but not quite,
> simple-
> > >integer ratios (2, 5/2, 3, and -3, respectively, for these
> examples).
> > >Metameantone is not precisely a simple n/d-comma meantone and
> hence its
> > >*exact* beat rate ratio of 1:1 is not a counterexample to this
> pattern.
> > >There is, however, a simple n/d-comma meantone which has a beat
> rate
> > >ratio of *almost* exactly 1:1 and hence follows this pattern,
> while of
> > >course being an extremely close approximation to metameantone. I
> won't
> > >spoil the answer for you Kraig should you decide to look into
this
> > >yourself.
> > >
> > >
> > >
> > >
> > >
> > >
> >
> > --
> > Kraig Grady
> > North American Embassy of Anaphoria Island <http://anaphoria.com/>
> > The Wandering Medicine Show
> > KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los
Angeles