Re: [tuning] Re: Some magic meantones

hi Gene,

i've shifted this thread over to here so as
not to bother the regular tuning list members.

as usual, i sense intuitively that the explanation
you've provided for me below has some real insight
buried in it somewhere ... but it's so cryptic
that i have no idea what you're saying.

can you please explain the numbers in brackets?

how do "we see that ... 7/26[-comma meantone]
is marginal for minor triads and really stinks
for major triads"? based on my understanding of
Woolhouse's work, i thought this was an "optimal"
meantone. ...?

(i apologize for being stupid, as the cause of
it is simply my lack of reading and following your
many posts here. thanks.)

-monz

----- Original Message -----
From: <gwsmith@svpal.org>
To: <tuning@yahoogroups.com>
Sent: Friday, February 28, 2003 3:56 PM
Subject: [tuning] Re: Some magic meantones

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> >
> > i don't know if 3/14-comma is "magic", but it and
> > 7/26-comma are the only fraction-of-a-comma meantones
> > in my list that you left out of yours ... was that
> > simply an oversight, or are those two not "magic"?
>
> "Magic" is a relative term. We have
>
> 3/14-comma brat = 15/4 major [15/4, -10/9, -6/15]
> minor [5/2, 3/10, 4/3]
>
> 7/26-comma brat = -15/4 major [-15/4, 10/21, -14/15]
> minor [-5/2, 7/10, -4/7]
>
> 4/15-comma brat = -9/2 major [-9/2, 5/12, -8/15]
> minor [-3, -2/3, -1/2]
>
> Note that if any one of the three, q-comma, major ratios,
> minor ratios, is exact, the other two are approximate.
>
> We see 4/15-comma is good for minor triads and marginal
> for major ones, 3/14-comma is pretty good for minor triads
> and fairly awful for major triads, and 7/26 is marginal for
> minor triads and really stinks for major triads.

monz, gene is talking about the *beat rate ratios* in the close-
voiced root-position triads, since bob brought that up. getting
different beatings into rhythmic synchrony with one another was *not*
one of woolhouse's criteria.

--- In tuning-math@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Gene,
>
>
> i've shifted this thread over to here so as
> not to bother the regular tuning list members.
>
> as usual, i sense intuitively that the explanation
> you've provided for me below has some real insight
> buried in it somewhere ... but it's so cryptic
> that i have no idea what you're saying.
>
> can you please explain the numbers in brackets?
>
> how do "we see that ... 7/26[-comma meantone]
> is marginal for minor triads and really stinks
> for major triads"? based on my understanding of
> Woolhouse's work, i thought this was an "optimal"
> meantone. ...?
>
> (i apologize for being stupid, as the cause of
> it is simply my lack of reading and following your
> many posts here. thanks.)
>
>
> -monz
>
>
> ----- Original Message -----
> From: <gwsmith@s...>
> To: <tuning@yahoogroups.com>
> Sent: Friday, February 28, 2003 3:56 PM
> Subject: [tuning] Re: Some magic meantones
>
>
> > --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > >
> > > i don't know if 3/14-comma is "magic", but it and
> > > 7/26-comma are the only fraction-of-a-comma meantones
> > > in my list that you left out of yours ... was that
> > > simply an oversight, or are those two not "magic"?
> >
> > "Magic" is a relative term. We have
> >
> > 3/14-comma brat = 15/4 major [15/4, -10/9, -6/15]
> > minor [5/2, 3/10, 4/3]
> >
> > 7/26-comma brat = -15/4 major [-15/4, 10/21, -14/15]
> > minor [-5/2, 7/10, -4/7]
> >
> > 4/15-comma brat = -9/2 major [-9/2, 5/12, -8/15]
> > minor [-3, -2/3, -1/2]
> >
> > Note that if any one of the three, q-comma, major ratios,
> > minor ratios, is exact, the other two are approximate.
> >
> > We see 4/15-comma is good for minor triads and marginal
> > for major ones, 3/14-comma is pretty good for minor triads
> > and fairly awful for major triads, and 7/26 is marginal for
> > minor triads and really stinks for major triads.

hi paul,

thanks. i've been following the thread enough
to surmise that those numbers had something to
do with beat ratios, but i'm still very unclear
as to what the numbers are actually representing,
as Gene posted them without any kind of label.

for example,

>> 4/15-comma brat = -9/2 major [-9/2, 5/12, -8/15]
>> minor [-3, -2/3, -1/2]
>>
>> ... We see 4/15-comma is good for minor triads
>> and marginal for major ones

OK, so i can see that the numbers for minor are
both smaller and less complex than those for major.
but what *exactly* does "minor [-3, -2/3, -1/2]"
*signify*?

can i please get a real explanation of that?

and what's the "-9/2"?

Gene and/or paul or anyone else: since my question
about 2/7-comma meantone the other day, i've gotten
very intrigued by it, and have been doing a lot of
research into it. can we please use that as an example?

thanks.

-monz

> From: <wallyesterpaulrus@yahoo.com>
> To: <tuning-math@yahoogroups.com>
> Sent: Saturday, March 01, 2003 1:01 PM
> Subject: [tuning-math] [tuning] Re: Some magic meantones
>
>
> monz, gene is talking about the *beat rate ratios* in the close-
> voiced root-position triads, since bob brought that up. getting
> different beatings into rhythmic synchrony with one another was *not*
> one of woolhouse's criteria.
>
> --- In tuning-math@yahoogroups.com, "monz" <monz@a...> wrote:
> > hi Gene,
> >
> >
> > i've shifted this thread over to here so as
> > not to bother the regular tuning list members.
> >
> > as usual, i sense intuitively that the explanation
> > you've provided for me below has some real insight
> > buried in it somewhere ... but it's so cryptic
> > that i have no idea what you're saying.
> >
> > can you please explain the numbers in brackets?
> >
> > how do "we see that ... 7/26[-comma meantone]
> > is marginal for minor triads and really stinks
> > for major triads"? based on my understanding of
> > Woolhouse's work, i thought this was an "optimal"
> > meantone. ...?
> >
> > (i apologize for being stupid, as the cause of
> > it is simply my lack of reading and following your
> > many posts here. thanks.)
> >
> >
> > -monz
> >
> >
> > ----- Original Message -----
> > From: <gwsmith@s...>
> > To: <tuning@yahoogroups.com>
> > Sent: Friday, February 28, 2003 3:56 PM
> > Subject: [tuning] Re: Some magic meantones
> >
> >
> > > --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > > >
> > > > i don't know if 3/14-comma is "magic", but it and
> > > > 7/26-comma are the only fraction-of-a-comma meantones
> > > > in my list that you left out of yours ... was that
> > > > simply an oversight, or are those two not "magic"?
> > >
> > > "Magic" is a relative term. We have
> > >
> > > 3/14-comma brat = 15/4 major [15/4, -10/9, -6/15]
> > > minor [5/2, 3/10, 4/3]
> > >
> > > 7/26-comma brat = -15/4 major [-15/4, 10/21, -14/15]
> > > minor [-5/2, 7/10, -4/7]
> > >
> > > 4/15-comma brat = -9/2 major [-9/2, 5/12, -8/15]
> > > minor [-3, -2/3, -1/2]
> > >
> > > Note that if any one of the three, q-comma, major ratios,
> > > minor ratios, is exact, the other two are approximate.
> > >
> > > We see 4/15-comma is good for minor triads and marginal
> > > for major ones, 3/14-comma is pretty good for minor triads
> > > and fairly awful for major triads, and 7/26 is marginal for
> > > minor triads and really stinks for major triads.