undefined

don't have time to read this now, but it looks
interesting:

Kelly, Robert T. 2003.

_Charting Enharmonicism on the Just-Intonation Tonnetz:
A Practical Approach to Neo-Riemannian Analysis_

http://garnet.acns.fsu.edu/~rtk1218/justtonnetz.pdf

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> don't have time to read this now, but it looks
> interesting:
>
>
> Kelly, Robert T. 2003.
>
> _Charting Enharmonicism on the Just-Intonation Tonnetz:
> A Practical Approach to Neo-Riemannian Analysis_
>
> http://garnet.acns.fsu.edu/~rtk1218/justtonnetz.pdf
>
>
>
> -monz

This paper talks about many of the same things as my paper and things
I've been posting here in response to Joseph. Everyone here should
read it.

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > don't have time to read this now, but it looks
> > interesting:
> >
> >
> > Kelly, Robert T. 2003.
> >
> > _Charting Enharmonicism on the Just-Intonation Tonnetz:
> > A Practical Approach to Neo-Riemannian Analysis_
> >
> > http://garnet.acns.fsu.edu/~rtk1218/justtonnetz.pdf
> >
> >
> >
> > -monz

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> This paper talks about many of the same things as my paper and
things
> I've been posting here in response to Joseph. Everyone here should
> read it.

Kelley's ideal V7 is interesting; he ideally wants it to be 1-5/4-3/2-
25/14, which makes the 7th 1003.8, 3.8 cents sharper than 12-et.
Paul's favorite 9/5 is 17.6 cents sharper, 16/9 is 3.9 cents flatter,
and (smooth, man, smooth) 7/4 is 31.2 cents flatter. One
interpretation of what Kelly is doing here is that in effect, he is
going with meantone; 2/(25/14) = 28/25, and if this is taken to be a
tone of meantone, then the corresponding fifth is 2 sqrt(15)/5, a
698.1 meantone fifth, about 2/11-comma meantone, where we might
recall that 12-et is 1/11 comma.

His ideal or at least "cleanest compromise" diminished seventh is the
1-6/5-10/7-12/7 chord. He suggests this be reduced to the 5-limit as
1-6/5-64/45-128/75, which is equivalent in marvel (225/224-planar.)
He also suggests 1-6/5-7/5-9/5 could be reduced to the 5 limit as
1-32/27-64/45-16/9, which would involve 81/80 and 64/63, or in other
words the dominant temperament. He regards 1-6/5-36/25-9/5 as being a
more or less equivalent reduction, which under dominant it is,
involving 36/35, though you could get here just using 36/35-planar,
or bumping all the way up to 12-et.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > This paper talks about many of the same things as my paper and
> things
> > I've been posting here in response to Joseph. Everyone here
should
> > read it.
>
> Kelley's ideal V7 is interesting;

If I were Joseph, I'd ignore the V7 stuff in there for now . . .

> he ideally wants it to be 1-5/4-3/2-
> 25/14,

Well, this *is* very close to the dominant seventh chord in (huygens)
meantone, since a diminished fifth comes out as 10:7 there, and 5/4 *
10:7 = 25/14.

But really it's the parts of this paper that concern cylinders and
tori, and commas like 648:625 and the pythagorean comma
(531441:524288), that I wanted Joseph to look at . . .

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

> His ideal or at least "cleanest compromise" diminished seventh is
the
> 1-6/5-10/7-12/7 chord. He suggests this be reduced to the 5-limit as
> 1-6/5-64/45-128/75, which is equivalent in marvel (225/224-planar.)

Monz should take note that what Kelley is doing here and elsewhere
involves xenharmonic bridges. In fact, he could chart enharmonicism
on a just intonation tonnetz easily and consistently if he would just
pick a single xenharmonic bridge and stick with it. That means,
bridge using 36/35, 64/63, 126/125 or 225/224, but not all of them;
it seems clear however he has 12-equal on the brain, which is not
surprising considering the kind of music he is analyzing.

In case anyone wants to play this game, in 12-et you have xenharmonic
bridges to the 7-limit of 36/35, 64/63, 126/125, 225/224, and
5120/5103. If you were to analyze music in another et, you'd end up
with a different assortment of bridges; Paul for instance could
analyze music in the vast literature (which should exist, but alas
does not) in 22-et using 64/63, 875/864, 225/224, and 65625/645536.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> Paul for instance could
> analyze music in the vast literature (which should exist, but alas
> does not) in 22-et using 64/63, 875/864, 225/224, and 65625/645536.

I doubt I'd use that last one, as it's -3958 cents :)

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > This paper talks about many of the same things as my paper and
> things
> > I've been posting here in response to Joseph. Everyone here should
> > read it.
>
> Kelley's ideal V7 is interesting; he ideally wants it to
> be 1-5/4-3/2-25/14, which makes the 7th 1003.8, 3.8 cents
> sharper than 12-et.
>
> Paul's favorite 9/5 is 17.6 cents sharper, 16/9 is 3.9 cents
> flatter, and (smooth, man, smooth) 7/4 is 31.2 cents flatter.
>
> One interpretation of what Kelly is doing here is that
> in effect, he is going with meantone; 2/(25/14) = 28/25,
> and if this is taken to be a tone of meantone, then the
> corresponding fifth is 2 sqrt(15)/5, a 698.1 meantone fifth,
> about 2/11-comma meantone, where we might recall that 12-et
> is 1/11 comma.

the "standard" 1/4-comma meantone "minor-7th" is
~1006.843143 cents.

its close relative, the 31edo "minor-7th", is
~1006.451613 (exactly 1006 & 14/31) cents.

the 55edo "minor-7th" is 2^(46/55) and
~1003.636364 (exactly 1003 & 7/11) cents, which
is indeed very close to Kelly's "minor-7th".

55edo's close relative 1/6-comma meantone offers
~1003.258761 cents.

i knew right away that 55edo would be right nearby,
because 55edo does a great job of emulating 2/11-comma meantone.

-monz

hi Gene,

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

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> > His ideal or at least "cleanest compromise" diminished
> > seventh is the 1-6/5-10/7-12/7 chord. He suggests this
> > be reduced to the 5-limit as 1-6/5-64/45-128/75, which
> > is equivalent in marvel (225/224-planar.)
>
> Monz should take note that what Kelley is doing here and
> elsewhere involves xenharmonic bridges. In fact, he could
> chart enharmonicism on a just intonation tonnetz easily and
> consistently if he would just pick a single xenharmonic bridge
> and stick with it. That means, bridge using 36/35, 64/63,
> 126/125 or 225/224, but not all of them; it seems clear
> however he has 12-equal on the brain, which is not
> surprising considering the kind of music he is analyzing.

remember back in January 2002 when all of these ratios
kept coming up as unison-vectors in my analysis of
Schoenberg's theory?

/tuning-math/message/2798

12-equal on the brain for sure.

-monz

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > Paul for instance could
> > analyze music in the vast literature (which should exist, but
alas
> > does not) in 22-et using 64/63, 875/864, 225/224, and
65625/645536.
>
> I doubt I'd use that last one, as it's -3958 cents :)

There are an infinite number of arbitarily small xenharmonic bridges
you *could* use for 22-equal, but sadly, this isn't one of them.
Still, 65625/65536 might do ya.