Tuning Dictionary update: "Equal Temperament"

hello all,

a big update, with new names and lots of new links
in the list of composers/theorists, and some new
interval info in a few of the specific tunings, in
my Tuning Dictionary entry for "Equal Temperament":

http://www.ixpres.com/interval/dict/eqtemp.htm

(special thanks to Paul Erlich for much additional
new info for the list, and for his persistence in
"reminding" me to do the update!)

-monz
"all roads lead to n^0"

most excellent work, Monz - hats off!

Dante

> -----Original Message-----
> From: monz [mailto:monz@attglobal.net]
> Sent: Friday, September 13, 2002 5:16 PM
> To: tuning@yahoogroups.com
> Subject: [tuning] Tuning Dictionary update: "Equal Temperament"
>
>
> hello all,
>
>
> a big update, with new names and lots of new links
> in the list of composers/theorists, and some new
> interval info in a few of the specific tunings, in
> my Tuning Dictionary entry for "Equal Temperament":
>
> http://www.ixpres.com/interval/dict/eqtemp.htm
>
>
> (special thanks to Paul Erlich for much additional
> new info for the list, and for his persistence in
> "reminding" me to do the update!)
>
>
>
> -monz
> "all roads lead to n^0"
>
>
>
>
>
>
>
>
>
>
>
>
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--- In tuning@y..., "monz" <monz@a...> wrote:

I think a page linking to musical examples in various temperaments would be nice.

Awesome.

In the first graph there, I don't quite understand what are "X" and "y" in
this graph (and is there a "Z" (i.e. is it 3d?)

I'm sort of getting it, but not quite. . .

thanks much, Dante! it's always good to know that
my hard work is appreciated by my colleagues.

-monz

> From: "Dante Rosati" <dante.interport@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Friday, September 13, 2002 4:22 PM
> Subject: RE: [tuning] Tuning Dictionary update: "Equal Temperament"
>

> most excellent work, Monz - hats off!
>
> Dante
>
> > -----Original Message-----
> > From: monz [mailto:monz@attglobal.net]
> > Sent: Friday, September 13, 2002 5:16 PM
> > To: tuning@yahoogroups.com
> > Subject: [tuning] Tuning Dictionary update: "Equal Temperament"
> >
> >
> > hello all,
> >
> >
> > a big update, with new names and lots of new links
> > in the list of composers/theorists, and some new
> > interval info in a few of the specific tunings, in
> > my Tuning Dictionary entry for "Equal Temperament":
> >
> > http://www.ixpres.com/interval/dict/eqtemp.htm
> >
> >
> > (special thanks to Paul Erlich for much additional
> > new info for the list, and for his persistence in
> > "reminding" me to do the update!)
> >
> >
> >
> > -monz
> > "all roads lead to n^0"

hi Chris,

re:
http://www.ixpres.com/interval/dict/eqtemp.htm

> From: "Christopher Bailey" <cb202@columbia.edu>
> To: <tuning@yahoogroups.com>
> Sent: Saturday, September 14, 2002 6:10 AM
> Subject: [tuning] re: Tuning Dictionary update: "Equal Temperament"
>

>
> Awesome.
>
> In the first graph there, I don't quite understand what are
> "X" and "y" in this graph (and is there a "Z" (i.e. is it 3d?)
>
> I'm sort of getting it, but not quite. . .

in the *text description*, "x", "y", and "z" refer to the exponents
of the three prime-factors 2, 3, and 5.

for example, on the left side of the diagram you'll see the label
"meantone", and under it, the characteristic comma which vanishes.
in this case, the comma is labeled both as a ratio, 81:80,
and as a prime-factor exponent vector: [-4 4 -1].

that vector represents the expression 2^(-4) * 3^4 * 5^(-1), which
is the same as 1/16 * 81 * 1/5, which equals 81/80.

got it?

don't confuse my use of x, y, and z in the vector with the
dimensions of the graph. paul erlich created the original graph,
plotting various ETs against a triangular graph showing the
error of each ET's approximations of the minor-3rd, major-3rd,
and perfect-5th simultaneously. his original graph only had
the three blue lines, showing the JI ratios for those three
intervals. you'll have to ask paul to explain more about
the graphing coordinates.

i simply added the red lines, to connect families of ETs which
shared the same commas, then labeled the most significant families.

hope that helps.

-monz
"all roads lead to n^0"

hi Gene,

> From: "Gene Ward Smith" <genewardsmith@juno.com>
> To: <tuning@yahoogroups.com>
> Sent: Friday, September 13, 2002 6:35 PM
> Subject: [tuning] Re: Tuning Dictionary update: "Equal Temperament"
>

> --- In tuning@y..., "monz" <monz@a...> wrote:
>
> I think a page linking to musical examples in various
> temperaments would be nice.

yes, it would. but that will take quite a bit of time...
eventually. keep this page bookmarked -- it's going to
keep growing, just like the rest of my site.

-monz

Joe,

Lots of good work. Have you ever wondered how long it takes for all those images to download on a page? :)

Contact me off-list about the dictionary...

Cheers,
Jon

hi Jon,

> From: "Jon Szanto" <JSZANTO@ADNC.COM>
> To: <tuning@yahoogroups.com>
> Sent: Saturday, September 14, 2002 10:07 AM
> Subject: [tuning] Re: Tuning Dictionary update: "Equal Temperament"
>

> Joe,
>
> Lots of good work.

thanks!

> Have you ever wondered how long it takes
> for all those images to download on a page? :)

of course i've wondered ...
but i have DSL, so it doesn't bother *me*! :)

seriously, those lattices are all tiny little .gifs, and i've
specified the size of every one of them ... i did both of these
things deliberately to reduce the download time. what else
can i do except split the page up? ... which i didn't want to do,
but might after all if i keep adding data to the description
of each individual EDO.

> Contact me off-list about the dictionary...

will do.

-monz

--- In tuning@y..., "monz" <monz@a...> wrote:

> > I think a page linking to musical examples in various
> > temperaments would be nice.
>
>
>
> yes, it would. but that will take quite a bit of time...
> eventually. keep this page bookmarked -- it's going to
> keep growing, just like the rest of my site.

I think if you gave the systems you wanted and asked for urls it might go fairly easily.