Yahoo Tuning Groups Ultimate Backup tuning-math my paper nears completion

Paul Erlich wrote:

> I'd appreciate any comments or corrections . . . note that it's > incomplete, and the 46 horagrams are not included -- > > /tuning-math/files/perlich/coyotepaper1.doc

Is the "Sagittal" font available for download? (Be sure to send a copy of it with the paper.)

Augmented should be [7 0 -3> in the table at the end.

The mathematical parts looked easy enough to understand -- some of it seemed a little too obvious to me, but for the average reader who hasn't been following the tuning-math list it would be more of a challenge. A whole paper could be written just on the musical applications of wedgies, so it's probably just as well that they're not mentioned. But you should at least have some description of what a "bivector" is if you're going to include them in the tables.

A couple of brief notated musical examples would be nice, like a typical octatonic chord progression you might find in 12-ET music to illustrate the 648;625 comma (the A minor - C minor - Eb minor - F# minor cycle on my diminished temperament page for instance).

🔗Paul Erlich <perlich@aya.yale.edu>

Thanks, Dante . . .

Well, each temperament will be represented by a nice horagram
(floragrams not ready in time, unfortunately). Other than that, we'll
see if there's room and time for more individualized
discussions . . .

--- In tuning-math@yahoogroups.com, "Dante Rosati" <dante@i...> wrote:
> Wow, Paul, its looking great! Very clearly laid out and developed.
Is there
> going to be any discussion of the various temperaments at the end,
their
> characteristics & quirks? Or would that be for another different
paper?
>
> Dante
>
>
> > -----Original Message-----
> > From: Paul Erlich [mailto:perlich@a...]
> > Sent: Wednesday, June 30, 2004 10:13 PM
> > To: tuning-math@yahoogroups.com
> > Subject: [tuning-math] my paper nears completion
> >
> >
> > I'd appreciate any comments or corrections . . . note that it's
> > incomplete, and the 46 horagrams are not included --
> >
> >
/tuning-math/files/perlich/coyotepaper1.doc

🔗Paul Erlich <perlich@aya.yale.edu>

--- In tuning-math@yahoogroups.com, Herman Miller <hmiller@I...>
wrote:
> Paul Erlich wrote:
>
> > I'd appreciate any comments or corrections . . . note that it's
> > incomplete, and the 46 horagrams are not included --
> >
> >
/tuning-math/files/perlich/coyotepaper1.doc
>
> Is the "Sagittal" font available for download? (Be sure to send a
copy
> of it with the paper.)
>
> Augmented should be [7 0 -3> in the table at the end.
>
> The mathematical parts looked easy enough to understand -- some of
it
> seemed a little too obvious to me, but for the average reader who
hasn't
> been following the tuning-math list it would be more of a
challenge. A
> whole paper could be written just on the musical applications of
> wedgies, so it's probably just as well that they're not mentioned.
But
> you should at least have some description of what a "bivector" is
if
> you're going to include them in the tables.

Yes -- as I mentioned on the tuning list, the part of the paper about
combining commas (as well as temperament comnplexity) hasn't been
written yet. It would be nice to have a real clear exposition on the
hows and whys of 2x2 determinants . . . ;)

> A couple of brief notated musical examples would be nice, like a
typical
> octatonic chord progression you might find in 12-ET music to
illustrate
> the 648;625 comma (the A minor - C minor - Eb minor - F# minor
cycle on
> my diminished temperament page for instance).

If you could provide such notated examples for me to include, I'd be
extremely grateful. Dave Keenan provided the lattices that are in
there and one more that will be soon. I'll be sure to thank you both,
and Gene too.

🔗jjensen142000 <jjensen14@hotmail.com>

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
> I'd appreciate any comments or corrections . . . note that it's
> incomplete, and the 46 horagrams are not included --
>
> /tuning-math/files/perlich/coyotepaper1.doc

Ok, I read the draft and I have a list of comments. I'm an outsider
to this theory, so in that sense perhaps my comments might be
useful... or they could be a complete waste of everyones time!

1. Maybe you could make it clearer what exactly the goal of the
paper is; specifically if a lay person makes a big effort and
blasts thru all the math and lattice diagrams, they will be
rewarded with knowing ...?

2. I would change "musical ideas" to something like " a pattern
of notes" on p.1

3. p.2 and footnote vii Why is enharmonic equivalence now important?

4. p.4 Bras and kets? You could just say row vector and column
vector and stick to the formalism linear algebra rather than
quantum mechanics. Maybe it is hard to typeset column vectors
in MS Word?

5. I think the inner product would be more acceptable to people
is you said "a convenient shorthand" rather than "a fancier way".

6. "****Importance made clear below" Make it clear up front,
otherwise people won't make the effort to read it.

7. Right before the Temperment section: 732-819-8440 that looks
like somebody's phone number, rather than anything related to
the previous calculations (which I didn't do, by the way. sorry)

8. Middle of Temperment section: "The relevant possibilities here
include..." Why would someone want to temper out these things?
What musical goodies does it buy them?

--Jeff

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning-math@yahoogroups.com, "jjensen142000" <jjensen14@h...>
wrote:

> 4. p.4 Bras and kets? You could just say row vector and column
> vector and stick to the formalism linear algebra rather than
> quantum mechanics. Maybe it is hard to typeset column vectors
> in MS Word?

Bras and kets, or column vectors and row vectors, are just two ways of
depicting the same mathematical idea. The light really began to dawn
around here when we started using bras and kets; it gave us the
advantage of being able to distinguish a bibra from a biket from a
triket and once we did that, people suddenly seemed able to understand
what was going on with the multilinear algebra. Bras and kets are
easier to typeset, but the real payoff is that it makes the whole
thing a lot more clear here in ascii land.

Mathematicians don't normally use bras and kets, which were thought up
by a physicist and which isn't the way they were taught in grad
school, but there's no reason to let that worry us; our backgrounds
here vary.

🔗Paul Erlich <perlich@aya.yale.edu>

Thanks for your comments; everything helps.

--- In tuning-math@yahoogroups.com, "jjensen142000" <jjensen14@h...>
wrote:

> 1. Maybe you could make it clearer what exactly the goal of the
> paper is; specifically if a lay person makes a big effort and
> blasts thru all the math and lattice diagrams, they will be
> rewarded with knowing ...?

The end of the introduction says,

"The purpose of this paper is to bring to light a host of alternative
temperaments alongside the familiar ones. These should not be
understood merely as lists of pitches to be employed when tuning an
acoustical or electronic instrument. More importantly, they should be
seen as models for the conception and notation of new music,
regardless of the instruments or precise tuning strategies employed
in its implementation."

The lists of pitches are in the horagrams, which as I said are not
contained in this .doc file.

How can I make this seem more "rewarding"?

> 2. I would change "musical ideas" to something like " a pattern
> of notes" on p.1

I changed it to "patterns of notes" -- any objections?

> 3. p.2 and footnote vii Why is enharmonic equivalence now important?

Beethoven, Schubert, etc. would rely on such equivalence in their
compositions. It's necessary in order to circumnavigate commas like
128:125 and 32805:32768. Mathieu's book does some explicit analyses
showing this . . . I guess I should refer the reader to it?

> 4. p.4 Bras and kets? You could just say row vector and column
> vector and stick to the formalism linear algebra

I don't think that would work -- if you've been following this list,
we appear to need Grassmann algebra.

> rather than
> quantum mechanics.

No, this has nothing to do with quantum mechanics. Read the mathworld
links I provided. Also, I plan to include a 3-limit lattice earlier
with level pitch lines and thus motivate the "ket vector" definition
as a linear operator that mathworld alludes to.

> 5. I think the inner product would be more acceptable to people
> is you said "a convenient shorthand" rather than "a fancier way".

Right.

> 6. "****Importance made clear below" Make it clear up front,
> otherwise people won't make the effort to read it.

Umm . . . thanks, I'll try . . .

> 7. Right before the Temperment section: ************* that looks
> like somebody's phone number, rather than anything related to
> the previous calculations (which I didn't do, by the way. sorry)

OOPS!!!! Yikes. Don't call it.

> 8. Middle of Temperment section: "The relevant possibilities here
> include..." Why would someone want to temper out these things?
> What musical goodies does it buy them?

Basically all kinds of Romantic-period harmonic effects. For example,
being able to re-intepret the diminished seventh chord as the
dominant-function chord in four different keys, spaced 1/4 octave
apart from one another. This is one of the things that made Romantic
harmony able to play with a wider array of expectation/surprise
effects and to coherently explore much wider harmonic terrain. Let me
know what you think I should add in the paper and where. Or maybe a
reference to Mathieu will do?

Thanks a lot,
Paul

🔗Herman Miller <hmiller@IO.COM>

Paul Erlich wrote:

> If you could provide such notated examples for me to include, I'd be > extremely grateful. Dave Keenan provided the lattices that are in > there and one more that will be soon. I'll be sure to thank you both, > and Gene too.

Well, I don't have any good notation software, but I managed to put a couple of examples together with Voyetra Digital Orchestrator and some cutting and pasting in Paint Shop Pro. Unfortunately I couldn't figure out how to tell it to use sharps instead of flats, if it can even do that (probably not, since it's a MIDI editor).

But here's a notated version of my octatonic chord progression in 12-ET:

ftp://ftp.io.com/pub/usr/hmiller/music/octatonic.gif
(MIDI at http://www.io.com/~hmiller/music/ex/dim12.mid)

and the porcupine chord progression in 12-ET, which illustrates the 250;243 comma (which of course doesn't vanish in 12-ET, but does in porcupine temperament):

ftp://ftp.io.com/pub/usr/hmiller/music/porcupine.gif
(MIDI at http://www.io.com/~hmiller/midi/porcupine-12.mid)

🔗Carl Lumma <ekin@lumma.org>

>But here's a notated version of my octatonic chord progression in 12-ET:
>
>ftp://ftp.io.com/pub/usr/hmiller/music/octatonic.gif
>(MIDI at http://www.io.com/~hmiller/music/ex/dim12.mid)

Nice!

>and the porcupine chord progression in 12-ET, which illustrates the
>250;243 comma (which of course doesn't vanish in 12-ET, but does in
>porcupine temperament):
>
>ftp://ftp.io.com/pub/usr/hmiller/music/porcupine.gif
>(MIDI at http://www.io.com/~hmiller/midi/porcupine-12.mid)

An old fav. I don't remember hearing it in 12, though. What
a great comma.

You should cross-post this to MMM. It might fit with the discush.
Gene and Jon are having.

-Carl

🔗jjensen142000 <jjensen14@hotmail.com>

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
>> The end of the introduction says,
>
> "The purpose of this paper is to bring to light a host of
alternative
> temperaments alongside the familiar ones. These should not be
> understood merely as lists of pitches to be employed when tuning an
> acoustical or electronic instrument. More importantly, they should
be
> seen as models for the conception and notation of new music,
> regardless of the instruments or precise tuning strategies employed
> in its implementation."
>
> The lists of pitches are in the horagrams, which as I said are not
> contained in this .doc file.
>
> How can I make this seem more "rewarding"?
>

"You are going to see some really erotic horagrams if you make it
to the end of this paper. No one under 21 admitted"

I'm kidding :-)

I'm just of the opinion that you should maybe put more description
of the results in the opening paragraph (or abstract) so the general
reader will get fired up to read the whole thing.

That raises a question though: I assumed this paper was for a journal
like Xenharmonikon...I think you said something like "the editor made
me cut out a lot of complicated math". If this is not the case, then
a lot of my comments were not really relevant! (and probably sound
needlessly nitpicky)

> > 3. p.2 and footnote vii Why is enharmonic equivalence now
important?
>
> Beethoven, Schubert, etc. would rely on such equivalence in their
> compositions. It's necessary in order to circumnavigate commas like
> 128:125 and 32805:32768. Mathieu's book does some explicit analyses
> showing this . . . I guess I should refer the reader to it?
>

This is really interesting, to me. If possible, I would throw in
more details about this, although maybe that is a different paper...

> > 4. p.4 Bras and kets? You could just say row vector and column
> > vector and stick to the formalism linear algebra
>
> I don't think that would work -- if you've been following this
list,
> we appear to need Grassmann algebra.

I am unfortunately completely unable to follow the list; only
occassionally does something make sense, or someone writes an
expository paper like this one :-)

> > rather than
> > quantum mechanics.
>
> No, this has nothing to do with quantum mechanics.

I'm just saying that bras and kets are well known as quantum
mechanics formalism.

> > 8. Middle of Temperment section: "The relevant possibilities here
> > include..." Why would someone want to temper out these things?
> > What musical goodies does it buy them?
>
> Basically all kinds of Romantic-period harmonic effects. For
example,
> being able to re-intepret the diminished seventh chord as the
> dominant-function chord in four different keys, spaced 1/4 octave
> apart from one another. This is one of the things that made
Romantic
> harmony able to play with a wider array of expectation/surprise
> effects and to coherently explore much wider harmonic terrain. Let
me
> know what you think I should add in the paper and where. Or maybe a
> reference to Mathieu will do?

Like I said above, I think this stuff is really interesting, so
I guess I'll have to look at that book when you cite it.

As for your paper, I'm not sure what you should say here. Maybe
something like: "if you temper out the 648/625, you can do <blah>
and if you temper out 2048/2025 then <blah> and if you temper
out the pythagoream comma then you can reduce your set of keys
to 12, or some such thing"

--Jeff

> Thanks a lot,
> Paul

🔗Paul Erlich <perlich@aya.yale.edu>

--- In tuning-math@yahoogroups.com, Herman Miller <hmiller@I...>
wrote:
> Paul Erlich wrote:
>
> > If you could provide such notated examples for me to include, I'd
be
> > extremely grateful. Dave Keenan provided the lattices that are in
> > there and one more that will be soon. I'll be sure to thank you
both,
> > and Gene too.
>
> Well, I don't have any good notation software, but I managed to put
a
> couple of examples together with Voyetra Digital Orchestrator and
some
> cutting and pasting in Paint Shop Pro. Unfortunately I couldn't
figure
> out how to tell it to use sharps instead of flats, if it can even
do
> that (probably not, since it's a MIDI editor).
>
> But here's a notated version of my octatonic chord progression in
12-ET:
>
> ftp://ftp.io.com/pub/usr/hmiller/music/octatonic.gif
> (MIDI at http://www.io.com/~hmiller/music/ex/dim12.mid)
>
> and the porcupine chord progression in 12-ET, which illustrates the
> 250;243 comma (which of course doesn't vanish in 12-ET, but does in
> porcupine temperament):
>
> ftp://ftp.io.com/pub/usr/hmiller/music/porcupine.gif
> (MIDI at http://www.io.com/~hmiller/midi/porcupine-12.mid)

Thanks Herman. I can't view these in IE, for some reason. Do I have
to do something special?

🔗Paul Erlich <perlich@aya.yale.edu>

--- In tuning-math@yahoogroups.com, "jjensen142000" <jjensen14@h...>
wrote:
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
> wrote:
> >> The end of the introduction says,
> >
> > "The purpose of this paper is to bring to light a host of
> alternative
> > temperaments alongside the familiar ones. These should not be
> > understood merely as lists of pitches to be employed when tuning
an
> > acoustical or electronic instrument. More importantly, they
should
> be
> > seen as models for the conception and notation of new music,
> > regardless of the instruments or precise tuning strategies
employed
> > in its implementation."
> >
> > The lists of pitches are in the horagrams, which as I said are
not
> > contained in this .doc file.
> >
> > How can I make this seem more "rewarding"?
> >
>
> "You are going to see some really erotic horagrams if you make it
> to the end of this paper. No one under 21 admitted"
>
> I'm kidding :-)
>
> I'm just of the opinion that you should maybe put more description
> of the results in the opening paragraph (or abstract) so the general
> reader will get fired up to read the whole thing.

Oh, yes. There's still going to be an abstract added. Thanks.

> That raises a question though: I assumed this paper was for a
journal
> like Xenharmonikon...

Yes, it's for Xenharmonikon.

>I think you said something like "the editor made
> me cut out a lot of complicated math".

Well, he really didn't want the paper to be mathematical or mainly
concerned with math.

> If this is not the case, then
> a lot of my comments were not really relevant! (and probably sound
> needlessly nitpicky)

I'm trying to use the minimum of math needed to show where my results
are coming from, and why.

> > > 3. p.2 and footnote vii Why is enharmonic equivalence now
> important?
> >
> > Beethoven, Schubert, etc. would rely on such equivalence in their
> > compositions. It's necessary in order to circumnavigate commas
like
> > 128:125 and 32805:32768. Mathieu's book does some explicit
analyses
> > showing this . . . I guess I should refer the reader to it?
> >
>
> This is really interesting, to me. If possible, I would throw in
> more details about this, although maybe that is a different paper...

I'll try to expand on that footnote, thanks. Yes, I'd recommend
Mathieu's book, though he really ignores the whole "middle path" idea
(including meantone!) and jumps straight to 12-equal. Speaking
of "jumps", his theory in that regard is goofy, if I may say so. But
he does a great job showing how certain great pieces of Western music
require certain commas to vanish.

🔗Herman Miller <hmiller@IO.COM>

Paul Erlich wrote:
> --- In tuning-math@yahoogroups.com, Herman Miller <hmiller@I...> > wrote:
> >>Paul Erlich wrote:
>>
>>
>>>If you could provide such notated examples for me to include, I'd > > be > >>>extremely grateful. Dave Keenan provided the lattices that are in >>>there and one more that will be soon. I'll be sure to thank you > > both, > >>>and Gene too.
>>
>>Well, I don't have any good notation software, but I managed to put > > a > >>couple of examples together with Voyetra Digital Orchestrator and > > some > >>cutting and pasting in Paint Shop Pro. Unfortunately I couldn't > > figure > >>out how to tell it to use sharps instead of flats, if it can even > > do > >>that (probably not, since it's a MIDI editor).
>>
>>But here's a notated version of my octatonic chord progression in > > 12-ET:
> >>ftp://ftp.io.com/pub/usr/hmiller/music/octatonic.gif
>>(MIDI at http://www.io.com/~hmiller/music/ex/dim12.mid)
>>
>>and the porcupine chord progression in 12-ET, which illustrates the >>250;243 comma (which of course doesn't vanish in 12-ET, but does in >>porcupine temperament):
>>
>>ftp://ftp.io.com/pub/usr/hmiller/music/porcupine.gif
>>(MIDI at http://www.io.com/~hmiller/midi/porcupine-12.mid)
> > > Thanks Herman. I can't view these in IE, for some reason. Do I have > to do something special?

No, I don't know why it wouldn't work, unless you've got problems with displaying GIF files in general, or have some problem connecting to FTP sites. Try these:

http://www.io.com/~hmiller/music/octatonic.gif
http://www.io.com/~hmiller/music/porcupine.gif

Or these:

http://www.io.com/~hmiller/music/octatonic.png
http://www.io.com/~hmiller/music/porcupine.png

my paper nears completion

🔗Paul Erlich <perlich@aya.yale.edu>

🔗Dante Rosati <dante@interport.net>

🔗Herman Miller <hmiller@IO.COM>

🔗Paul Erlich <perlich@aya.yale.edu>

🔗Paul Erlich <perlich@aya.yale.edu>

🔗jjensen142000 <jjensen14@hotmail.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Paul Erlich <perlich@aya.yale.edu>

🔗Herman Miller <hmiller@IO.COM>

🔗Carl Lumma <ekin@lumma.org>

🔗jjensen142000 <jjensen14@hotmail.com>

🔗Paul Erlich <perlich@aya.yale.edu>

🔗Paul Erlich <perlich@aya.yale.edu>

🔗Herman Miller <hmiller@IO.COM>

🔗Paul Erlich <perlich@aya.yale.edu>

🔗Herman Miller <hmiller@IO.COM>

🔗Paul Erlich <perlich@aya.yale.edu>