Yahoo Tuning Groups Ultimate Backup tuning UNFAIRNESS TO ISACOFF : Read the book. Monz?

You know, most of the diatribes I've read about the Isacoff book are
*totally* unfair. I'm assuming most of the comments are by people
who haven't read the book. I actually finished it. I read the book.
It doesn't take very long.

Isacoff ends by *praising* Just Intonation in a very contemporary
setting at the end of the book, which greatly nuances any strong 12-
tET predilections that he has in it.

Remember, the following is at the *very end* of the book, where it
has the greatest impact on the reader. At least, it did to *me* and
I was the reader.

For example:

"Contemporary composers who place temperament at the core of
their work include Lou Harrison who has employed the mean-tone
tunings of Johann Philipp Kirnberger, a student of Bach who was
decidedly against equal temperament and distinguished composer
and scholar Easley Blackwood, a longtime professor at the University
of Chicago. Blackwood has written music using a variety of equal
temperaments, dividing the octave up into from thirteen to twenty-
four slices. These "microtonal" works are stunningly strange
sometimes edgy and dark , at other times brightly boisterous,
often
haunting and otherworldly.

"A flourishing circle of just-intonation advocates with ties to
Eastern mysticism includes clusters of adherents in New York and
California. One is W.A. Mathieu, who first became known as a jazz
musician, studied with Blackwood, whom he credits with imparting
important mathematical insights into the nature of
temperament. `Then I heard Northern Indian music,' he
relates, `and found in it a king of purity that I longed for but
couldn't achieve or understand.' He studied under Indian
master musician Pandit Pran Nath, became friends with innovative
composer Terry Riley, and developed his own approach to the
similarities and differences between pure and equal-tempered
tunings."

He then goes on to discuss a private piano recital of Michael
Harrison, a student of Pandit Pran Nath and La Monte Young:

"After a considerable amount of time, the music stopped. No one
moved. Someone on the floor said, "My whole body is resonating."
The piano was silent, but we were all still spinning in a musical
vortex. I looked at Glass [ed. namedropping Philip Glass here by the
author] on the couch; his eyes were closed. My mind wandered to the
lamps in the room, the decorations on the walls..."

I mean, really.

How can people say this book is only *pro 12-tET?* That's nuts.

Read the book.

Sure, there are such passages in it, and maybe they are too strong in
some ways, but they are certainly contradicted by the "CODA" at the
very end. His emphasis actually mirrors our current musical scene,
where 12-tET is still *very* dominant but where stirrings of
alternate tunings are happening.

And Isacoff is *very much* a supporter of these new happenings.

Come on.

Read the book.

Sure, on an intellectual level it's a little light. It also happens
to be quite well written. Maybe a little light, but, still, engaging
writing. There's a certain talent to that.

I'm tempted to think that the notoreity of this book is well deserved
and warranted.

There is *nothing* wrong with this book. It's a good (light) book on
tuning history/theory. Maybe it's just a little "pop" but so what.

In fact, it reminds me quite a bit of Joe Monzo's fanciful efforts,
but watered down substantially and in a novelistic writing style.

Monzo, have you read this book?

You could do this, too.

Read the book.

🔗paulerlich <paul@stretch-music.com>

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> You know, most of the diatribes I've read about the Isacoff book
are
> *totally* unfair. I'm assuming most of the comments are by
people
> who haven't read the book. I actually finished it. I read the
book.
> It doesn't take very long.
>
> Isacoff ends by *praising* Just Intonation in a very
contemporary
> setting at the end of the book, which greatly nuances any
strong 12-
> tET predilections that he has in it.
>
> Remember, the following is at the *very end* of the book,
where it
> has the greatest impact on the reader. At least, it did to *me*
and
> I was the reader.
>
> For example:
>
> "Contemporary composers who place temperament at the
core of
> their work include Lou Harrison who has employed the
mean-tone
> tunings of Johann Philipp Kirnberger, a student of Bach who
was
> decidedly against equal temperament and distinguished
composer
> and scholar Easley Blackwood, a longtime professor at the
University
> of Chicago. Blackwood has written music using a variety of
equal
> temperaments, dividing the octave up into from thirteen to
twenty-
> four slices. These "microtonal" works are stunningly strange
> sometimes edgy and dark , at other times brightly
boisterous,
> often
> haunting and otherworldly.
>
> "A flourishing circle of just-intonation advocates with ties to
> Eastern mysticism includes clusters of adherents in New York
and
> California. One is W.A. Mathieu, who first became known as a
jazz
> musician, studied with Blackwood, whom he credits with
imparting
> important mathematical insights into the nature of
> temperament. `Then I heard Northern Indian music,' he
> relates, `and found in it a king of purity that I longed for but
> couldn't achieve or understand.' He studied under Indian
> master musician Pandit Pran Nath, became friends with
innovative
> composer Terry Riley, and developed his own approach to the
> similarities and differences between pure and equal-tempered
> tunings."
>
> He then goes on to discuss a private piano recital of Michael
> Harrison, a student of Pandit Pran Nath and La Monte Young:
>
> "After a considerable amount of time, the music stopped. No
one
> moved. Someone on the floor said, "My whole body is
resonating."
> The piano was silent, but we were all still spinning in a
musical
> vortex. I looked at Glass [ed. namedropping Philip Glass here
by the
> author] on the couch; his eyes were closed. My mind
wandered to the
> lamps in the room, the decorations on the walls..."
>
> I mean, really.
>
> How can people say this book is only *pro 12-tET?* That's
nuts.
>
> Read the book.
>
> Sure, there are such passages in it, and maybe they are too
strong in
> some ways, but they are certainly contradicted by the "CODA" at
the
> very end. His emphasis actually mirrors our current musical
scene,
> where 12-tET is still *very* dominant but where stirrings of
> alternate tunings are happening.
>
> And Isacoff is *very much* a supporter of these new
happenings.
>
> Come on.
>
> Read the book.
>
> Sure, on an intellectual level it's a little light. It also happens
> to be quite well written. Maybe a little light, but, still, engaging
> writing. There's a certain talent to that.
>
> I'm tempted to think that the notoreity of this book is well
deserved
> and warranted.
>
> There is *nothing* wrong with this book. It's a good (light) book
on
> tuning history/theory. Maybe it's just a little "pop" but so what.
>
> In fact, it reminds me quite a bit of Joe Monzo's fanciful efforts,
> but watered down substantially and in a novelistic writing style.
>
> Monzo, have you read this book?
>
> You could do this, too.
>
> Read the book.
>
> jp

monz shouldn't be singled out here. basically a mob mentality
was at work.

i opened the book to a random page. the pictures of 17-tone and
19-tone renaissance keyboards, followed by the colorful
description of vicentino's 31-tone microtonal music, left my
mouth watering. every other book in the bookstore has erased
the use of extended meantones, and hence the possibility of
expressive microtonality firmly withing the western notational
tradition, from history.

those few pages alone, combined with what you're quoting here,
joseph, are enough for me to say "thank goodness for isacoff"!

so far the only errors that have been pointed out have been of an
exceedingly technical nature, of the kind a general musical
reader wouldn't retain anyway.

what i have yet to hear is a single error in the *story* isacoff tells.
he does *not* claim that bach used equal temperament (thanks
julie). so what is everyone's problem with it?

🔗genewardsmith <genewardsmith@juno.com>

🔗paulerlich <paul@stretch-music.com>

🔗jpehrson2 <jpehrson@rcn.com>

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

/tuning/topicId_35407.html#35441

>
> The story he tells is that progressive thinkers are the ones
heading towards 12-et, and the conservative stick-in-the-muds are the
ones who are interested in other temperaments, which is tendentious.
He also overstates the importance of 12-et in the development of
musical style. Why doesn't he simply lay out what happened with out
the editorialzing and bullshit about intellectual history, which he
isn't good at anyway?
>

****Gene, I agree he does a bit of this and I'm sure that's what has
pushed certain people's "buttons..."

However, he *totally* contradicts this point of the view in his CODA
and elsewhere, and shows various sides to tuning, as a study, more
than some of the "offended" give him credit.

> Moreover, it is sloppy. I found it annoying for the same reason I
sometimes find popularizations of science or math annoying when they
can't get it right, but as I said it is way better than, to take a
particularly egregious example, vos Savant's book on Fermat's Last
Theorem.

***I'm sure, Gene, that somebody with *your* background would find
this book annoying.

As for *me* I enjoyed it thoroughly... :)

Well... acutally it was maybe written a little on the light side for
my "taste..."

🔗jpehrson2 <jpehrson@rcn.com>

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

/tuning/topicId_35407.html#35437

>
> monz shouldn't be singled out here. basically a mob mentality
> was at work.

****Sorry. That was obviously written poorly.

I wasn't singling out Monz at all, since he has expressed an interest
in the book and so far, to my knowledge, has not been critical of it.

I was merely wondering if he read it, since it reminds me of Monz'
*own* colorful writings, maybe deluted down and written in a more
*novelistic* style.

I just thought this was something that Monz could also do if he chose
to, maybe even a bit more intelligently than Isacoff. I just want
Monz to be a big "hit" that's all...

>
> i opened the book to a random page. the pictures of 17-tone and
> 19-tone renaissance keyboards,

***There are some *wonderful* illustrations in the book. What are
some of the things I learned from the book??

Page 33: A *wonderful* Renaissance engraving that shows a whole
building build out of "musical elements." I'd never seen that
engraving before

Page 50: I'd forgotten the text from which our "Do, Re, Mi" was
derived...

Page 53: I'd forgotten what the _Roman de Fauvel_ was all about.
Asinine of me.

Page 63: Actually, I never thought about the fact that the
word "comma" really has the *same* derivation as our
*written* "comma"... a gap. Never thought of that. Me bozo.

Page 87: I'd forgotten that Leonardo di Vinci created musical
instruments....

Page 93: The idea of comparing "perspective" and "temperament" was
interesting. Rather specious, except to those smoking something, but
interesting...

Page 100: There were some good and, SIMPLE, explanations of some of
the "issues" of Just Intonation tunings, which I *knew* but they were
shown very clearly.

Page 116: HERE WAS THE BEST PART OF THE BOOK FOR ME. I never really
understood the application of Euclid and analytic geometry (if that
is what it is) to subdividing the octave into 12 equal parts. Murray
Barbour talks about this in his _Tuning and Temperament_ but I
never "got it." It was clear in the Isacoff. Maybe it was *wrong*
(Gene can say) but it was *clear* anyway... :)

I never understood why geometrical math might have been *easier* for
them at that time than finding the 12th root of 2, but I think I do
now...

Page 127: He spends quite a bit of time with Vincentino whom I'm
beginning to think was one of our most important alternate tuning
ancestors...

Page 162: The "invention" of 12-equal for lute frets in the
proportion 18:17 (which I didn't know) and the subsequent discussion
of the early invention by Chu Tsai-yu where the fifth is given as
749:500 was fascinating. If I had learned this, it never was
presented in such a way that I retained it...

Page 182: Diagrams of alternate keyboards with 27 and 32 notes...and
discussion of Zarlino's keyboard with 19 notes to the octave.

Page 205ff: The discussion about Rameau. Actually I never knew that
Rameau was such a proponent of equal temperament, and never knew
he "invented" the concepts of chord *inversions.* Well, maybe I
learned that at one time, and I certainly knew about his
contributions to *harmony* but I forgot it. Also, the contrasting of
that approach with that of Rousseau was very interesting.

Page 217: He actually mentions the gentleman we have had on his
list... right now I forget his name, who came up with the theories of
Bach's tuning through Bach's personal seal, etc., etc.

Page 226: And I mention the paean to Just Intonation that is
basically this *entire* "CODA" and which controverts whatever 12-tET
predilection Isacoff had through the rest of the book.

It ends as a tribute to Just Intonation!

You were right, Paul, for "calling me" on joining the alternate
tuning "wolf pack" (literally) without reading the book.

Joseph

🔗genewardsmith <genewardsmith@juno.com>

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

It's Euclid and synthetic geometry.

> I never understood why geometrical math might have been *easier* for
> them at that time than finding the 12th root of 2, but I think I do
> now...

Even in the 17th century, people were much more comfortable with the Greek point of view, which based numbers on geometry, than with the new viewpoint which based geometry on numbers; that began to change in the 18th century, and now I find the typical freshman is much happier with analytic geometry than synthetic geometry.

> Page 127: He spends quite a bit of time with Vincentino whom I'm
> beginning to think was one of our most important alternate tuning
> ancestors...

I don't think he understands Vincentino--he says the Archecembalo does JI ("commas and all") whereas if Barbour is correct, it was more or less a 31-et instrument. That's just the sort of thing I don't like; if Barbour is wrong he at least ought to raise the issue. He never relates him to Huygens, and never seems to get it that 31-et and 19-et are real alternatives to 12-et in the sense that they have the same ability to modulate universally.

> Page 162: The "invention" of 12-equal for lute frets in the
> proportion 18:17 (which I didn't know) and the subsequent discussion
> of the early invention by Chu Tsai-yu where the fifth is given as
> 749:500 was fascinating.

Of course, 749/500 is 1/9-comma, not 1/11-comma, and moreover was never used in practice. It really has nothing much to do with anything.

> It ends as a tribute to Just Intonation!

Which is pretty funny, given the tenor of some of his other remarks. He seems to present a thesis, then undercut it, then present it again, then undercut it again. Why not just skip the tiresome editorializing? He wants to make it a story of progress and of finding *the* solution, and it's more complicated than that.

🔗jpehrson2 <jpehrson@rcn.com>

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

/tuning/topicId_35407.html#35461

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > Page 116: HERE WAS THE BEST PART OF THE BOOK FOR ME. I never
really
> > understood the application of Euclid and analytic geometry (if
that
> > is what it is) to subdividing the octave into 12 equal parts.
>
> It's Euclid and synthetic geometry.
>
> > I never understood why geometrical math might have been *easier*
for
> > them at that time than finding the 12th root of 2, but I think I
do
> > now...
>
> Even in the 17th century, people were much more comfortable with
the Greek point of view, which based numbers on geometry, than with
the new viewpoint which based geometry on numbers; that began to
change in the 18th century, and now I find the typical freshman is
much happier with analytic geometry than synthetic geometry.
>

***Hi Gene!

Certainly it must be more common, since I'd never even hear of the
latter...

> > Page 127: He spends quite a bit of time with Vincentino whom I'm
> > beginning to think was one of our most important alternate tuning
> > ancestors...
>
> I don't think he understands Vincentino--he says the Archecembalo
does JI ("commas and all") whereas if Barbour is correct, it was more
or less a 31-et instrument. That's just the sort of thing I don't
like; if Barbour is wrong he at least ought to raise the issue. He
never relates him to Huygens, and never seems to get it that 31-et
and 19-et are real alternatives to 12-et in the sense that they have
the same ability to modulate universally.

****That was *my* typo: Vicentino...

Hmmm. Well, there are some serious errors there, admittedly.
Naturally, I would go with Barbour if I were looking for "accuracy.."

>
> > Page 162: The "invention" of 12-equal for lute frets in the
> > proportion 18:17 (which I didn't know) and the subsequent
discussion
> > of the early invention by Chu Tsai-yu where the fifth is given as
> > 749:500 was fascinating.
>
> Of course, 749/500 is 1/9-comma, not 1/11-comma, and moreover was
never used in practice. It really has nothing much to do with
anything.
>

***Could'da fooled *me*... Well, I'm beginning to see what you mean.
I'm glad I didn't memorize that number as something important!

> > It ends as a tribute to Just Intonation!
>
> Which is pretty funny, given the tenor of some of his other
remarks. He seems to present a thesis, then undercut it, then present
it again, then undercut it again. Why not just skip the tiresome
editorializing? He wants to make it a story of progress and of
finding *the* solution, and it's more complicated than that.

***Well, it's easy to tell what intellectual level he's on, right
from the very beginning.

However, it really is a "fun" read, and makes people enthusiastic
about tuning...

Maybe there should be a companion "addendum" book sold.

It could be a kind of "for further reading" project, and gingerly
make corrections and amplifications for "more advanced" readers.

My guess is that if such a partnership with Isacoff could take place
without Isacoff getting offended, it would sell quite a few copies
and get things straight.

Somebody like Monzo would be the ideal candidate to write something
like that, but it couldn't get too complex or it wouldn't work.

I mean a rather "Intermediate" level of the same material,
considering the Isacoff is, obviously, for "beginners..."

Just a thought.

🔗paulerlich <paul@stretch-music.com>

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> Page 100: There were some good and, SIMPLE, explanations
of some of
> the "issues" of Just Intonation tunings, which I *knew* but they
were
> shown very clearly.

partch is rather underhanded in his *skirting* of these issues.
why not have this book on the shelf in the bookstore near partch?
around where i live, you walk into a bookstore and on tuning, you
see helmholtz, partch, and lots of books with no mention of
meantone, but no barbour, blackwood, fokker, hall, hill,
jorgenson, lindley and turner-smith, mandelbaum, etc. . . any of
these might explain the issues better than isacoff, but at least
isacoff *is* there to mention they exist. this is better than nothing.

>
> Page 116: HERE WAS THE BEST PART OF THE BOOK FOR
ME. I never really
> understood the application of Euclid and analytic geometry (if
that
> is what it is) to subdividing the octave into 12 equal parts.
Murray
> Barbour talks about this in his _Tuning and Temperament_ but
I
> never "got it." It was clear in the Isacoff. Maybe it was *wrong*
> (Gene can say) but it was *clear* anyway... :)
>
> I never understood why geometrical math might have been
*easier* for
> them at that time than finding the 12th root of 2, but I think I do
> now...

this is also quite important. why did the greeks and romans
obsess over rational scales to the degree that they did? *this* is
why. others will hang me for saying it, but it's plain as day.

> Page 127: He spends quite a bit of time with Vincentino whom
I'm
> beginning to think was one of our most important alternate
tuning
> ancestors...

agreed -- note the spelling (Vicentino).

> Page 205ff: The discussion about Rameau. Actually I never
knew that
> Rameau was such a proponent of equal temperament, and
never knew
> he "invented" the concepts of chord *inversions.* Well, maybe I
> learned that at one time, and I certainly knew about his
> contributions to *harmony* but I forgot it. Also, the contrasting
of
> that approach with that of Rousseau was very interesting.

can you summarize rousseau's approach? maybe i should just
buy the book if i want to find out about this? gene?
>
> Page 217: He actually mentions the gentleman we have had
on his
> list... right now I forget his name, who came up with the
theories of
> Bach's tuning through Bach's personal seal, etc., etc.

kellner
>
> You were right, Paul, for "calling me" on joining the alternate
> tuning "wolf pack" (literally) without reading the book.

ah now the anonymous tipper has been revealed!

🔗paulerlich <paul@stretch-music.com>

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
>
> I don't think he understands Vincentino--he says the
>Archecembalo does JI ("commas and all") whereas if Barbour
>is correct, it was more or less a 31-et instrument.

i'd like to hear margo or someone comment on this -- a
prominent tuning theorist published a ji system of vicentino in
1/1 -- but was this ever the tuning of the archicembalo?

>That's just the sort of thing I don't like; if Barbour is wrong he at
>least ought to raise the issue. He never relates him to
>Huygens, and never seems to get it that 31-et and 19-et are
>real alternatives to 12-et in the sense that they have the same
>ability to modulate universally.

does he simply fail to mention that? does costeley get a mention
in his book at all? no?

or does he actually make statements that would *contradict* this
fact? that would be pretty serious . . .

> He wants to make it a story of progress and of finding *the*
>solution, and it's more complicated than that.

true, but don't you think there's *some* truth to that? don't you
think there were musicians who felt most comfortable with an
aristoxenus view of tuning but couldn't see a rigorous
implemetation of it until stevin came along?

🔗monz <joemonz@yahoo.com>

> From: jpehrson2 <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, March 10, 2002 3:15 PM
> Subject: [tuning] "wolf" pack, rat pack [Isacoff]
>
>
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> /tuning/topicId_35407.html#35437
>
> >
> > monz shouldn't be singled out here. basically a mob mentality
> > was at work.
>
> ****Sorry. That was obviously written poorly.
>
> I wasn't singling out Monz at all, since he has expressed an interest
> in the book and so far, to my knowledge, has not been critical of it.
>
> I was merely wondering if he read it, since it reminds me of Monz'
> *own* colorful writings, maybe deluted down and written in a more
> *novelistic* style.
>
> I just thought this was something that Monz could also do if he chose
> to, maybe even a bit more intelligently than Isacoff. I just want
> Monz to be a big "hit" that's all...

thanks for all of that, Joe -- i appreciate your vote
of confidence in my work. :)

no, i haven't been critical of Isacoff's book yet, because
i haven't read it. i decided that since bad reviews of
it were surfacing here, i'd wait until a library got it
so that i could read it without helping to stuff Isacoff's
pockets.

given the mixed reports coming in now, i may just pick
up a copy -- it's beginning to sound like an interesting
read, and with my penchant for tuning-theory history,
it seems like a book i'd very much enjoy -- provided that
it gives the facts correctly.

> Page 116: HERE WAS THE BEST PART OF THE BOOK FOR ME. I never really
> understood the application of Euclid and analytic geometry (if that
> is what it is) to subdividing the octave into 12 equal parts. Murray
> Barbour talks about this in his _Tuning and Temperament_ but I
> never "got it." It was clear in the Isacoff. Maybe it was *wrong*
> (Gene can say) but it was *clear* anyway... :)
>
> I never understood why geometrical math might have been *easier* for
> them at that time than finding the 12th root of 2, but I think I do
> now...

Joe, at the El Paso Microhoot last November, and in my
webpage "Speculations on Sumerian Tuning"
http://www.ixpres.com/interval/monzo/sumerian/sumeriantuning.htm

(see "How a Sumerian could approximate 12-tone equal-temperament",
beginning about 1/2-way down the page), i outline the procedure
whereby using fairly simple base-60 math, someone 5,000 years ago
*could* have calculated a tuning that was audibly identical
to 12edo.

i went thru all the trouble to figure this out simply
because it is documented that Babylonians of c. 1600 BC
could find arbitrarily close approximations of 2^(1/2)
a/k/a SQRT(2) . i show on my webpage that the Sumerian
written symbols which were retained by the Babylonians
give all the essentials of the math problems, so the
methods go back to Sumerian culture. i simply wanted
to put the numbers "out there" so that Sumerologists who
might recognize these numbers on tablets will know that
they've probably stumbled onto a new tuning text.

anyway, my point in all this rambling is that 12edo
*could* have been calculated as long ago as c. 3,000 BC
in Sumer -- the method for solving the problem existed ...

*but*, the mathematical theory of roots and powers
was not formulated until the 1500s, and without that,
musicians would have a hard time giving a clear presentation
of 12edo (or any EDO) in *numbers*, whereas a geometrical
diagram could show how to produce the tuning quite accurately.

> Page 162: The "invention" of 12-equal for lute frets in the
> proportion 18:17 (which I didn't know)

you must have missed the *many* times i've posted statements
here concerning Vincenzo Galilei's advocacy of 18:17 (c. 1596)
as the ideal ratio for lute frets.

> Page 205ff: The discussion about Rameau. Actually I never knew that
> Rameau was such a proponent of equal temperament, and never knew
> he "invented" the concepts of chord *inversions.* Well, maybe I
> learned that at one time, and I certainly knew about his
> contributions to *harmony* but I forgot it. Also, the contrasting of
> that approach with that of Rousseau was very interesting.

Rameau's most fundamental contribution to music-theory was
the idea of a "fundamental bass": that all harmony is merely
a working-out of the 5-limit harmonies implied by a "fundamental"
bass line, which need not be exactly the same as the real
bass line.

Eurocentric music-theory is indeed indebted to Rameau
in a very big way, and Rameau's conceptions changed several
times over his long career as a theorist -- i say this
so that you don't read Gossett's English translation
of the _Traitï¿½ de l'harmonie_ (Rameau's original published
1722, and this the only one of Rameau's treatises translated
in full, AFAIK), and think you know the deal; the only
way to get a full understanding of Rameau's immense
contribution to music-theory is to get a good overview
of his whole output, preferably by reading the French
originals (something i haven't done yet myself).

but anyway, the fundamental-bass idea was one that
really stuck. it led to such widespread ideas as,
for example, the "diminished-7th" chord as representing
the 10:12:14:17 harmonics of a "missing root", and has
its modern analogue in Terhardt's "virtual pitch" theory.

> Page 217: He actually mentions the gentleman we have had on his
> list... right now I forget his name, who came up with the theories of
> Bach's tuning through Bach's personal seal, etc., etc.

that would be Herbert Anton Kellner.

-monz

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🔗monz <joemonz@yahoo.com>

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, March 10, 2002 5:36 PM
> Subject: [tuning] Re: "wolf" pack, rat pack [Isacoff]
>
>
> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > I never understood why geometrical math might have
> > been *easier* for them at that time than finding the
> > 12th root of 2, but I think I do now...
>
> this is also quite important. why did the greeks and romans
> obsess over rational scales to the degree that they did? *this* is
> why. others will hang me for saying it, but it's plain as day.

Joe, in addition to the responses to this from Gene and paul,
i've added some comments of my own in another post.

but what paul is saying here is really the crux of the matter:
to most ancient theorists, music *was* number -- the two were
interchangeable. therefore, an irrational tuning was no
tuning at all, merely a scale that might or might not be
pleasing to the ear, but in either case *did not* represent
"attunement".

to an ancient theorist who subscribed to this Pythagorean
dictum (by which i do *not* imply 3-limit!), the process
of harmonization could only be acheived and explained by
the various mixtures of integer numbers ... and that's
what's known as "rational".

with the advent of clear understanding and writing on
factorization and logarithms c. 1600, "irrational"
tunings could now also be explained in terms of rather
simple numerical calculations, thus allowing theorists
to see "harmony" in a whole new light.

based only on what i've read here about Isacoff's book,
i think this, more than anything else, is his central thesis.

-monz

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🔗jpehrson2 <jpehrson@rcn.com>

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

/tuning/topicId_35407.html#35493

> > From: paulerlich <paul@s...>
> > To: <tuning@y...>
> > Sent: Sunday, March 10, 2002 5:36 PM
> > Subject: [tuning] Re: "wolf" pack, rat pack [Isacoff]
> >
> >
> > --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> >
> > > I never understood why geometrical math might have
> > > been *easier* for them at that time than finding the
> > > 12th root of 2, but I think I do now...
> >
> > this is also quite important. why did the greeks and romans
> > obsess over rational scales to the degree that they did? *this*
is
> > why. others will hang me for saying it, but it's plain as day.
>
>
> Joe, in addition to the responses to this from Gene and paul,
> i've added some comments of my own in another post.
>
> but what paul is saying here is really the crux of the matter:
> to most ancient theorists, music *was* number -- the two were
> interchangeable. therefore, an irrational tuning was no
> tuning at all, merely a scale that might or might not be
> pleasing to the ear, but in either case *did not* represent
> "attunement".
>
> to an ancient theorist who subscribed to this Pythagorean
> dictum (by which i do *not* imply 3-limit!), the process
> of harmonization could only be acheived and explained by
> the various mixtures of integer numbers ... and that's
> what's known as "rational".
>
>
> with the advent of clear understanding and writing on
> factorization and logarithms c. 1600, "irrational"
> tunings could now also be explained in terms of rather
> simple numerical calculations, thus allowing theorists
> to see "harmony" in a whole new light.
>
> based only on what i've read here about Isacoff's book,
> i think this, more than anything else, is his central thesis.
>
>
>
> -monz
>

****Thanks, Monz. Yes, I believe you are correct here about
his "central thesis" but he didn't seem to bring together what you
just mentioned concerning rational and irrational numbers immediately
above. At least I don't remember him doing that...

best,

Joe

🔗paulerlich <paul@stretch-music.com>

🔗monz <joemonz@yahoo.com>

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, March 10, 2002 9:26 PM
> Subject: [tuning] Re: "wolf" pack, rat pack [Isacoff]
>
>
> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > ****Thanks, Monz. Yes, I believe you are correct here
> > about his "central thesis" but he didn't seem to bring
> > together what you just mentioned concerning rational
> > and irrational numbers immediately above. At least I
> > don't remember him doing that...

well, ok ... then there's the "intermediate" book i need
to write to accompany Isacoff's! :)

> well, from what gene wrote, i don't believe isacoff really
> understands the rational/irrational distinction at all.
>
> but i don't think it's the central point of temperament. it's perhaps
> the central point of *monz's* view of temperament, though in fact
> temperament has very little to do with exact interval values,
> irrational or otherwise -- rather it has to do with making the same
> old consonant intervals fit together in one way or another. monz
> misses this point in his 'rational implications of meantone
> tunings' work, his recent et page table/lattices and comments,
> and many prior discussions on this list.

ok paul, since you never tire of repeating this observation
about my work, i guess i should formally propose the
"Monzo Theory of Temperament" so that no-one will be
confused into thinking that i am representing the consensus
opinion. consider it hereby proposed.

any other adherents besides Marc Jones?

-monz

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🔗paulerlich <paul@stretch-music.com>

🔗genewardsmith <genewardsmith@juno.com>

🔗monz <joemonz@yahoo.com>

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, March 10, 2002 9:37 PM
> Subject: [tuning] Re: "wolf" pack, rat pack [Isacoff]
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > ok paul, since you never tire of repeating this observation
> > about my work, i guess i should formally propose the
> > "Monzo Theory of Temperament" so that no-one will be
> > confused into thinking that i am representing the consensus
> > opinion. consider it hereby proposed.
>
> the monzo theory of temperament is self-contradictory. monzo
> doesn't think that 31-equal is *just barely* meantone, or
> 50-equal *even less* meantone, does he?

no, of course not. there's some kind of misunderstanding here...

it seems to me that you're implying (if not stating outright)
that there is no value to the gallery of colored and greyscale
lattices that i've added to the "equal temperament" definition
http://www.ixpres.com/interval/dict/eqtemp.htm

since Joe Pehrson asked us to keep this discussion onlist,
and if this is correct, please submit a post explaining in
great detail why there's no value to these, because...

> > any other adherents besides Marc Jones?
>
> marc has demonstrated a clear understanding of
> temperaments, and i doubt he's ever agree that 12-equal is *just
> barely* diesic, or any of the other fallacies you've posted.

in private email, Marc called me a "visionary" when i
made these additions to that page, and said that to him
the most remarkable thing was that not only had i done
the same thing he did many years ago, but that my color
lattices use the same color mapping as his did!

apparently, Marc and i are both seeing something that
you and perhaps many others are missing. perhaps neither
of us can explain what that is, in which case my explanations
on the webpage are wrong in the ways you point out, but
i don't know with what to replace them.

so, i don't know ... my gut feeling is that these
lattices are displaying some kind of valuable information
about the relationship of equal-temperaments and JI.
what i need to do is pursue this discussion until i
figure out how to explain what that information is.

and i still haven't seen the McCartney lattices that
you've been touting as the "correct" version of what
you believe i attempted to do here. where are they?
can anyone post an example?

-monz

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🔗genewardsmith <genewardsmith@juno.com>

🔗jpehrson2 <jpehrson@rcn.com>

🔗paulerlich <paul@stretch-music.com>

🔗genewardsmith <genewardsmith@juno.com>

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

> this is also quite important. why did the greeks and romans
> obsess over rational scales to the degree that they did? *this* is
> why. others will hang me for saying it, but it's plain as day.

Since the time of Eudoxus, the Greeks had a rigorous definition of, in effect, the positive real numbers from his theory of ratios. However, in practical terms they had a hard time dealing with rational numbers, much less irrational ones. They unfortunately never learned from the Babylonians how to write numbers to a base.

Also, the contrasting
> of
> > that approach with that of Rousseau was very interesting.
>
> can you summarize rousseau's approach? maybe i should just
> buy the book if i want to find out about this? gene?

Rousseau protruded himself into music theory, and one of the funny bits in Isacoff is the description of Rameau at the premire of Rousseau's opera, ghosted by Philidor.

I never read Rousseau on music, but it sounds just like you'd think from Isacoff's description--melody is an expression of untamed erotic fervor, and is better than harmony, which is too darned civilized and calculating. Italian opera is better than French because it is more emotional, partly because the French language is better at logic than emotion, and partly because the Italians care first and formost about melody, not harmony.

🔗genewardsmith <genewardsmith@juno.com>

🔗graham@microtonal.co.uk

In-Reply-To: <a6h2cm+eead@eGroups.com>
Gene:
> > I don't think he understands Vincentino--he says the
> >Archecembalo does JI ("commas and all") whereas if Barbour
> >is correct, it was more or less a 31-et instrument.

Paul:
> i'd like to hear margo or someone comment on this -- a
> prominent tuning theorist published a ji system of vicentino in
> 1/1 -- but was this ever the tuning of the archicembalo?

I still think you should read what Vicentino said about this. From my
reading, both Isacoff and Barbour are correct here. The Archicembalo is
more or less a 31-et instrument, and it does JI, commas and all. Remember
there are two tunings of it.

I think I read that 1/1 article online, but can't find a reference now.
It was somewhat misleading in showing the scale in terms of ratios. A lot
of them weren't given by Vicentino, but inferred from other notes and
intervals he did give. And IIRC 11:9 wasn't given for the neutral third,
although V. did give 5.5:4.5 which is the same thing. The fact V. didn't
write it as 11:9 suggests he wasn't too hot on mathematics, so I don't
consider the ratios he gives to be of any importance. Of course, this is
all interpretation, so to make up you own mind you'll have to get the
treatise.

Graham

🔗Afmmjr@aol.com

🔗jpehrson2 <jpehrson@rcn.com>

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

/tuning/topicId_35407.html#35502

> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > with the advent of clear understanding and writing on
> > factorization and logarithms c. 1600, "irrational"
> > tunings could now also be explained in terms of rather
> > simple numerical calculations, thus allowing theorists
> > to see "harmony" in a whole new light.
> >
> > based only on what i've read here about Isacoff's book,
> > i think this, more than anything else, is his central thesis.
>
> It's far from clear Isacoff even understands the math involved. He
seems to think that the rational numbers aren't dense, but discrete
> (page 39) and his explanation of what an irrational number is is
gibberish. As I remarked before, he seems to think Pythagoras
expected the Pythagorean comma to be 1, which is bizarre, and thinks
that the explanation of why 2^n = 3^m never happens, involving
elementary number theory, is a "contemporary" explanation Pythagoras
would presumably not have known. So far as logarithms go, he thinks
> 2 and 3/2 are incommensurate, whereas he should have said log 2 and
> log 3/2 are incommensurate.

***You know, a cat like that really should have gone over the book
with a "math guy." I can't believe he didn't "stoop" to do that...
it would have been a *much* better book....

🔗manuel.op.de.coul@eon-benelux.com

🔗monz <joemonz@yahoo.com>

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, March 10, 2002 6:00 PM
> Subject: [tuning] Re: "wolf" pack, rat pack [Isacoff]
>
>
> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > Somebody like Monzo would be the ideal candidate to
> > write something like that,
>
> i'd hope monz would first get a firmer grasp of how temperament
> works. no offense, monz, but that *is* the title of isacoff's book,
> and monz has lived under some *severe* *core*
> misconceptions here, for some time now (i still love him as a
> great friend and ji tuning theorist).

paul, composers very frequently *do* use tempered tunings
in ways in which they intend to emulate JI harmonies.
i don't just mean the basic JI concords ... i mean larger
harmonic structures (such as big fat chords) or key-center
relationships.

i suppose how well various temperaments do this is the
main thing i'm trying to show on my "equal tempermaments"
colored and shaded lattices.

-monz

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🔗paulerlich <paul@stretch-music.com>

--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > From: paulerlich <paul@s...>
> > To: <tuning@y...>
> > Sent: Sunday, March 10, 2002 9:37 PM
> > Subject: [tuning] Re: "wolf" pack, rat pack [Isacoff]
> >
> >
> > --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > > ok paul, since you never tire of repeating this observation
> > > about my work, i guess i should formally propose the
> > > "Monzo Theory of Temperament" so that no-one will be
> > > confused into thinking that i am representing the
consensus
> > > opinion. consider it hereby proposed.
> >
> > the monzo theory of temperament is self-contradictory.
monzo
> > doesn't think that 31-equal is *just barely* meantone, or
> > 50-equal *even less* meantone, does he?
>
>
> no, of course not. there's some kind of misunderstanding
here...

well then, please post your logic determining that 12-equal is
'just barely' diesic (augmented), and then use the same logic to
fill in the blanks here:

12-equal is __________ diminished (octatonic);
31-equal is __________ meantone;
50-equal is __________ meantone . . .

>
> it seems to me that you're implying (if not stating outright)
> that there is no value to the gallery of colored and greyscale
> lattices that i've added to the "equal temperament" definition
> http://www.ixpres.com/interval/dict/eqtemp.htm

i'm just stating that it's possible to use them incorrectly, as you
did in determining that 12-equal is 'just barely' diesic
(augmented).

let's get down to the nitty-gritty, monz! come back down to earth, o
nimbal visionary! you can't answer my objections by simply
claiming you're above me.

> perhaps neither
> of us can explain what that is, in which case my explanations
> on the webpage are wrong in the ways you point out, but
> i don't know with what to replace them.

i've been trying to tell you this. there was a whole week last
month where i posted and posted about exactly this but you
seemed to read virtually nothing.
>
>
> and i still haven't seen the McCartney lattices that
> you've been touting as the "correct" version of what
> you believe i attempted to do here. where are they?
> can anyone post an example?

it's very simple. for example, 0 would be at the center still. then
each of the consonant intervals would be the *integer* assigned
to that consonance. and so on, in lattice fashion. it's the way i've
always done et lattices. so you'd get a 0 for the 128\125 and the
648\625 in 12-equal, and a 0 for the 81\80 in 31-equal and
50-equal, correctly showing how these temperaments work.
currently, your lattices are misleading even you yourself in this
regard.

now you'll reply that these don't show the error from ji. of course, i
already answered this in great length, last month.

🔗paulerlich <paul@stretch-music.com>

--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > From: paulerlich <paul@s...>
> > To: <tuning@y...>
> > Sent: Sunday, March 10, 2002 6:00 PM
> > Subject: [tuning] Re: "wolf" pack, rat pack [Isacoff]
> >
> >
> > --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> >
> > > Somebody like Monzo would be the ideal candidate to
> > > write something like that,
> >
> > i'd hope monz would first get a firmer grasp of how
temperament
> > works. no offense, monz, but that *is* the title of isacoff's
book,
> > and monz has lived under some *severe* *core*
> > misconceptions here, for some time now (i still love him as a
> > great friend and ji tuning theorist).
>
>
> paul, composers very frequently *do* use tempered tunings
> in ways in which they intend to emulate JI harmonies.
> i don't just mean the basic JI concords ... i mean larger
> harmonic structures (such as big fat chords) or key-center
> relationships.

indeed.

> i suppose how well various temperaments do this is the
> main thing i'm trying to show on my "equal tempermaments"
> colored and shaded lattices.

the fact that 648;625 vanishes in 12-equal has a lot to do with
how big fat chords and key-center relationships work in
12-equal. yet your colored and shaded lattices seem to tell a
different story -- at least when interpreted in the way you yourself
interpreted them when coming to the conclusion that 12-equal is
'just barely' diesic.

think about it! not just in the abstract -- put forward some
examples!

🔗Orphon Soul, Inc. <tuning@orphonsoul.com>

On 3/11/02 12:37 AM, "paulerlich" <paul@stretch-music.com> wrote:

>> any other adherents besides Marc Jones?
>
> marc has demonstrated a clear understanding of temperaments, and i doubt he's
> ever agree that 12-equal is *just barely* diesic, or any of the other
> fallacies you've posted.

Actually I just got home from Beatlefest. Thirty hours of 12 tone. Yeah
yeah yeah.

Trying to remember what diesic means. I stared at it for a few seconds and
I noticed that with the addition of "u" it's an anagram for suicide. I
should really eat something. It was a long weekend.

I said as of 1998 I started acknowledging 12-equal as a temperament again
more or less. Sort of the same way Johnny Reinhard has said "even 12 is
microtonal" or somesuch, that 12 itself is still just another temperament
and like Stairway to Heaven probably only makes people sick when they find
it to be played out.

That's not what you're talking about, is it. I'll try to catch up on posts
tonight.

Marc

🔗Orphon Soul, Inc. <tuning@orphonsoul.com>

On 3/11/02 1:15 AM, "monz" <joemonz@yahoo.com> wrote:

>> marc has demonstrated a clear understanding of temperaments, and i doubt he's
>> ever agree that 12-equal is *just barely* diesic, or any of the other
>> fallacies you've posted.
>>
> in private email, Marc called me a "visionary" when i made these additions to
> that page, and said that to him the most remarkable thing was that not only
> had i done the same thing he did many years ago, but that my color lattices
> use the same color mapping as his did!

Well by that having been a *private* email, (hmm) I should maybe append that
it wasn't something that I was specifically keeping away from the mass
library. Like hey psst Monz you vision man you go boy. I was thinking more
in terms of, oh I don't know what they're called. Visionary might not have
even been the word I meant. I meant more literally, that you seem to have
had the same kind of "visions" that I have, possibly because of all of the
intense time you've spent on your own, doing just that, trying to visualize
things.

And I think I mentioned on the phone, the color mapping wasn't identical,
this started because I found your "hot and cold" colorings for sharp and
flat interesting as a contrast. The *shadings* were identical. Except I
stopped the graph when it hits black, in other words, not so much whether
some interval miles away is accurate to whatever note it happens to fall
near, but whether it could be *derived* from so many fourths or fifths plus
or minus so many thirds which, I mentioned, in very large temperaments, at
the pixel level, results in what looks like tubes with a seeming thickness
and angle. The colors I used were based on the RGB wheel. But the shading
was identical. Which gave the "tubes" even more of a cylindrical look,
because of the brightness in the middle and the black around the edges.

> apparently, Marc and i are both seeing something that you and perhaps many
> others are missing. perhaps neither of us can explain what that is, in which
> case my explanations on the webpage are wrong in the ways you point out, but i
> don't know with what to replace them.

Well personally the color schemes, on a scale a little bit less than an
Excel cell and a little bit larger than a pixel, served me at one point as
an easy reminder, a sort of mental flashcard icon, of the general wind
(either pronunciation) of a temperament, which way the wind tends to blow,
and how it winds around the pool of thirds and fifths.

If you want to cross reference this with my other vaccuum babbles, see
convergence webs and logic grids. This is basically why I wanted to see
this kind of shading scheme, to see how far a temperament could walk on its
own with cycles of fifths and thirds. And for that much, it has its own
meditative purposes but I hope I didn't make them sound more important than
just another one of those side studies.

> so, i don't know ... my gut feeling is that these lattices are displaying some
> kind of valuable information about the relationship of equal-temperaments and
> JI. what i need to do is pursue this discussion until i figure out how to
> explain what that information is.

I should probably catch up a little and see what's been going on.

The lattices are useful, but if you're looking for a leg up over the
mountain, it's ultimately just one reference scheme which if you stare at
for too long, well, it can be addictive to get wrapped up in the crystal
structure of multidimensional visions.

Anyhoo. Like the "left turn" sign I mentioned. If you're going to pursue
the JI-vs-ET visualizations, well, I don't know. I think you should maybe
desensitize to the physical visual stimuli and keep trying to make different
ones. You know, look at it from different angles.

I'll be back later. Gotta go.

Marc

🔗monz <joemonz@yahoo.com>

> From: Orphon Soul, Inc. <tuning@orphonsoul.com>
> To: Tuning List <tuning@yahoogroups.com>
> Sent: Monday, March 11, 2002 11:45 AM
> Subject: Re: [tuning] Re: "wolf" pack, rat pack [Isacoff]
>
>
> On 3/11/02 1:15 AM, "monz" <joemonz@yahoo.com> wrote:
>
> >> marc has demonstrated a clear understanding of temperaments, and i
doubt he's
> >> ever agree that 12-equal is *just barely* diesic, or any of the other
> >> fallacies you've posted.
> >>
> > in private email, Marc called me a "visionary" when i made these
additions to
> > that page, and said that to him the most remarkable thing was that not
only
> > had i done the same thing he did many years ago, but that my color
lattices
> > use the same color mapping as his did!
>
> Well by that having been a *private* email, (hmm) I should maybe append
that
> it wasn't something that I was specifically keeping away from the mass
> library. Like hey psst Monz you vision man you go boy. I was thinking
more
> in terms of, oh I don't know what they're called. Visionary might not
have
> even been the word I meant. I meant more literally, that you seem to have
> had the same kind of "visions" that I have, possibly because of all of the
> intense time you've spent on your own, doing just that, trying to
visualize
> things.

sorry about that. it's just that i'm getting (and i sense that
paul is too) so frustrated over the inability of paul and i to
fully understand each other's ideas about this that i hastily
typed that into my post to give me enough confidence to continue
trying to hold up my end of the debate. i should have asked
you first... my bad.

also sorry about scrambling the comparisons you made of my
lattices and yours -- thanks for fixing that.

and thanks for all your other invaluable comments. like paul,
i'm beginning to feel that i need to take a break from this
for a while.

-monz

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🔗genewardsmith <genewardsmith@juno.com>

🔗Afmmjr@aol.com

Isacoff Errors p. 216-217 with the text appearing as in the book, though sentence by sentence:

Equal temperament was not the, however, the only tuning proposed to accommodate this new musical trend.
----The wrong implication as Werckmeister preceded ET on keyboards

Werckmeister developed an irregular temperament that came to be known as âwell temperament.â
-----Werckmeister called it, and likely named it âwell temperamentâ

In Werckmeisterâs well-tempered tuning, certain keys were more in tune than others, but none were so out of tune as to be unplayable.
-----No key were was more dissonant than Pythagorean, which was still heard in the culture.

Therefore, as a musical work moved from one key center to another, the shift would become blatant: the more far-reaching the displacement, the more grating the harmonies.
-----Not blatant at all, at least most people do not register any difference at all. And there is nothing grating other than a modern predisposition. Isacoff clearly has not heard the tuning.

This variegationâa kind of perspective through audible shadingâwas seized upon as a good thing by opponents of equal temperament, who saw in Werckmeisterâs system the advantage of a built-in musical syntax.
-----This happens after Werckmeister and after Bach, not during the Baroque.

Changes in a pieceâs scales and harmonies were now overlaid with an added expressive element: a dramatic change in the quality of sound, depending on which tones the music revolved around at a given moment.
-----Baroque composers were careful not to overexpose the foreign keys or chords. Here Isacoff is at the tip of the iceberg regarding its potential expressivity.

(Of course, this change would only occur on keyboard instruments; strings and woodwinds were left to pursue their own musical grammars.)
-----Poppycock. Woodwinds always played, along with the strings of the Baroque, with the ever present keyboard. There is no separate grammar.

Advocates claimed for well temperament the bonus of giving each key its own character; but for many, subjecting a keyboard to gradations of âin-and out-of-tunenessâ offered little in the way of musical value.
-----This is ignorance of the value of key character. It shows up the value for melody âala the Rousseau bit since the ecstatic free nature of melody is better represented. And more in the way of musical value, not less.

Indeed, Werckmeister himself eventually became an advocate for equal temperament.
-----This is a lie. Werckmeister supported his chromatic tuning throughout his entire life, as I have previously exposed on this list.

The German critic and composer Friedrich Wilhelm Marpurgâwho, at the request of the heirs of Bach, wrote a preface for a new edition of the masterâs âArt of Fugueââoffered a terse critique of the well-tempered system in 1776: Diversity in the character of the keys,â he wrote, âwill serve only to increase a âdiversityâ of bad sounds in the performance.
-----Marpurg was the director of the lottery and a bitter man. He is writing against Kirnberger (who was supported by CPE Bach and others).

There is controversy to this day over whether Bach preferred equal or well temperament. Some theorists contend that there is internal evidence in his musicâdifferences in the way he handled different keysâto suggest he had well temperament in mind.
-----Yet there is little by Isacoff to represent the âotherâ side fairly.

(One modern scholar insists that he has broken the code of Bachâs âsecret tuningâ by unraveling the images in the composerâs personal seal, which contained seven points and five dashes. However, his secret solution conflicts with statements about temperament made by musicians in Bachâs circle.)
-----Rather crude not to mention Herbertâs name. Why not indicate what âconflictsâ there were with statements in Bachâs circle?

There is as much evidence on the other side: Bachâs biographer Johann Nikolaus Forkel reported, for example, that Bach moved so subtly through the keys that listeners never noticed the change; this suggests equal temperament.
-----And yet Forkel is one of the clearest that Bach is not equal temperament. None of this proves that Bach used anything different than Werckmeister. Only Isacoff is suggesting ET.

His obituary made a similar comment about the artful way in which he tuned his instruments
-----And tuning Werckmeister is MUCH faster than tuning 12-tET

Whatâs more, Bach used two different spellings of a single key for paired pieces in his Well-Tempered Clavier, as if to announce that he considered re-sharp and mi-flat equal.

Just couldnât let this pass, best, Johnny Reinhard

🔗paulerlich <paul@stretch-music.com>

--- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:

> in other words, not so much whether
> some interval miles away is accurate to whatever note it happens to
fall
> near,

which is monz's emphasis,

but whether it could be *derived* from so many fourths or fifths plus
> or minus so many thirds

ah. this sounds like exactly what i've been emphasizing _contra_ monz.

> which, I mentioned, in very large temperaments, at
> the pixel level, results in what looks like tubes with a seeming
thickness
> and angle.

is there any way you could let us see this?

> The colors I used were based on the RGB wheel. But the shading
> was identical. Which gave the "tubes" even more of a cylindrical
look,
> because of the brightness in the middle and the black around the
edges.

> The lattices are useful, but if you're looking for a leg up over the
> mountain, it's ultimately just one reference scheme which if you
stare at
> for too long, well, it can be addictive to get wrapped up in the
crystal
> structure of multidimensional visions.
>
> Anyhoo. Like the "left turn" sign I mentioned. If you're going to
pursue
> the JI-vs-ET visualizations, well, I don't know. I think you
should maybe
> desensitize to the physical visual stimuli and keep trying to make
different
> ones. You know, look at it from different angles.

marc, i think we were seperated at birth.

🔗paulerlich <paul@stretch-music.com>

🔗Orphon Soul, Inc. <tuning@orphonsoul.com>

On 3/11/02 4:54 PM, "monz" <joemonz@yahoo.com> wrote:

>
> sorry about that. it's just that i'm getting (and i sense that
> paul is too) so frustrated over the inability of paul and i to
> fully understand each other's ideas about this that i hastily
> typed that into my post to give me enough confidence to continue
> trying to hold up my end of the debate. i should have asked
> you first... my bad.
>

Ehh no biggie. It just brings up a small matrix of implications which I
hope I cleared up, you know, I'm not saying no one else is a visionary,
etc...

> also sorry about scrambling the comparisons you made of my
> lattices and yours -- thanks for fixing that.
>

Yeah well I know how it gets.

> and thanks for all your other invaluable comments. like paul,
> i'm beginning to feel that i need to take a break from this
> for a while.

That's what got me last year. I mean I know I was talking about things that
other people *could* understand. I just didn't have any kind of concept of
how long it might take for new terms and a slight twist on things to really
sink in with people. At first sight it looked like "I can't tell what
you're talking about, but listen to THIS. THIS is EASY." And it's taken a
year to see it was probably the same to anyone else when I was talking.

As Crowley once said, the problem in communication isn't lack of sympathy in
thought, it's lack of sympathy in speech. The thoughts in the minds are
identical. This is more where I was heading about you coming up with the
same potato carving as I did, in terms of the "color/x axis fifth/y axis
third" model. Which goes all the way back to my first minglings of 10 years
ago. With the exception of maybe the "lattices" and the BRUN ALGORITHM,
when I first saw Mandelbaum's dissertation on 19 tone, my mouth hit the
floor mainly because almost EVERY other diagram and chart in the entire BOOK
was something that I'd come up with in the previous few months. Talk about
Close Encounters.

Yeah so. Maybe you should take a breather. Just take a step back and work
on stuff for awhile without trying to immediately sew everything into the
current ongoings. A week off might do ya good.

Marc

🔗monz <joemonz@yahoo.com>

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, March 11, 2002 3:01 PM
> Subject: [tuning] mccartney lattice (was: Re: "wolf" pack, rat pack
[Isacoff])
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > and i still haven't seen the McCartney lattices that
> > you've been touting as the "correct" version of what
> > you believe i attempted to do here.
>
> what do you mean? it's on your very own website:
>
> http://www.ixpres.com/interval/tagawa/72edo.htm
>
> about 2/3 of the way down.

ah ... you mean Rick's "Bingo Card" diagram, yes?

> notice that 6 fifths up and 6 fifths down both land you on the same
> note. this means that the pythagorean comma vanishes in 72-equal,
> which is correctly indicated in the top graph on
>
> http://www.ixpres.com/interval/dict/eqtemp.htm
>
> however, going by the 72-equal color table/lattice you provide, 6
> fifths up (36.7) does *not* land you on the same 72-equal degree as 6
> fifths down (35.3). thus, by the same logic you used to conclude that
> 12-equal is 'just barely' diesic (augmented), you'd have to conclude
> that the pythagorean comma doesn't vanish in 72-equal, which would be
> an error.

hmm ... ok, you're not telling me anything new; this is
the same kind of thing you said last month. and yes, i
understand what you're saying.

so then, what *would* you say the colors on my lattices
are showing? it's *something* having to do with the
relationship of EDOs to JI, but what?

(and please be aware that the main reason none of the
erroneous statements have been deleted from the webpage
is that i've just been too busy with other stuff lately.)

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

🔗Orphon Soul, Inc. <tuning@orphonsoul.com>

On 3/11/02 5:30 PM, "paulerlich" <paul@stretch-music.com> wrote:

> --- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote: On 3/11/02 12:37
> AM, "paulerlich" <paul@s...> wrote:
>
>> Actually I just got home from Beatlefest. Thirty hours of 12 tone. Yeah
>> yeah yeah.
>>
> you're a lucky cat. hey, we could have a discussion about what commas vanish
> in lucy in the sky with diamonds. i'd really like to.
>

Look for the comma with the wolf in her eyes and she's gone.
(BOOM BOOM BOOM)

Sort of threw me when I saw you (pl) were talking about "McCartney
commas"... AAAA

>> Trying to remember what diesic means.
>>
> we're now calling it augmented, and i believe it's what *you* called
> 'augmented meantone'.
>

Okay I must be getting old. I couldn't remember, so I went to Monz' Marc to
English dictionary page and it wasn't there. It wasn't there because I
forgot to include it. (@&*#^$%&)

Diesis. 128:125, that guy, right.

Ugh. You know what.

What I called "augmented meantone" (AMT) is what *you* guys call "magic".
That's the 19-22-41-60-63 series right? I called it that because the scale
nests give you a grid with two thirds up and two thirds down, so you get the
D-F#-A# type chords without being able to go any further, so... You get the
augmented fifth, or augmented chord.

The scales using "3 major thirds = octave" I called "third-octave meantone,"
(3MT), same as "4 minor thirds = octave" I called "quarter-octave meantone,"
(4MT).

I think given the list of "meantone strains" I was looking at, I might well
have matched up "augmented meantone" as intuitively being that in which "3
major thirds = octave." This, meaning more that the "meantone" quality, (or
regardless of the actual term I used for the category) would be much more
intutively connectable to "that which is made {meantone}" rather than "that
which is a token of the limitations of the strain."

Of course "strains" I got because of the idea of these paradoxes being a
virus in JI. Ha.

Since my definitions are being made public and this is one of the more
confusing ones, I should probably clarify this now. My use of "meantone" in
the last 10 years was used as an extension of the property of the "4 fifths
= major third" paradox as it appeared in equal temperaments. I took
"meantone" as the name of a supercategory in which any number of any
interval equalling another interval could be considered and correlated with
other temperaments. And Lo, I notice in the last couple of months,
somewhere in the "ticker" of the tuning list, people are coming up with the
same lists of temperaments, so. I don't have to translate to realize we're
talking about the same thing.

Marc

🔗monz <joemonz@yahoo.com>

> From: Orphon Soul, Inc. <tuning@orphonsoul.com>
> To: Tuning List <tuning@yahoogroups.com>
> Sent: Monday, March 11, 2002 5:04 PM
> Subject: Re: [tuning] Re: "wolf" pack, rat pack [Isacoff]
>
>
> On 3/11/02 4:54 PM, "monz" <joemonz@yahoo.com> wrote:
>
> >
> > sorry about that. it's just that i'm getting (and i sense that
> > paul is too) so frustrated over the inability of paul and i to
> > fully understand each other's ideas about this that i hastily
> > typed that into my post to give me enough confidence to continue
> > trying to hold up my end of the debate. i should have asked
> > you first... my bad.
> >
>
> Ehh no biggie. It just brings up a small matrix of implications which I
> hope I cleared up, you know, I'm not saying no one else is a visionary,
> etc...

i hope that *is* cleared up for everyone else now, because
i certainly never took anything you said to imply that i
was the only visionary.

> As Crowley once said, the problem in communication isn't lack of sympathy
in
> thought, it's lack of sympathy in speech. The thoughts in the minds are
> identical. This is more where I was heading about you coming up with the
> same potato carving as I did, in terms of the "color/x axis fifth/y axis
> third" model. Which goes all the way back to my first minglings of 10
years
> ago. With the exception of maybe the "lattices" and the BRUN ALGORITHM,
> when I first saw Mandelbaum's dissertation on 19 tone, my mouth hit the
> floor mainly because almost EVERY other diagram and chart in the entire
BOOK
> was something that I'd come up with in the previous few months. Talk
about
> Close Encounters.

i know what you mean. the first and only time i ever
saw Mandelbaum's book was at Johnny Reinhard's one day,
and the same thing happened to me. i had been drawing
my own lattices for about 2 or 3 years. i was even more
surprised when i finally saw Erv Wilson's work for the
first time, because his resembles my own even more.

> Yeah so. Maybe you should take a breather. Just take a step back and
work
> on stuff for awhile without trying to immediately sew everything into the
> current ongoings. A week off might do ya good.

i'm really thinking along the lines of an indefinite
vacation, to concentrate on getting some CDs of my
compositions done.

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

🔗Orphon Soul, Inc. <tuning@orphonsoul.com>

On 3/11/02 5:35 PM, "paulerlich" <paul@stretch-music.com> wrote:

> --- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:
>
>> in other words, not so much whether some interval miles away is accurate to
>> whatever note it happens to fall near,
>>
> which is monz's emphasis,
>
>> but whether it could be *derived* from so many fourths or fifths plus or
>> minus so many thirds
>
> ah. this sounds like exactly what i've been emphasizing _contra_ monz.
>

Okay. I still haven't had a chance to catch up but. I think if anything,
this "tube" effect would turn into an infinite row of tubes by Monz' plot.
He saw something slightly different from what I saw. A slightly custom
color scheme pasted over the infinite sea, rather than the exact weight a
temperament on its own can pull. It's a different correlation.

Well if anything, it's a slight insight into the whole "convergence web"
mindset. That if you can use the Brun algorithm folding up octaves fifths
thirds and say 13:12s to divine temperaments in which the *RELATIVE*
inaccuracies of the intervals are drastically decreasing... Then... Well
that was it. One of my first thoughts was, well, you probably can get a lot
of different intervals in these temperaments that YOU CAN DEFINE IN TERMS OF
fifths thirds and 13:12s.

Also this seems to go back to this mutual desensitization I've noticed
between the sensitivity to temperament density VERSUS sensitivity to
interval size. Monz' model seems to show the temperament as a grid, and
wherever the sea has ripples, there they are; the fix on interval size.
Mine shows the harmonic web of thirds and fifths against a temperament WEB
of thirds and fifths; anything ignored would be "blacker than black", more
than one full note inaccurate.

>> which, I mentioned, in very large temperaments, at the pixel level, results
>> in what looks like tubes with a seeming thickness and angle.
>>
> is there any way you could let us see this?
>

Yeah it wouldn't be too difficult. Where? Upload to the tuning files?

What's interesting is the tubes are infinite. That meaning, that there are
always smaller and smaller commas that so many fifths and thirds IN A
TEMPERAMENT will always find a way of representing an interval by going so
many fifths, THEN so many thirds, THEN so many fifths, just sort of
zigzagging its way into umm... An almost serialist fractal.

It's not that complicated. If you think about the ALMOST fibonacci way that
smaller commas are revealed, in the Brun algorithm if nowhere else, you flip
back and forth between (-x,y) and (x,-y) fifths and thirds which, if you
think about PLOTTING them, gives you an angle that is constantly narrowing.
So that's the direction of the tube. The width??? I can't for the life of
me. I know it has something to do with the path perpendicular to the tube.

>> The colors I used were based on the RGB wheel. But the shading was
>> identical. Which gave the "tubes" even more of a cylindrical look, because
>> of the brightness in the middle and the black around the edges.
>>
>> The lattices are useful, but if you're looking for a leg up over the
>> mountain, it's ultimately just one reference scheme which if you stare at for
>> too long, well, it can be addictive to get wrapped up in the crystal
>> structure of multidimensional visions.
>>
>> Anyhoo. Like the "left turn" sign I mentioned. If you're going to pursue
>> the JI-vs-ET visualizations, well, I don't know. I think you should maybe
>> desensitize to the physical visual stimuli and keep trying to make different
>> ones. You know, look at it from different angles.
>>
> marc, i think we were seperated at birth.

It gets like that doesn't it. I once thought David Finnamore was me having
traveled back through time to mess with my own mind.

What in these three paragraphs made you say this?

Marc

🔗genewardsmith <genewardsmith@juno.com>

🔗paulerlich <paul@stretch-music.com>

--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > From: paulerlich <paul@s...>
> > To: <tuning@y...>
> > Sent: Monday, March 11, 2002 3:01 PM
> > Subject: [tuning] mccartney lattice (was: Re: "wolf" pack, rat pack
> [Isacoff])
> >
> >
> > --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > > and i still haven't seen the McCartney lattices that
> > > you've been touting as the "correct" version of what
> > > you believe i attempted to do here.
> >
> > what do you mean? it's on your very own website:
> >
> > http://www.ixpres.com/interval/tagawa/72edo.htm
> >
> > about 2/3 of the way down.
>
>
> ah ... you mean Rick's "Bingo Card" diagram, yes?
>
>
> > notice that 6 fifths up and 6 fifths down both land you on the same
> > note. this means that the pythagorean comma vanishes in 72-equal,
> > which is correctly indicated in the top graph on
> >
> > http://www.ixpres.com/interval/dict/eqtemp.htm
> >
> > however, going by the 72-equal color table/lattice you provide, 6
> > fifths up (36.7) does *not* land you on the same 72-equal degree as 6
> > fifths down (35.3). thus, by the same logic you used to conclude that
> > 12-equal is 'just barely' diesic (augmented), you'd have to conclude
> > that the pythagorean comma doesn't vanish in 72-equal, which would be
> > an error.
>
>
> hmm ... ok, you're not telling me anything new; this is
> the same kind of thing you said last month. and yes, i
> understand what you're saying.
>
> so then, what *would* you say the colors on my lattices
> are showing? it's *something* having to do with the
> relationship of EDOs to JI, but what?

here's a proposal.

let's leave the general idea of the colors intact -- they can be useful for showing how the consonances as a whole deviate from ji (as you showed me with the curious "lines" in your cylindrical meantone lattices). like marc (if i've understood him correctly), though, i wouldn't wrap the colors around mod anything -- they should just smoothly get redder, or greener, or whatever as you go further out. i'd also prefer it if *absolute error*, rather than *relative error*. this will show immediately which of the consonant intervals bear the brunt of the error, and in what proportions.

planes to incorporate the 7- and 11-identities should, at the very least, run in planes _perpendicular_ to the 3-5 plane. otherwise, the angles of the bands of color continue to merely present the error vector in the 3-5 plane.

can we agree that the *numbers* in the table should be 'mccartney style'; that is, very simply, the actual et notes as they occur in their own harmonic lattice, rather than where they sit with respect to the parallel ji lattice (as rarely would such a parallel be musically relevant).

if you wish, i will write a program to implement all these ideas in matlab, run it for all the ets on your page, and give you the results, to replace the tables you have up currently. in addition, the colors will change smoothly rather than in a blocky fashion, and the grid will be hexagonal, not rectangular.

do you accept my proposal?

>
> (and please be aware that the main reason none of the
> erroneous statements have been deleted from the webpage
> is that i've just been too busy with other stuff lately.)
>
>
> -monz
>
>
>
>
>
> _________________________________________________________
> Do You Yahoo!?
> Get your free @yahoo.com address at http://mail.yahoo.com

🔗paulerlich <paul@stretch-music.com>

--- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:

> Well if anything, it's a slight insight into the whole "convergence web"
> mindset. That if you can use the Brun algorithm

hey marc,

in case this interests you (since we're really identical twins),

this is my understanding as regards the brun algorithm.

historically, there have been many algorithms applied that do what the brun algorithm does, and they all give slightly different results.

none of them is 'perfect' like the euclidean algorithm is for single dyads (ratios of two numbers).

most recently, the ferguson-forcade algorithm was developed and is 'perfect'.

but for these problems, for tunings with a reasonable number of notes, a brute-force approach seems best to me.

in other words, try out *all* the possibities, and come up with an error measure that will pick out the 'best' ones.

there's been quite a bit of this on the tuning-math list, for equal temperaments, and even more so for linear temperaments.

i say this not to put you down or to question you but to encourage you to share your ideas more frequently on the tuning-math list, where they will much more often become 'seeds' around which mutual intelligibility, and mutual enlightenment, coalesce.

> anything ignored would be "blacker than black", more
> than one full note inaccurate.

but why cut it off there? maybe then it should just go into shades of gray or something? there's nothing particularly important or noticeable that happens at the point the color 'fades to black', is there? please tell me, i want to learn (and make a nice set for monz, if he pleases).

> Yeah it wouldn't be too difficult. Where? Upload to the tuning files?

you bet!
> >>
> > marc, i think we were seperated at birth.
>
>
> It gets like that doesn't it. I once thought David Finnamore was me having
> traveled back through time to mess with my own mind.
>
> What in these three paragraphs made you say this?

more the general picture you're painting than the particulars (which i couldn't understand, but it sounded like the right 'colors').