The book: The Idea That Solved Music's Greatest Riddle

Hello ALL,

Any suggestions regarding the book

Temperament : The Idea That Solved Music's Greatest Riddle
by Stuart M. Isacoff
Publication date: November 13, 2001
Publisher: Knopf
Binding:Hardcover
Subjects: Musical temperament; Musical intervals and scales; Music

Regards,
Haresh.

--- In tuning@y..., "Haresh BAKSHI" <hareshbakshi@h...> wrote:
> Hello ALL,
>
> Any suggestions regarding the book
>
> Temperament : The Idea That Solved Music's Greatest Riddle
> by Stuart M. Isacoff
> Publication date: November 13, 2001
> Publisher: Knopf
> Binding:Hardcover
> Subjects: Musical temperament; Musical intervals and scales; Music
>
> Regards,
> Haresh.

Almost certainly this tells the story of the discovery and eventual
adoption of 12-tET as the standard tuning in the West. What sort
of "suggestions" are you looking for?

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., "Haresh BAKSHI" <hareshbakshi@h...> wrote:
> > Hello ALL,
> >
> > Any suggestions regarding the book
[ ................]
>

Paul uvaacha:
> Almost certainly this tells the story of the discovery and eventual
> adoption of 12-tET as the standard tuning in the West. What sort
> of "suggestions" are you looking for? >>>>

Whether it would make instructive reading for me.

Regards,
Haresh.

[Haresh wrote:]
>>Hello ALL,
>>
>>Any suggestions regarding the book
>>
>>Temperament : The Idea That Solved Music's Greatest Riddle
>>by Stuart M. Isacoff
>>Publication date: November 13, 2001
>>Publisher: Knopf
>>Binding:Hardcover
>>Subjects: Musical temperament; Musical intervals and scales; Music

[Paul E:]
>Almost certainly this tells the story of the discovery and eventual
>adoption of 12-tET as the standard tuning in the West. What sort
>of "suggestions" are you looking for?

Right. Amazon.com gives the following description: "A fascinating and
hugely original book that explains how a vexing technical puzzle was
solved, making possible some of the most exquisite music ever written."
And, yes, it's good old 12-tET he's talking about. There are several
reviews presented. Publishers Weekly includes the following: "Forecast:
Knopf's prestige guarantees sales to major music collections, and
Isacoff's national media appearances (NPR, etc.) may mean good general
sales."

I wonder if Isacoff discusses the relative qualities of thirds in
various tunings, or if he simply whitewashes 12-tET altogether.

JdL

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

> Almost certainly this tells the story of the discovery and eventual
> adoption of 12-tET as the standard tuning in the West.

The title made me hope it was about Lucy tuning, unlikely as that
seems.

--- In tuning@y..., genewardsmith@j... wrote:

> The title made me hope it was about Lucy tuning, unlikely as that
> seems.

Why would you hope it was about LucyTuning? The argument for applying
pi to tuning is totally bogus, dude.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., genewardsmith@j... wrote:

> > The title made me hope it was about Lucy tuning, unlikely as that
> > seems.

> Why would you hope it was about LucyTuning? The argument for
applying
> pi to tuning is totally bogus, dude.

It's what I call "benign numerology"--it works well, even if the
argument is bogus.

The reason it brought Lucy tuning to mind is that the title seems to
deliberately recall "Longitude : The True Story of a Lone Genius Who
Solved the Greatest Scientific Problem of His Time." The Lone Genius
in question, John Harrison, if I understand correctly invented Lucy
tuning. Besides as I pointed out a while back the Lucy/Harrison third
itself can be used as a generator. Numerology lives!

--- In tuning@y..., genewardsmith@j... wrote:

> The reason it brought Lucy tuning to mind is that the title seems
to
> deliberately recall "Longitude : The True Story of a Lone Genius
Who
> Solved the Greatest Scientific Problem of His Time."

I figured that was why.

> The Lone Genius
> in question, John Harrison, if I understand correctly invented Lucy
> tuning.

Yes.

> Besides as I pointed out a while back the Lucy/Harrison third
> itself can be used as a generator.

What can't?

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > --- In tuning@y..., genewardsmith@j... wrote:
>
> > > The title made me hope it was about Lucy tuning, unlikely as
that
> > > seems.
>
> > Why would you hope it was about LucyTuning? The argument for
> applying
> > pi to tuning is totally bogus, dude.
>
> It's what I call "benign numerology"--it works well, even if the
> argument is bogus.
>
Bob:
I don't really buy Lucy tuning, but find the metaphor fascinating. I
refer to the Pi-th part of an octave (coming out to be a tempered
third that implies fifths tuned at -6.46 cents from just, near the
1/3-comma end of the 1/4- to 1/3-comma range). The very idea of the
Pi-th part of an octave implies that two to any integer power is the
same point on a circle, a nice geometric metaphor for octave
equivalence, the latter concept one to which almost all of us surely
subscribe.

So the major thirds correspond geometrically to a circle having
rolled through two radians, thus having become precisely adjacent
along the line it is rolling to its initial position, while a
complete revolution around its circumference represents the octave at
a distance of Pi from the starting point. This geometrically
illustrates a relationship between Pi and the diameter as analogous
to the relationship between just major thirds and the octave. The
ancient Chinese approximation of Pi as 3.0 is thus geometrically
analogous to 12-tET (chuckle), where three major thirds become
exactly an octave.

It's at the very least a fun idea. I would expect this kind of
metaphorical reasoning to be reflexively repulsive to minds
irrevocably stuck in the western scientific paradigm. However
astrology is based on this kind of poetic analogy or metaphor, and
such thinking is, far from being foreign to traditional thought in
the ancient past, absolutely indigenous and central to it until
relatively recent times (i.e., up until the last few, short little
centuries).

Finally,if I may say it without committing myself to Lucy tuning, for
one I do not reject such thinking out of hand, since I believe it to
have been responsible for a whole slew of amazing discoveries that
turned out to be quite practical for the cultures that implemented
them. I believe this is a mode of thought that can have great power
at a deep level, and that we wrongly limit ourselves when we accept
only the linear reasoning of "modern" thought as the only "true"
paradigm.

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

> > Besides as I pointed out a while back the Lucy/Harrison third
> > itself can be used as a generator.

> What can't?

If you throw a dart at a large chart of the octave you probably won't
land next to something as good as Magic.

Greetings,
I was able to scan what I believe to be a rough version of this some time
ago at a professor's desk(here at Vanderbilt) and was hugely disappointed.
The author seems to be of the opinion that Bach discovered 12 ET.
Furthermore, if I remember correctly, he also states that ET made the music
of Mozart and Beethoven possible!
All in all, it struck me as a naive, gross over-simplification of the
evolution of our modern ET, and totally missed the musical implications of
well-tempered effects. All it will do is prolong the ignorance. <sigh>
Ed Foote
Nashville, Tn.

Correction to my previous post under "Re: The book: The Idea That
Solved Music's Greatest Riddle":

[In reference to Lucy tuning]
"So the major thirds correspond geometrically to a circle having
rolled through two radians, thus having become precisely adjacent
along the line it is rolling to its initial position, while a
complete revolution around its circumference represents the octave at
a distance of Pi from the starting point."

Should read:
"So the major thirds correspond geometrically to a circle having
rolled through two radians, thus having become precisely adjacent
to its initial position along the line on which it is rolling, while
a complete revolution around its circumference represents the octave
at a distance of 2*Pi from the starting point."

The full corrected text follows:
--- In tuning@y..., BobWendell@t... wrote:
> --- In tuning@y..., genewardsmith@j... wrote:
> > --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > > --- In tuning@y..., genewardsmith@j... wrote:
> >
> > > > The title made me hope it was about Lucy tuning, unlikely as
> that
> > > > seems.
> >
> > > Why would you hope it was about LucyTuning? The argument for
> > applying
> > > pi to tuning is totally bogus, dude.
> >
> > It's what I call "benign numerology"--it works well, even if the
> > argument is bogus.
> >
> Bob:
> I don't really buy Lucy tuning, but find the metaphor fascinating.
I
> refer to the Pi-th part of an octave (coming out to be a tempered
> third that implies fifths tuned at -6.46 cents from just, near the
> 1/3-comma end of the 1/4- to 1/3-comma range). The very idea of the
> Pi-th part of an octave implies that two to any integer power is
the
> same point on a circle, a nice geometric metaphor for octave
> equivalence, the latter concept one to which almost all of us
surely
> subscribe.
>
So the major thirds correspond geometrically to a circle having
rolled through two radians, thus having become precisely adjacent
to its initial position along the line on which it is rolling, while
a complete revolution around its circumference represents the octave
at a distance of 2*Pi from the starting point. This geometrically
> illustrates a relationship between Pi and the diameter as analogous
> to the relationship between just major thirds and the octave. The
> ancient Chinese approximation of Pi as 3.0 is thus geometrically
> analogous to 12-tET (chuckle), where three major thirds become
> exactly an octave.
>
> It's at the very least a fun idea. I would expect this kind of
> metaphorical reasoning to be reflexively repulsive to minds
> irrevocably stuck in the western scientific paradigm. However
> astrology is based on this kind of poetic analogy or metaphor, and
> such thinking is, far from being foreign to traditional thought in
> the ancient past, absolutely indigenous and central to it until
> relatively recent times (i.e., up until the last few, short little
> centuries).
>
> Finally,if I may say it without committing myself to Lucy tuning,
for
> one I do not reject such thinking out of hand, since I believe it
to
> have been responsible for a whole slew of amazing discoveries that
> turned out to be quite practical for the cultures that implemented
> them. I believe this is a mode of thought that can have great power
> at a deep level, and that we wrongly limit ourselves when we accept
> only the linear reasoning of "modern" thought as the only "true"
> paradigm.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> > > Besides as I pointed out a while back the Lucy/Harrison third
> > > itself can be used as a generator.
>
> > What can't?
>
> If you throw a dart at a large chart of the octave you probably
won't
> land next to something as good as Magic.

Right, but aren't the optimal Magic generators _smaller_ than the
Lucy/Harrison major third? Why pick that value?

The L.A. Times just ran a review of the book. It's at:

print version

http://www.latimes.com/templates/misc/printstory.jsp?slug=la%2D000093181nov22

javascript:void(window.open('/templates/misc/emailstory.jsp?slug=la%2D000093181nov22', '_blank',
'width=300,height=410,resizable=1'))

The review is as follows:

http://www.latimes.com/features/lifestyle/la-000093181nov22.story

BOOK REVIEW

Tuning Into Music's Mathematical Nature

TEMPERAMENT: The Idea that Solved Music's Greatest Riddle; \o7 By Stuart
Isacoff\f7 ; Alfred A. Knopf $23, 262 Pages

By TED LIBBEY
SPECIAL TO THE TIMES

November 22 2001

Blame it on Pythagoras. That music's greatest "riddle" should be about intonation seems, on the
face of it, rather silly. After all, our
ears should tell us when two notes are in tune with one another, shouldn't they?

The answer, as Stuart Isacoff makes clear in this charming book, is no, not by a long shot. But
the reason musicians have long
disagreed about tuning is not that their ears have changed so much in the last 21/2 millenniums.
Rather, it's that their philosophies
have. How great minds--many of them musical, some of them apparently not--were able to disagree
over the nature and meaning of
consonance, and how those disagreements produced problems with the tuning of our musical scale, is
the subject of Isacoff's book.
And because, once upon a time, music was a subject deemed worthy of scientific, philosophical and
moral inquiry, Isacoff's treatment
turns out to be as much a whirlwind tour of Western culture's big ideas as it is a musicological
investigation. To the ancient mind,
music was a readily perceivable representation of cosmic order, its measured perfection and pure
cadences at once a reflection of "the
harmony of the spheres" and a means by which man could be in touch with the divine. The ancients'
assumption that music provided
a connection between the earthly and the celestial was embraced by influential Christian writers
such as St. Augustine (354-430) and
eventually became a fundamental tenet of medieval music theory. A crucial role in this process was
played by the early Christian
philosopher Boethius (470-525), whose "De Musica" reconciled neo-Platonic and Aristotelian
cosmology with Christian belief, and
introduced the Pythagorean concept of musical ratios. Ah, Pythagoras!

Anyone who has studied geometry knows it was Pythagoras (circa 582 to circa 500 BC) who showed
that the sum of the squares of
the sides of a right triangle is equal to the square of the hypotenuse. This same Pythagoras,
observing the effects of vibrating strings,
noticed that beautiful, agreeable sounds were produced when the lengths of the strings were in
certain ratios to one another, such as
3:2 (for the fifth, which refers to the distance, say, between middle C on the piano and the G
above) and 4:3 (for the fourth, say, from
C to F). The Pythagorean concept that consonance depended on simple ratios became the foundation
for the medieval Christian
notion of a universe ordered according to mathematical principles and reflecting the divine
presence, and of music as a potent physical
manifestation of that order--in essence, music as numbers made audible.

The problem was that this theory, on which early systems of tuning were based, didn't quite work
in practice. Stacking perfectly tuned
fifths or fourths on top of one another did not produce a satisfactory-sounding octave. Singers
could get around the difficulty, but it
was impossible for instruments with a fixed tuning, especially keyboard instruments, to do so.
Some kind of stretching or shrinking
of the intervals between notes had to occur, and that practice came to be called "temperament."
Isacoff discusses the various
temperaments that were tried, particularly "just" intonation (which tries to keep some of the
Pythagorean ratios) and "mean-tone"
temperament (in which the fifths are shortened, sacrificing a little more of the ideal),
characterizing their strengths and weaknesses
with great skill.

The author's description of how these things sound, though insightful and easily grasped by the
layman, necessarily falls short of the
reality. You simply can't imagine how good--and bad--a harpsichord in mean-tone temperament can
sound until you've heard it
demonstrated. At the Smithsonian, we used to do this by playing "God Save the King" in G major
(marvelously bright and sonorous),
and then a half step lower in F sharp major (where it sounded as though every note were wrong).

All of this sets the table, of course, for the "equal temperament" tuning in use today, a
compromise system that appeared early in the
1700s and in which only the octave is pure, but every half step between notes is exactly the same
distance from its neighbor. Isacoff
shows us how musicians and philosophers wrestled with the theoretical and theological implications
of this idea for centuries, before
the weight of pragmatism finally won out over dogma.

The heroes of this story are the composers Adrian Willaert and Vincenzo Galilei (father of the
astronomer), the scientist Daniel
Bernoulli and the composer-theorist Jean Philippe Rameau. The villains--well, let's not call them
that--those who lined up on what
proved to be the wrong side of the issue, a more numerous lot, include the theorist Gioseffo
Zarlino (on the wrong side of many
issues), the astronomer Johannes Kepler, philosopher-mathematician Rene Descartes, even Sir Isaac
Newton.

Isacoff looks at the question of temperament primarily from the standpoint of the keyboard, not
surprising considering his expertise
in the piano and its literature. But the real payoff for equal temperament was modulatory freedom,
in instrumental music of all kinds.
It was not just being able to compose a piece of music in any one of the 24 major and minor keys,
and have it sound good--as Bach
did in "The Well-Tempered Clavier"--but being able to modulate freely within a given piece to any
key: to depart from a "home" key
or tonal center, to take an excursion, and to return. This led to a grand expansion of musical
form and to the psychological and
emotional impact of the music of Mozart, Beethoven, Schubert, Wagner and so many others. Isacoff
could have said much more
about this than he does, but perhaps that will be the subject of his next book.

*

Ted Libbey is the author of "The NPR Guide to Building a Classical CD Collection."

For information about reprinting this article, go to http://www.lats.com

Haresh BAKSHI wrote:

> Hello ALL,
>
> Any suggestions regarding the book
>
> Temperament : The Idea That Solved Music's Greatest Riddle
> by Stuart M. Isacoff
> Publication date: November 13, 2001
> Publisher: Knopf
> Binding:Hardcover
> Subjects: Musical temperament; Musical intervals and scales; Music
>
> Regards,
> Haresh.

--- In tuning@y..., Rick Tagawa <ricktagawa@e...> wrote:
> The L.A. Times just ran a review of the book. It's at:

It sounds like garbage, judging by this review.

In-Reply-To: <9tksr6+hfsq@eGroups.com>
Rick Tagawa:
> > The L.A. Times just ran a review of the book. It's at:

I've found another one!

<http://www.economist.com/books/displayStory.cfm?Story_ID=863341>

I suppose they must be all over the place by now.

Gene:
> It sounds like garbage, judging by this review.

It sounds like a very well written book that takes the opposite side to
what we'd prefer. Although this review does mention "Post-war music has
seen renewed interest in older tunings as well as experiments with other
alternatives, as Mr Isacoff relates in his coda."

So who are they calling dry and shrivelled?

Graham

--- In tuning@y..., graham@m... wrote:

> > It sounds like garbage, judging by this review.

> It sounds like a very well written book that takes the opposite
side to
> what we'd prefer.

Well-written ignorance is even more pernicious than badly-written
ignorance, and the review makes it sound as if meantone and its
advocates are presented as the Evil Empire.

--- In tuning@y..., genewardsmith@j... wrote:

/tuning/topicId_30161.html#30570

> --- In tuning@y..., graham@m... wrote:
>
> > > It sounds like garbage, judging by this review.
>
> > It sounds like a very well written book that takes the opposite
> side to
> > what we'd prefer.
>
> Well-written ignorance is even more pernicious than badly-written
> ignorance, and the review makes it sound as if meantone and its
> advocates are presented as the Evil Empire.

Hello Gene!

Doesn't the review also seem to imply that Bach used *equal* tempered
rather than *Well* tempered systems, and that "solved" everything...
that seemed to be in there to me...

JP

Joe!
I think they think they solved the riddle caused they postponed the problem for a century or
two until
a) the technology existed where we can now actually hear how bad 12 ET once we can hear exact
b) the musical language having exhausted it possibilities and out of desperation was forced to
move away from pitch all together. Hence the rise of noise and sound hoping that something else
would appear when that got exhausted. no system was better then having to go back to "gulp" 12 :(
Isn't this old hat though with McClain showing how plato solved this. And as we know, Plato is
never wrong

jpehrson@rcn.com wrote:

> --- In tuning@y..., genewardsmith@j... wrote:
>
> /tuning/topicId_30161.html#30570
>
> > --- In tuning@y..., graham@m... wrote:
> >
> > > > It sounds like garbage, judging by this review.
> >
> > > It sounds like a very well written book that takes the opposite
> > side to
> > > what we'd prefer.
> >
> > Well-written ignorance is even more pernicious than badly-written
> > ignorance, and the review makes it sound as if meantone and its
> > advocates are presented as the Evil Empire.
>
> Hello Gene!
>
> Doesn't the review also seem to imply that Bach used *equal* tempered
> rather than *Well* tempered systems, and that "solved" everything...
> that seemed to be in there to me...
>
> JP
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

/tuning/topicId_30161.html#30663

> Joe!
> I think they think they solved the riddle caused they
postponed the problem for a century or
> two until
> a) the technology existed where we can now actually hear how bad
12 ET once we can hear exact
> b) the musical language having exhausted it possibilities and out
of desperation was forced to
> move away from pitch all together. Hence the rise of noise and
sound hoping that something else
> would appear when that got exhausted. no system was better then
having to go back to "gulp" 12 :(
> Isn't this old hat though with McClain showing how plato solved
this. And as we know, Plato is
> never wrong
>

Hi Kraig!

Well, you make a good point in that as soon as "totally organized" 12-
tET serial music started to appear, chance music and noise music were
soon to follow...

JP

--- In tuning@y..., jpehrson@r... wrote:

> > Well-written ignorance is even more pernicious than badly-written
> > ignorance, and the review makes it sound as if meantone and its
> > advocates are presented as the Evil Empire.

> Doesn't the review also seem to imply that Bach used *equal*
tempered
> rather than *Well* tempered systems, and that "solved"
everything...
> that seemed to be in there to me...

The review states it outright, I think, and implies that Mozart and
Beethoven used it, and could not have composed the music they did
otherwise. Presumably the book, at minimum, did not disabuse him of
such notions.