Klarinet Archive - Posting 000444.txt from 1999/02

From: LeliaLoban@-----.com
Subj: [kl] Musical/mathematical interview
Date: Thu, 11 Feb 1999 16:12:56 -0500

JJONES@-----.EDU wrote:

> One of my highschool's requirements for graduation is a senior
> project. For our research paper portion of this project we have to
> use a personal interview as a source. I am investigating the
> connections between mathematics and music, and as a result, was
> wondering if anyone out there with credentials in the two areas might
> be willing to be interviewed.

Edwin Lacy writes,
>>I'm referring to the beliefs of Johann Sebastian Bach with regard to
numerology. For example, in the famous Passacaglia in C Minor, there are 21
statements of the ground bass. In at least some analyses I have seen, the
work can be divided into two sections, one containing 13 statements of the
pattern, and the other consisting of 8. Then, the first section can be
subdivided into groups of 13 and 8 statements, and the second into groups of 8
and 5 statements. As many will recognize, the numbers 3, 5, 8, 13, and 21 are
consecutive numbers in the Fibonacci series. They also bear a relationship to
the "golden mean," in that if each number in the series is divided by the one
following it, the result that is derived as you progress through the series
comes closer and closer to the golden mean, sometimes approximated as 61.8%.
(according to my memory of this topic from long ago).>>

[snip] >>During Bach's time, the number 3 was regarded as the ideal number,
because of the reference to the Holy Trinity.>>

In addition, numerologists use the number 21 as a symbol for the world or the
universe (card number 21 in the Tarot deck is The World), and as a number of
good omen, as in, "You can have the world." Furthermore, 2+1@-----. Readers who
want an overview of the numerological system Bach may have used might take a
look at "A note on numerology," Ch. 14 of _Bach_ by Malcolm Boyd (Schirmer
Books, 1997) and the related notes and bibliography.

If you want an earful about music and math, interview an organ builder.
(Think about it: the organ in the Mormon Tabernacle in Utah, for instance, has
more than 10,000 tuned pipes.) Bach, in his own time, was better known as a
virtuoso organist than as a composer. Organ builders sought his opinions
eagerly, despite his notoriety for testing instruments to (and beyond) their
limits.

I'm in the middle of a possibly permanent hiatus in writing a probably
unpublishable novel called _Passacaglia and Fugue_ about a pipe organist's
obsession with Bach, math and numerology. Therefore I feared to respond to
this topic lest I write 100,000 words of crackpottery on the subject and get
myself going on that damned book again. (This is not false modesty. Darrell
Schweitzer, a friend who's co-editor of _Weird Tales_ and a superb writer,
took a look at my first chapter and pronounced it nearly unreadable.) Can't
resist after reading the posts from Edwin Lacy and Dan Leeson. I will --
what's the gender-neutral expression of "manfully"? -- oh hell -- I will
womanfully refrain from the 100,000 words with the warning that nobody should
ask me any questions about this stuff unless you want to plumb with scientific
exactitude the depths of my ignorance about all things mathematical. (The
book is a horror novel. I'm a mathematical moron and definitely not a fit
subject for an interview. In a horror story, you see, you don't have to do
the calculations. You just have to come up with a vague idea of them, then
say the character did them and here's what happened next. You notice on
"Buffy" how they never superimpose a chart with any of Willow's Eye of Newt
recipes, the way they would on a cooking show?)

However, as preliminary research for whomever you do interview, you might take
a look at _Godel, Escher, Bach: An Eternal Golden Braid_ , by Douglas R.
Hofstadter, who won a Pulitzer Prize for this book (Basic Books, 1979; still
in print from Vintage). The "o" in "Godel" is supposed to have an umlaut over
it, but my computer won't render it to and from ASCII except as gibberish.
The jacket calls the book "a metaphorical fugue on minds and machines in the
spirit of Lewis Carroll." I won't try to explain it any better than that, but
it's superb, and it's a must-read for anyone interested in the relationship of
music (especially Bach's music) to mathematics.

Hofstadter writes about mathematics and logic in the sense that your teacher
probably intends, but if you think the worthy academic might put up with
something a bit farther out there, take a look at:

Ruth Tarlow, _Bach and the Riddle of the Number Alphabet_ (Cambridge, 1991).
She explores Bach's use of (and belief in) the Hebrew system of gematria,
which assigns a number value to each letter of the alphabet. Learning this
system was much in vogue among German Christians of Bach's time. Occultists
believe that Bach used gematria to build secret messages into many of his
compositions. There's considerable credible evidence that Bach knew the
basics of gematria, although the extent to which he may (or may not) have been
a true believer is debatable.

If you read German, look for Friedrich Smend, _Johann Sebastian Bach bei
seinem Namen gerufen_ (Kassel, 1950). If anyone knows of an English
translation, please point me to it! Smend uses musical examples and evidence
of Bach's involvement with the Mizler society to argue that Bach knew and used
gematria for cabbalistic purposes. Smend has attracted many followers among
occultists who have taken his arguments (which already walk pretty far on the
wild side) to extremes worthy of "Buffy, the Vampire Slayer."

As Ed Lacy says,
>>There is sufficient material in this study for several doctoral
dissertations. For a person so inclined, it would be a totally engrossing
subject.>>

I started researching the novel while still abstaining from making music.
Couldn't keep hands off any more. Bach and numerology were what led me back
to playing the clarinet, which is, after all, just another kind of pipe.

Lelia
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
"The ten canons in the _Musical Offering_ are among the most sophisticated
canons Bach ever wrote. However, curiously enough, Bach never wrote them out
in full. This was deliberate. They were posed as puzzles to King Frederick.
It was a familiar musical game of the day to give a single theme, together
with some more or less tricky hints, and to let the canon based on that theme
be "discovered" by someone else. In order to know how this is possible, you
must understand a few facts about canons...."
Douglas R. Hofstadter, _Godel, Escher, Bach_.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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