Klarinet Archive - Posting 000430.txt from 1999/02

From: "Edwin V. Lacy" <el2@-----.edu>
Subj: [kl] Musical/mathematical interview
Date: Thu, 11 Feb 1999 08:28:45 -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.

I'm sorry to be rather late in responding to this thread. I don't have
enough credentials in mathematics to be a candidate to be interviewed, but
I would like to mention a topic concerning the relationship between music
and math which has always intrigued me. 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).

There are many other examples of Bach's fascination with numbers. Just
last night I attended an organ recital where some of his Chorale Preludes
were performed. One of them is based on a certain melody, the words of
which refer to the Holy Spirit, the 3rd member of the Trinity. Bach casts
this chorale in triple meter, with a strong accent on the 3rd beat of each
measure: one, two, THREE, one, two, THREE, etc. During Bach's time, the
number 3 was regarded as the ideal number, because of the reference to the
Holy Trinity.

There is sufficient material in this study for several doctoral
dissertations. For a person so inclined, it would be a totally engrossing
study. Any takers?

Ed Lacy
el2@-----.edu

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