From: [deleted for privacy]
To: rusin@math.niu.edu
Subject: math and music project
Date: Tue, 06 Mar 2001 17:44:57 -0500

Mr. Rusin:

I recently completed a Science Fair project about mathematical patterns in 
J.S. Bach's "Invention #1."  I used your site as a reference, and it was 
very helpful.  I am very grateful that it was available to me during my 
research>  I was hoping that you would post my project on your website.  It 
is written in standard science fair project format, but feel free to edit it 
in any way.

Thank you for your time,
Mary Frances Maloney



From: Dave Rusin <rusin@math.niu.edu>
Date: Tue, 22 May 2001 08:46:42 -0500 (CDT)
To: [deleted for privacy]
Subject: Re: math and music project

Some time ago you sent me your science fair project. I must apologize; I
am only now getting around to look at it. Since you expressed interest
in having me post it to the website I will be happy to do so. Let me
comment that this is a nice project. You could have avoided all the
complicated decimals by simply counting half-steps starting with the
lowest notes; in Excel, this amounts to changing the treble notes,
for example, using the formula  Round(Ln($A1/440)/Ln(2) + 9)  so that
the first note is "1", the next (two half-steps higher) is "3", and so on.
Thanks again for sending this.
dave


ABSTRACT

Most great music draws on the repetition of one or more key themes
throughout the piece.  The purpose of this experiment is to discover
whether or not those key themes are linked mathematically, in
J. S. Bach's "Invention No. 1."  The numerical frequencies of the
notes in this piece were written out in a spreadsheet program to look
for patterns within them.  Their natural logarithms were found, and
the differences between the logarithms were calculated. Eight-note
sequences were added, and compared to each other to look for
similarities.  Some of these themes repeated in the piece as often as
sixty-two times.