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 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.