All Science Fair Projects

Title: Mathemusicians: How to Play Music Notes with Mathematical Equations

Objectives/Goals

The objective of my project is to prove that music notes are mathematically
realated, and to find an
equation that will explain the relation. I hypothesized that different lengths
of a 60cm. string where the
fret is placed, will produce speculated note and will fit in a mathematical
equation.

Methods/Materials

I used a monochord that consists of a single string with one fixed bridge and a
movable fret. I plucked the
open string, and I measured the frequency with the CBL (I connected a microphone
to the CBL and linked
the calculator to the CBL and used the program SOUND and FREQ to find the
frequncy of the note)and it
was the frequency of the "do" in the first octave. I also used the intellitouch
tunner to confirm the result.
With the same method, at the length 30cm, I could hear the #do# again. Then I
tried to define an octave. I
had to find a multiplier that could be used 12 times (there are 13 half steps in
each octave) to produce 30
from 60. I wrote an equation 30 = 60 x12. x = 1/ 12, also a geometric sequence,
where t13 = 30 , t1= 60,
and t13 = t1 * r 13-1 . Both ways, the ratio = 0.943874313. I used the
multiplier (ratio) to find the length
for all the 13 notes in one octave. I put the fret to the calculated lengths and
plucked the string and
measured the frequency. The frequency of the notes produced by calculated
lengths was the frequency of
my speculated notes. I worked on three different octaves, and repeated the same
procedure for each octave
more than ten times; the result always supported my hypothesis. I also worked on
the frequency of the
notes to find if they fit in a mathematical equation.
Results
The results supported my hypothesis. I proved that there is a lot of math in
music.

Conclusions/Discussion

1. I found out that the string length for each note, in any given octave fits
in a geometric sequence.
2. Two notes that are one octave apart, the string lengths are in a ratio of
1:1/2.
3. The note sol, in all the octaves is 2/3 of the length of the string.
4. The ratio works for all the octaves.
5. In each measure the tempo given should be maintained mathematically. If the
time signature is 3:4 the note lengths should add up to #.
6. As you move one octave higher, the frequency of all the notes are doubled.
7. By looking at the graph for the string length, one can see the resemblance
of a Grand Piano.

Summary Statement

Mathematical relation in the music notes.

Help Received

Mother helped to prepare the board.