Applied Mathematics is a way to use math to solve problems in the real world, like in economics, engineering, and medicine. 

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.

Can a single equation predict every note on a musical scale? A monochord is a one-string instrument with one fixed bridge and a movable fret. You pluck the open string and measure its frequency with a microphone sensor.

You then search for a multiplier that produces all 13 half-steps in one octave. Starting with a 60 cm string, you need a ratio that reaches 30 cm after 12 multiplications. That ratio turns out to be about 0.9439. You move the fret to each calculated length and check the frequency.

The measured notes match the predicted ones every time. The pattern holds across three octaves and more than ten trials each. You also find that notes one octave apart always have a 2:1 frequency ratio.

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.

 

String Length and Musical Notes

Playing music with mathematical formulae

Discover the intriguing connection between math and music, as Eugenia Cheng, mathematician and concert pianist, delves into the fascinating story of how mathematicians' advancements in calculating the 12th root of two enabled Bach to write music in every key. Prepare to be awed by the intricate relationship between these two seemingly unrelated disciplines.

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Math is all about numbers, patterns, and solving problems. Computer science is about using math and technology to create computer programs and solve real-world problems. Together, they help us understand how things work, how to solve problems, and how to use technology to make our lives better!

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1000 Science Fair Projects with Complete Instructions

String Length and Musical Notes

Hypothesis

Method & Materials

Results

Why do this project?

Also Consider

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