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Mathematics of Music

Figure from experiment 35 from Physics with Vernier

Introduction

The musical scale used in western music originated with the ancient Greeks. Originally there were seven primary notes to a scale. This is called a diatonic scale and even non-musicians are familiar with it as do-re-me-fa-so-la-ti-do. This scale can be played with the white keys on a piano keyboard, starting with C. As you go through a diatonic scale, it is eight steps from do back to do again. For this reason, this range of notes is called an octave.

Over time, five more notes were added to the western musical scale. This 12-note scale is called a chromatic scale. For a scale starting with C, the five extra notes are played on a piano keyboard by pressing the black keys.

Musical scales are tied closely to mathematics. You will use a Microphone to record the waveform of the sound that is produced. By performing a mathematical analysis of the waveform called a Fast Fourier Transform (FFT), you can break the wave pattern into its component frequencies and determine the fundamental frequency of the sound. Your challenge is to measure the frequencies of all the notes of a chromatic scale and then to determine a mathematical pattern.

The frequencies of two notes played at the same time that sound good to our ears usually have a special mathematical relationship. In this lab, you will investigate the mathematics behind intervals that are commonly used in music.

For this lab, an electronic keyboard is recommended, but you can use other instruments if they are available.

Objectives

  • Determine the frequencies of the notes of a musical scale.
  • Examine the differences and ratio between these notes.
  • Determine the mathematical patterns used in musical scales.

Sensors and Equipment

This experiment features the following Vernier sensors and equipment.

Additional Requirements

You may also need an interface and software for data collection. What do I need for data collection?

Standards Correlations

See all standards correlations for Physics with Vernier »

Physics with Vernier

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2ABack and Forth Motion
2BBack and Forth Motion
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4BDetermining g on an Incline
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10Atwood's Machine
11Newton's Third Law
12Static and Kinetic Friction
13Air Resistance
14Pendulum Periods
15Simple Harmonic Motion
16Energy of a Tossed Ball
17Energy in Simple Harmonic Motion
18AMomentum, Energy and Collisions
18BMomentum, Energy and Collisions
19AImpulse and Momentum
19BImpulse and Momentum
20Centripetal Accelerations on a Turntable
21Accelerations in the Real World
22Ohm's Law
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27Electrical Energy
28APolarization of Light
28BPolarization of Light (Rotary Motion Sensor)
29Light, Brightness and Distance
30Newton's Law of Cooling
31The Magnetic Field of a Permanent Magnet
32Sound Waves and Beats
33Speed of Sound
34Tones, Vowels and Telephones
35Mathematics of Music

Experiment 35 from Physics with Vernier Lab Book

<i>Physics with Vernier</i> book cover

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