Construction of the Musical Scale

The purpose of this activity is to investigate the scale that is most commonly used for Western-style music, and to listen to some of the consonance it can produce.

Theory

The pitch of a note is determined by its frequency, and the human ear perceives notes as differences in frequency ratios, rather than differences in the relative amplitude of the frequency.

The ratios of the 12-note mean scale used for most Western-style music is governed by a number of restrictions. First, the frequency ratio of the same note from one octave to the next is 2:1 (higher note to lower note). Each octave is divided into 12 parts, with the same frequency ratio between each of the adjoining notes in the octave. The illustration below shows each of the notes in an octave, on a piano keyboard.

11 Octave (2:1 frequency ratio between notes)

2Tonic Note (Low Note)

3Harmonic (High Note)

4Adjacent Note (Note Frequency Ratio = 2(1/12))

The frequencies of this 12-note scale can be expressed as shown below.

n

fn = 2 12 f 0

f 0(Hz) : Tonic Note Frequency

f 12(Hz): Harmonic Frequency

fn(Hz) : Frequency of nth Note (n = 1, 2, 3, ....12)

1Frequency (Hz)

2Low Note

3High Note

Generally, notes consist of sound waves of different frequencies and amplitudes. Producing two notes of different pitches at the same time sounds pleasing to the human ear, and such notes are said to be “consonant.” Two notes whose frequency ratio is the ratio of two simple integers are very consonant.

2-8-1

English

Activity:tivity: SetupSetup

￿Equipment

Piano (Sound Source) Computer (MIDI Sound Source)

Audio Measurement Setup (EA-200, graphic scientific calculator, data communication cable)

￿Setting Up

uTake care so there is no unwanted noise in the area where you are conducting the activity.

1

1 Piano

 

2 Computer (MIDI

2

Sound Source)

 

3 EA-200

 

3

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