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14 Ratio and proportion

Every musical note has a frequency. !is is measured

in hertz (Hz).

!e frequency tells you how many times a string
playing that note will vibrate every second.

!is table shows the frequency of some of the notes
in the musical scale, rounded to one decimal place.

Note C D E F G A B C 1

Frequency (Hz) 261.6 293.7 329.6 349.2 392.0 440.0 493.9 523.3

!ere are very simple ratios between the frequencies of some of these notes.
Frequency of C : frequency of C = 2 : 1 because 523.3 ÷ 261.6 = 2.00 or 2 or 2 : 1
1
1
Frequency of G : frequency of C = 3 : 2 because 392.0 ÷ 261.6 = 1.50 or 3 or 3 : 2
2
Frequency of A : frequency of D = 3 : 2 because 440.0 ÷ 293.7 = 1.50 or 3 or 3 : 2
2
Frequency of A : frequency of E = 4 : 3 because 440.0 ÷ 329.6 = 1.33 or 4 or 4 : 3
3

!e frequencies of G and C are in the same proportion as the frequencies of A and D; they both have
the same ratio, 3 : 2.
Can you "nd some other ratios from the table that are equal to 3 : 2?

!e frequencies of A and E are in the ratio 4 : 3.

Can you "nd some other pairs of notes in the same proportion, with a ratio of 4 : 3?

Can you "nd any notes where the frequencies are in the ratio 5 : 4?

When the ratio of the frequencies is 2 : 1, one note is an octave higher than the other.
C is an octave higher than C.
1
Can you "nd the frequency of D , which is an octave higher than D? What about other notes?
1

Can you "nd the frequency of the note that is an octave lower than C?

In this unit you will compare ratios, and interpret and use ratios in a range of contexts. You will also
solve problems involving direct proportion and learn how to recognise when two quantities are in
direct proportion.

14 Ratio and proportion 135