Digital Sound & Music: Concepts, Applications, & Science, Chapter 3, last updated 6/25/2013
38
Note Frequency
C4 261.63 Hz
C4# (B4♭)
277.18Hz
D4 293.66 Hz
D4# (E4♭)
311.13 Hz
E4 329.63 Hz
F4 349.23 Hz
F4# (G4♭)
369.99 Hz
G4 392.00 Hz
G4# (A4♭)
415.30 Hz
A4 440.00 Hz
A4# (B4♭)
466.16 Hz
B4 493.88 Hz
C5 523.25 Hz
Table 3.13 Frequencies of notes from C4 to C5
It’s interesting to note how the ratio of two frequencies in an interval affects our
perception of the interval’s consonance or dissonance. Consider the ratios of the frequencies for
each interval type, as shown in Table 3.14. Some of these ratios reduce very closely to fractions
with small integers in the numerator and denominator. For example, the frequencies of G and C,
a perfect fifth, reduce to approximately 3:2; and the frequencies of E and C, a major third, reduce
to approximately 5:4. Pairs of frequencies that reduce to fractions such as these are the ones that
sound more consonant, as indicated in the last column of the table.
Interval Notes in Interval Ratio of Frequencies Common Perception of Interval
perfect unison C 261.63/261.63 = 1/1 consonant
minor second C C# 277.18/261.63 1.059/1 dissonant
major second C D 293.66/261.63 1.122/1 dissonant
minor third
C D E♭
311.13/261.63 1.189/1 6/5 consonant
major third C D E 329.63/261.63 1.260/1 5/4 consonant
perfect fourth C D E F 349.23/261.63 1.335/1 4/3 strongly
consonant
augmented
fourth
C D E F# 369.99/261.63 1.414/1 dissonant
perfect fifth C D E F G 392.00/261.63 1.498/1 3/2 strongly
consonant
minor sixth
C D E F G A♭
415.30/261.63 1.587/1 8/5 consonant
major sixth C D E F G A 440.00/261.63 1.681/1 5/3 consonant
minor seventh
C D E F G A B♭
466.16/261.63 1.781/1 dissonant
major seventh C D E F G A B 493.88/261.63 1.887/1 dissonant
perfect octave C C 523.26/261.63 = 1/1 consonant
Table 3.14 Ratio of beginning and ending frequencies in intervals
There’s a physical and mathematical explanation for this consonance. The fact that the
frequencies of G and C have approximately a 3/2 ratio is visible in a graph of their sine waves.
Figure 3.45 shows that three cycles of G fit almost exactly into two cycles of C. The sound
waves fit together in an orderly pattern, and the human ear notices this agreement. But notice
that we said the waves fit together almost exactly. The ratio of 392/261.63 is actually closer to
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