Digital Sound & Music: Concepts, Applications, & Science, Chapter 3, last updated 6/25/2013

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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