Audio Frequency Interval Experiments

Experiments in this page demonstrate that human perception of audio frequency is logarithmic. An interval is the change in frequency between two audio frequencies. An interval ratio is the ratio of the two frequencies. Human brain perceives two intervals (that is, the degree of jump from the first frequency to the second) to be equal if and only if their interval ratios are equal.

Experiment A below may be better suited to musicians or someone with some form of musical training. Experiment B below may be better suited to someone who has no background in music.

Experiment A

• Play interval 1 first. It goes from 440 Hz to 493.88 Hz. The difference between the frequencies is 53.88 Hz. The second frequency is 12% more than the first.

• Then play interval 2. It goes from 880 Hz to 987.77 Hz. The difference between them is 107.77 Hz. The second frequency is again 12% more than the first.

• Now play interval 3. It goes from 880 Hz to 933.88 Hz. The difference between them is 53.88 Hz. The second frequency is only 6% more than the first.

• Do intervals 1 and 2 feel equal? That's because both have 12% increase in frequency.

• Do intervals 1 and 3 feel unequal? That's because interval 1 has 12% increase in frequency whereas interval 2 has only 6% increase in frequency.

• The interval used in 1 and 2 is one tone (two semitones). The interval used in 3 is less than a tone. This difference in the intervals may be too small for non-musicians to discern. Go to the next section to see another experiment with larger intervals that might be easier for non-musicians.

Experiment B

• Play interval 1 first. It goes from 400 Hz to 480 Hz. The difference between the frequencies is 80 Hz. The second frequency is 20% more than the first.

• Then play interval 2. It goes from 800 Hz to 960 Hz. The difference between them is 160 Hz. The second frequency is again 20% more than the first.

• Now play interval 3. It goes from 800 Hz to 880 Hz. The difference between them is 80 Hz. The second frequency is only 10% more than the first.

• Do intervals 1 and 2 feel equal? That's because both have 20% increase in frequency.

• Do intervals 1 and 3 feel unequal? That's because interval 1 has 20% increase in frequency whereas interval 2 has only 10% increase in frequency.

• If the intervals sound unpleasant to you because the frequencies do not correspond to any valid notes or intervals in music, go to the previous section to see another experiment for musicians.