When two pitches are sustained simultaneously, a new pitch is produced whose frequency is the difference between the frequencies of the two original pitches. Therefore, the resulting pitch is called a difference tone. The difference tone interacts with the original sounding pitches and produces an infinite series of other difference tones of decreasing intensity.
The more precisely an interval corresponds with its position in the harmonic series, the more resonant it becomes because newer difference tones reinforce previously sounding frequencies found in the harmonic series. As the discrepancy between the size of a sounding interval and its theoretically “perfect” size increases, the more the frequencies produced deviate from those in the harmonic series.
In simpler terms, the more exact the interval size, the more resonant it is because it is somewhat literally less “dissonant.” A good analogy would be like a camera coming into focus. As the camera comes into focus, the image becomes more clear and less distorted.
Musicians can use difference tones to increase their awareness of pitch and interval sizes. For this exercise, play an ascending or descending major scale with a drone on the starting tonic pitch.
Adjust to the drone by listening for the difference tones in the examples below. Not all difference tones are easily heard by the human ear. In theory, all of the pitches in the example below should exist but might not be heard. Difference tones of the first two orders have been notated with diamond-shaped noteheads. These will likely be the easiest ones to hear.
You will notice that the pitch of the difference tones changes depending on the size of the interval between you and the drone. When you can hear only the pitches notated in the example, the interval size is correct.
Rather than focus on each individual pitch, try to imagine the entire harmonic structure. For this reason, harmonic analysis is provided below each example.
