The Harmonics of Overtones: Exploring Sum and Difference Tones

The technical term for two people or instruments singing or playing two different notes simultaneously and creating the perception of an additional note due to the interaction of their two sound waves is called a resultant tone, or more technically, combination tone. This phenomenon can be described in terms of sum tones and difference tones, which are tones that arise from the combination of the original frequencies. In music, these tones are controlled by the specific relationships between the notes being played.

Understanding Sum and Difference Tones

When two pitches interact, they tend to create both sum and difference tones. This is influenced by a variety of factors, including resonance and distortion. More complex or distorted sounds will usually have more interactions, and these tones can be more or less fully expressed based on the resonance of the surroundings.

Sum and difference tones are tones generated at both the frequency that is the sum of the two and also the difference of the two. These tones will also generate their own sum and difference tones relative to each other and the original tones, creating a complex sonic potential. This can be mitigated or enhanced by the acoustic environment in which the music is played. This is why concert halls sound better than typical residential spaces, as they provide excellent resonance and acoustics.

Practical Applications: Hearing Sum and Difference Tones

The easiest way to hear a difference tone is when tuning two guitar strings. When you fret the lower string to match the pitch of the higher string, and the top note is tuned to A440 Hz, the lower note is either too high (A442) or too low (A438), resulting in a difference of 2 Hz, which you hear as a "wahh wahh" at 2 beats per second. As the interval between the two pitches gets larger, you can actually perceive the pitch of the difference tone. For example, when a soprano sings A440 and a C note a major third above it (C550), the difference tone you hear is 110 Hz, which is the A, an octave and a third below middle C. This is known as "ringing" the chord and can sound fuller and richer if the C is perfectly tuned.

The same effect can be observed with the sum tone. When a bass and a tenor sing an A (110 Hz) and an E (165 Hz), the sum tone is 275 Hz, which sounds like an alto singing middle C. If the initial notes are not in tune, the sum tone will be some dissonant note that does not contribute to the harmony. This works best with just intonation, where the intervals are based on the harmonic series, but equal temperament, as used in pianos and electronic instruments, can also produce these tones, though not as consistently.

The Role of Overtones in Musical Ensembles

Any note that is not a pure sine wave contains harmonics, which combine in the same way as the fundamentals do, only more softly. This combination of overtones in large string sections and very in-tune choirs gives a "sheen" to the sound of the group. If you have a good sense of tuning, you can make a small number of voices or instruments sound much more numerous than they actually are by exploiting these interactions.

In conclusion, the phenomenon of resultant tones, often referred to as sum and difference tones, is a fascinating aspect of music and sound. Understanding and harnessing the effects of these tones can significantly enhance the richness and complexity of musical performances. Whether in a concert hall or a recording studio, the knowledge of these acoustic phenomena can help musicians and producers create more intense and engaging musical experiences.