Subjective Tones

When two single-frequency tones are present in the air at the same time, they will interfere with each other and produce a beat frequency. The beat frequency is equal to the difference between the frequencies of the two tones and if it is in the mid-frequency region, the human ear will perceive it as a third tone, called a "subjective tone" or "difference tone". The difference tones are always present, but they can be made prominent by using two high, clear tones like the notes of a flute. With two flutes you can produce a "trio for two flutes". This phenomenon can also be produced with one brass instrument (multiphonics). If a French horn player plays one note and hums another, then the subjective tone which is the difference between them can sometimes be heard clearly.

One important role of subjective tones is the missing fundamental effect whereby a correct sense of pitch for a musical sound may be maintained even if the poor fidelity of the sound reproduction has filtered out some of its lower harmonics.

Missing Fundamental Effect

The subjective tones which are produced by the beating of the various harmonics of the sound of a musical instrument help to reinforce the pitch of the fundamental frequency. Most musical instruments produce a fundamental frequency plus several higher tones which are whole-number multiples of the fundamental. The beat frequencies between the successive harmonics constitute subjective tones which are at the same frequency as the fundamental and therefore reinforce the sense of pitch of the fundamental note being played.

If the lower harmonics are not produced because of the poor fidelity or filtering of the sound reproduction equipment, you still hear the tone as having the pitch of the non-existant fundamental because of the presence of these beat frequencies. This is called the missing fundamental effect. It plays an important role in sound reproduction by preserving the sense of pitch (including the perception of melody) when reproduced sound loses some of its lower frequencies.

The presence of the beat frequencies between the harmonics gives a strong sense of pitch for instruments such as the brass and woodwind instruments. For percussion instruments such as the cymbal, the sense of pitch is less definite because there are non-harmonic overtones present in the sound.

Multiphonics

One of the applications of subjective tones is the production of three tones by a single brass player. The player plays a note in the usual way but in addition hums a second note into the mouthpiece. The beat frequency between these two notes produces a third tone. Such tones are sometimes called multiphonics.