What is a “tone”?

Question

Some musical instruments are capable of making sounds called "tones." For example, a piano, a tuba, a saxophone, a violin, etc. These are all instruments capable of making "tones." Some percussive instruments are also capable of making tones, example timpani, glockenspiel, xylophone. But some instruments are not. For instance, a snare drum. A gong. Sleigh bells. The triangle. These instruments are non-tonal.

I am trying to find a good definition of what exactly a tone is. Some related concepts seem to be

• Frequency -- the number of occurrences of a repeating event per unit of time
• Pitch -- the quality that makes it possible to judge sounds as "higher" and "lower"; the perceptual analog of frequency.

My Question

What is a good working definition of a "tone"?

I want something that will allow me to understand why something like a snare drum isn't tonal.

Answer 1

In terms of the physical acoustics a good reference point to start at is to consider a very long (effectively infinite) chain of pressure pulses/waves of fixed shape that repeat identically at some fixed repetition interval. In terms of the spectral content, this means that there are a set of narrow spectral peaks all at integer multiples of the fundamental frequency, which is the the pulse repetition rate. Note that a single sine wave is a special case: the fundamental but no overtones. Nowadays, this is most easily done with a synthesizer. What you find is that people can order these types of sounds in terms of pitch, and the ordering only depends on the repetition rate, and not on any of the details of the shape of the pulse that is repeated. This type of sound is the "crystalization" of what it means for a sound to be pitched, and thus be tonal.

An important feature of these exactly repeating sounds is that the spectral content is localized at integer multiples of the fundamental frequency that is the inverse of the repetition rate. This uniform separation between the overtones interacts with our hearing system in a special way.

Most real instruments have some deviations from this ideal, vibrating strings have inharmonicities so the overtones are not exact integer multiples; piano notes have an intrinsic decay so there is no exact repeating going on. So most musical sounds are not (cannot be) realizations of the mathematical ideal. As you allow for the spectral peaks to become wider, or have the centers of their spectral peaks move away from being integer multiples of the fundamental, how these physical changes are perceived is a complex question of psychoacoustics. For small (in some sense) deviations people still hear clearly defined pitches that they can combine tonally.

Most drums and cymbals aren't tonal, though a mix of their shorter decay time, and from the fact that they don't produce a regularly repeating sound wave; their spectra don't have the characteristic of evenly spaced partials. Although various overtones exist, they are not structured in a way that is commensurate with how we perceive tonal sounds.

(This description is based on Chpt. 2of Fundamental of Musical Acoustics by A. Benade.)