Suomeksi | In English

Partial tones

Sounds have traditionally been classified into tones and noise (with various subtypes such as white, pink and red noise). Noise has no clear pitch. Many percussion instruments, such as cymbals, the triangle, membrane drums, etc, produce noises, and there is a rich repertoire of words describing various types of noises (such as splash, clang, ring, creak).When a text is sung, many of the consonants (s, h, t, p) are noises, while vowel sounds have a perceivable pitch.

All sounds consist of sine wave shaped oscillations known as partial tones. Both noise and tones produced with musical instruments consist of various frequencies the ear perceives as a whole. Sounds with no more than one frequency (f) can only be generated using technical devices. Sounds produced using an acoustic instrument or by singing consist of a fundamental frequency (which is also partial tone) and overtones that are mostly integer multiples of the frequency of the first harmonic (2f, 3f, 4f, etc). These multiples constitute the harmonic series. The following notation illustrates the first 16 overtones of the harmonic series. Theoretically speaking, the harmonic series continues to infinity at decreasing intervals.


Observations on partial tones

The fundamental frequency or the first harmonic is the perceived pitch of the sound. When a musical instrument produces a great C, the attention of the ear focuses only on the fundamental frequency (the first harmonic). All other harmonics are heard as much weaker; indeed, hearing the other harmonics at all requires considerable experience.

The second harmonic sounds an octave higher than the first harmonic. Its frequency (measured in Hz) is twice that of the fundamental. The second harmonic can sometimes be detected in the timbre of an instrument such as the flute, where the same fingering can be used to produce tones (D1 and D2, for example) from the first and the second octave range simultaneously using the so-called overblowing technique.

The third harmonic sounds just a perfect fifth from the second harmonic, although the difference between the two tones (measured in Hz) remains the same. The difference in frequency between the successive harmonics is always the same. Ear, therefore, perceives the pitch differences logarithmically: the interval between 100 Hz and 200 Hz is perceived to be the same as the interval between 1000 Hz and 2000 Hz. In both cases, the difference constitutes an octave.

The 4th, 5th and 6th harmonics form the tones of the so-called pure major triad. The prevalence of the major triad has sometimes been validated with this “physical” phenomenon.

The 7th harmonic is noticeably low and shows the most severe departure from any equally tempered system, while the 8th harmonic is exactly two octaves above the perceived pitch of the sound.

A natural harmonic series corresponding with the theoretical harmonic series can be produced using many acoustic instruments. When produced using stringed instruments they are called flageolet tones, while players of wind instruments speak of overblowing (using the same fingering to produce tones belonging to a natural harmonic series). A natural harmonic series, however, consists of tones, not just pure tones.

Clarinets and other wind instruments with a so-called cylindrical bore produce an octave and a fifth when overblown. Instruments using a conical bore or two open ends (such as the flute, the oboe, the saxophone and the brass winds) produce an octave and all of its natural overtones when overblown.

The timbre that is characteristic of the clarinet is a result of its very weak even (4th, 6th, 8th, ...) harmonics. Early synthesizers and electronic organs produced a timbre resembling a clarinet synthetically using only the odd harmonics.

Harmonics whose numbers are a power of 2 (such as 4, 8, 16, 32, etc) are the octave multiples of the fundamental frequency (the first harmonic). All “fifths” are 3 · 2n (3rd, 6th, 12th etc) while all “major thirds” are 5 · 2n (5th, 10th, 20th etc).

The series of partial tones may also be inharmonic. When it is, the term partials may be used to refer to its partial tones instead of calling them harmonics. The ratios between inharmonic partials are not integers. In practice, however, the frequencies of the partial tones produced by acoustic instruments also differ slightly from the theoretical series of perfect harmonics. This difference creates a sensation of vividness and a certain “roughness”.

Self-study exercise: Partial tones

Practice forming different timbres using the applet below. Select a pitch name (for example, B) and start the program. Then listen to the individual harmonics by adjusting the sliders (beginning with the first one). The display shows how the waveform changes from a sine wave to a more complex waveform.

When you change the tone, the auditory sensation becomes a timbre, and distinguishing the individual harmonics becomes nearly impossible. You can change the frequency and the intensity of the sound using the sliders at the bottom.