The Overtone Series Derivation of Tonic Triad – Tonal Model Timbre Chord Spacing

Pitch The perception of pitch is a result of vibration. A body such as a string or column of air vibrates at a particular frequency producing a characteristic pitch. E.g. When a string vibrates at 440 cycles per second (Hz), the note A is perceived.

Fundamental Pitch The perceived pitch is known as the fundamental pitch. The string does not vibrate at the same speed throughout its length.

Overtones Halfway through the length of the string, it barely vibrates at all producing a node. This divides the string into two shorter strings lengths that each vibrate at twice the speed of the complete string. This produces another pitch an octave above the fundamental known as an overtone.

Many Overtones The string also vibrates over 1/3 of its length, 1/4 of its length and so on. The result is that there are many overtones produced above the fundamental pitch. These overtones are too soft to be individually perceived but are nevertheless present.

Overtone Series The overtone pitches result in the following series.

Tonic and Dominant Notice that the first two overtones correspond to the Tonic and Dominant Scale Degrees of the fundamental pitch’s scale. This accounts for the importance of tonic and dominant in tonal music as well as the tonal desire to move by fifths.

Tonic Triad Notice also that the fundamental and first five overtone pitches produce the tonic triad. This is often used to explain the tonal tendency to always want to return to the tonic triad.

Timbre Timbre refers to “colour” of sound. A clarinet and saxophone can play the same pitches but will sound different because of their timbre. Timbre results from the fact that instruments produce overtones with different amplitudes (volumes).

Clarinet vs. Saxophone The clarinet timbre differs from the saxophone because of the relative strengths of their overtones.

Flutey vs. Nasally Generally, an instrument that produces stronger overtones will have a more nasal sound (oboe). An instrument that has weaker overtones will sound more pure (flute). The stronger overtones account for the greater penetrating ability of the oboe but also for its reduced ability to blend with other instruments.

Spacing Traditional spacing of chords usually follows the overtone series. In other words, low pitches are separated by wider gaps than higher pitches. This is because the lower pitches have more perceptible overtones (within hearing range). A low pitch triad will therefore sound muddy (low triad on the piano).

Spacing Effects While the traditional model spaces notes according to the overtone series, interesting effects and chord colours can be created by counteracting the overtone series. A very dark sound can result from combining low instruments with small intervals.