The Overtone Series

As we noted in the section on pitch, an octave consists of two pitches whose frequencies are in the ratio of 1:2 (i.e. A0= 55hz and A1=110 hz). The upper pitch, being a perfect multiple of the lower, acoustically reinforces it, resulting in what we call a consonance.

If we continue to add new pitches that are multiples of the fundimental, we call these multiples overtones or harmonics. The original pitch on the bottom is called the fundamental. Each multiple is called an overtone (or harmonic). The following chart shows the first fourteen overtones above the pitch C1:

Note that some of the overtones are slightly out of tune with our Western tuning scales. These notes are shown in parentheses.

The overtone series forms the basis for tonal music of the common practice period. It is important for musicians to be familiar with the overtone series in order to understand why music functions as it does.

What can we learn from the overtone series?

If we look at the interval of each note above the fundamental (reducing those greater than an octave) we discover that the perfect intervals of P8 and P5 are closest to the fundamental. These most strongly "fit" or reinforce the fundamental, forming what we call a consonance. As we move from left to right (farther away from the fundamental) the frequencies are not as closely related, and so we consider those intervals more dissonant. Notice that the interval P4 does not appear until far into the overtone series. This is why for many years (1000-1750 c.a.) musicians considered the seemingly "perfect" interval of P4 to be a dissonance. In fact, it wasn't until approximately the year 1300 until a third was considered "consonant"!

Also important is the set of intervals between each of the notes. Including the intervalic inversions, we may derive a more comprehensive chart of relative consonance and dissonance that has influenced musicians of all periods. Since the tritone does not appear in the series, it is the most removed or dissonant interval. One may also think of consonance and dissonance in terms of harmonic stability and instability, since this is how composers have used these intervals in their music.

This forms the basis for the theory of tonal harmonic function, which will be explored in the following sections.

Links:

• Next section: Chords (Triads and Seventh Chords)
• Table of Contents