Harmonic Series

What it is

The harmonic series is the set of frequencies a vibrating string produces simultaneously. A string does not sound one pitch; it sounds many, and their relationship is fixed by physics. Practising this is easier with the free chromatic tuner. See the left hand section for everything related.

The lowest is the fundamental, which is the pitch the ear identifies as the note. Above it, at mathematically determined intervals, sit the overtones.

Understanding the series explains harmonics, tone colour, resonance, and why instruments sound different from one another.

The physics

A string fixed at both ends vibrates along its whole length, producing the fundamental.

It simultaneously vibrates in halves, producing a pitch an octave above. In thirds, producing an octave and a fifth. In quarters, two octaves. In fifths, two octaves and a major third. And so on, indefinitely, with each successive division producing a higher and quieter component.

All of these happen at once. What the ear hears as a single note is the fundamental accompanied by a stack of overtones.

The pitches

Taking a low G as the fundamental, the series runs:

G, the fundamental. G an octave above. D, an octave and a fifth above. G, two octaves above. B, two octaves and a major third above. D, two octaves and a fifth above. Then progressively closer intervals as the series climbs.

The intervals get smaller as the series ascends, which is why the lower overtones are the ones that matter musically and the higher ones blur into tone colour.

Notably, some of the higher overtones do not correspond to notes in equal temperament. The seventh partial is noticeably flatter than the equal-tempered minor seventh, which is a real acoustic fact with consequences for intonation.

Why it explains harmonics

Every point where the string stays still during one of these subdivisions is a node.

Touching the string at a node suppresses everything that does not have a node there, isolating a single overtone.

The midpoint is a node for the octave division, so touching there produces the octave. A third of the way along is a node for the third division, producing the twelfth. And so on.

Harmonics are not a trick; they are a way of selecting one component of what the string is already doing.

Why it explains tone colour

Two instruments playing the same pitch sound different because the balance of overtones differs.

A violin, a flute and a voice all produce the same fundamental on a given note. What distinguishes them is which overtones are strong and which are weak.

On a single instrument, the same principle explains why bow position changes the sound. Bowing near the bridge excites more upper overtones, producing a bright sound. Bowing over the fingerboard excites fewer, producing a soft one. Sul ponticello and sul tasto are applications of this.

Why it explains resonance

When a note is played, other strings that share overtones with it vibrate sympathetically.

Playing a D on the A string sets the open D string vibrating, because they share a fundamental relationship. The instrument rings more than the single note alone would explain.

This is why playing in tune produces a fuller sound than playing slightly out of tune. In tune, the sympathetic resonances reinforce. Out of tune, they do not.

Students often notice that certain notes ring more than others without knowing why. This is the answer, and knowing it turns an accident into a tool for checking intonation.

Practical consequences

Intonation checking. A note that makes the instrument ring is more likely in tune than one that does not. Listening for resonance is a usable intonation check.

Tone colour control. Understanding that contact point selects overtones makes sul tasto and sul ponticello intuitive rather than arbitrary.

Harmonics. Knowing where the nodes are and why makes finding them a matter of understanding rather than memorisation.

Double stop tuning. Intervals sound in tune when their overtones align. Listening for the elimination of beating is listening to the harmonic series.

Where it comes up

It underlies everything but is rarely discussed explicitly in lessons.

It appears in music theory coursework, in acoustics, and in any serious study of tone production.

Students who understand it find several previously arbitrary-seeming techniques suddenly make sense, which is why it is worth teaching even though it is not itself a technique.

How it is taught

Usually by demonstration rather than explanation.

Playing a low note and listening for the overtones, which are audible with attention. Playing a note and watching another string vibrate sympathetically. Finding the harmonics and connecting them to the divisions of the string.

The mathematics can be shown, but the sound is more convincing, and a student who has heard the series is far more likely to remember it than one who has only read about it.

Most students pick left-hand work like Harmonic Series up faster with weekly feedback than from any article. Private and group violin lessons are available in Sugar Hill, Cumming and Sandy Springs. Reach us on 470-789-2422 or book a no-commitment evaluation lesson.