The harmonic series, and why open strings ring

Play one note on the violin and you're actually hearing many notes at once. This is the physics under intonation, under "why the major scale sounds natural," and under why your open strings ring.

One string, many pitches

A vibrating string moves as a whole length — and, at the same time, in halves, thirds, quarters, fifths, and so on. Each of those extra vibrations makes a fainter, higher pitch stacked on the main one. The stack is the harmonic series, and the pitches arrive at exact whole-number multiples of the lowest one (called the fundamental).

Above an open G, the first several are:

60 bpm

The first five harmonics of the open G string, at 1×, 2×, 3×, 4×, 5× the fundamental frequency. The intervals they make: the fundamental, then the octave (×2), then an octave + a fifth (×3), then two octaves (×4), then + a major third (×5). They arrive in order of consonance — the most blended intervals first.

Two things fall out of this

Why some intervals are "perfect." The octave, fifth and fourth sit at the very bottom of the series, with the simplest ratios (2:1, 3:2, 4:3). That's why they sound so pure, why they tune so cleanly by ear, and why the violin is strung in fifths.

Why the major triad sounds "natural." Look at harmonics 4, 5 and 6 — G, B, D. That's a G major chord, sitting inside a single vibrating string. The major scale and the major triad aren't arbitrary; they're the low overtones of any note, written out.

Natural harmonics

Touch the string lightly (don't press) at exactly the halfway point, and you silence the fundamental and let only the ×2 harmonic sound — a clear, glassy note an octave up. Touch at 1/3 and you get the ×3 (an octave and a fifth). These are natural harmonics — Stage 3 taught how they're written (a small circle over the note); Stage 6 will drill playing them. Here, they're proof the series is real: you can pick out one member of the stack and hear it alone.

Try it

Try

On the open D string, rest your 3rd finger lightly where you'd normally stop the octave D (about halfway up the string) — barely touching, no weight. Draw the bow. A pure, floaty D an octave above the open string sings out. That's the ×2 harmonic, isolated. Slide the light touch toward the bridge to about a third of the way and you'll find the ×3, a fifth higher still.

The usual mistake

Imagining a played note as a single clean frequency. It never is — it's a fundamental plus a whole ladder of overtones, and the particular mix is what makes a violin sound like a violin and not a flute or a beep. When you hear a note "bloom" or "ring," you're hearing its overtones line up and reinforce.