Harmonics and timbre
A note is the sum of many frequencies; their balance decides the timbre, and on guitar you can isolate some of them as natural harmonics.
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A note is the sum of many frequencies; their balance decides the timbre, and on guitar you can isolate some of them as natural harmonics.
Applied
When you pluck a string, it doesn't just vibrate as a whole. At the same time it vibrates in two halves, three thirds, four quarters… Each of those vibrations produces a frequency: the fundamental and its harmonics, whole-number multiples of it. Your ear fuses them into a single note, but their balance decides the timbre: why a guitar doesn't sound like a flute even when they play the same note.
The first harmonics of A at 110 Hz, one after another. Notice how they form smaller and smaller intervals:
Pick a vibration mode: the second splits the string in two and sounds an octave higher; the third splits it in three and sounds an octave and a fifth above:
| Harmonic | Frequency on the 5th string | Interval from the fundamental | Fret to play it |
|---|---|---|---|
| 1 | 110 Hz | unison | open string |
| 2 | 220 Hz | octave | 12 |
| 3 | 330 Hz | octave and a fifth | 7 and 19 |
| 4 | 440 Hz | two octaves | 5 |
| 5 | 550 Hz | two octaves and a major third | near 4 |
In the sound lab, additive mode sums harmonics at whatever strength you choose. Start with the fundamental alone and add harmonics one by one:
Additive synthesisAnd on the guitar: rest a fretting-hand finger right over the 12th fret of the fifth string without pressing, pluck the string and lift the finger. You'll hear a natural harmonic. Repeat at frets 7 and 5.
You can get the harmonic of any fretted note: hold a fret with your fretting hand and, with the picking hand, touch the string twelve frets higher while plucking. There's also the pinch harmonic: the pick and the edge of the thumb hit the string almost together, and depending on the spot a high harmonic jumps out, a staple of rock.
Helmholtz was the first to explain timbre as the result of combining harmonics. Today we know that the attack, how each harmonic evolves over time and the instrument's resonances also matter; those resonances boost certain frequency bands called formants. Because of their stiffness, real strings have harmonics slightly sharper than exact multiples; this is inharmonicity, more noticeable on thick strings.