Overtones
When an instrument plays a note, it is attempting to generate a specific fundamental frequency. For example, if we play the low open A string, we expect a fundamental frequency at 110 Hz. Overtones are pitches that are present in an instrument by nature of the instrument itself above the fundamental frequency, following the harmonic series. Distortion will add a lot more. Overtones are not the notes in a chord played above the bass frequency - that is simply several fundamentals played at the same time. Each of those fundamentals will have their own overtones.
Harmonic Series
The harmonic series is simply the set of all frequencies n multiples above the fundamental.
| Harmonic Order | Pitch | Note | Interval |
|---|---|---|---|
| 1 | 110 Hz | A | Unison |
| 2 | 220 Hz | A | Octave |
| 3 | 330 Hz | E | Perfect 5th |
| 4 | 440 Hz | A | Octave |
| 5 | 550 Hz | C♯ | Major 3rd |
| 6 | 660 Hz | E | Perfect 5th |
| 7 | 770 Hz | G | Minor 7th |
| 8 | 880 Hz | A | Octave |
Effect on Tone
The best way to analyze the impact of overtones on the tone of a sound is to look at synthesized waveforms. A synthesized wave adds or subtracts overtones to alter the waveform. Since the overtones are part of the harmonic series and are divisible by the fundamental without a remainder, adding them produces a new periodic waveform at the fundamental frequency. In other words, looking at the wave on an oscilliscope will change shape as overtones are increased or lessened.
- Sine wave - The sine wave is just the fundamental without overtones. It sounds very dark and dull, like using the guitar's neck pickup and reducing the tone knob to 0. Vocally, it is similar to humming.
- Triangle wave - A triangle wave has progressively diminishing overtones, so the waveform is most impacted by the those closest to the fundamental. It sounds brighter and more interesting than a pure sine wave. Vocally it sounds like "aaaaaa".
- Square wave - A square wave has perfect overtones extending out to infinity with the same volume as the fundamental. As expected it sounds bright, but it doesn't sound shrill. Actually it sounds quite pleasing. Vocally it sounds like "ooooo".
Applied to Guitar
Guitar strings tend to have lots of overtones by nature. This is heightened by several things:
- New strings
- Using a pick vs. fingers
- Playing harmonics vs. open strings vs. fretted notes
- Using higher values on the tone knob
- Picking location on the string
- Picking style/angle/strength
Distortion also tends to emphasize overtones. The most basic method of distortion is clipping, where the peaks of the waves are "cut-off" or flattened. If the guitar signal is a sine wave, it becomes clear to see that the greater the clipping that occurs, the more the signal resembles a square wave, which we know has high levels of overtones.
Applied to Synthesizers
Synths can often start by synthesizing different waveforms such as triangle or square waves. These waveforms can be viewed as a composite of infinite number of sine waves along the fundamental frequency's harmonic series, with different relative volumes. For instance, a triangle wave's overtones appear to be less and less prominent as frequency and harmonic order increase, while a square wave has infinite overtones of equal volume.
Synths often have resonance and cutoff controls - these simply control a low-pass filter. The cutoff control changes the cutoff frequency, reducing overtones beyond that point. "Resonance" affects the filter's resonance at the cutoff frequency, possibly boosting overtones near the cutoff frequency relative to the fundamental. These controls are often automated or manipulated gradually over a repeated riff or progression to make it more interesting and/or to build energy into the next section.