Understanding how guitars and strings produce sound is the first step to understanding the physics of distortion.
We hear the words fundamental, harmonics, distortion and total harmonic distortion (THD) quite often when discussing music and sound. Let’s consider these from a couple of angles and see how they relate to guitar tone. We’ll start with some basic terminology and take a look at how guitars and guitar strings produce sound. Once we grasp those things, it’s easier to understand the ways that stompboxes and amps generate distortion—our topic in Pt. 2.
One of the first things guitar players learn (after “Smoke on the Water”) is how to play a harmonic at the 12th fret. (The beginning to “Roundabout” is a classic example of the musical use of harmonics.) The fundamental is the lowest frequency that a fretted or open string produces. The second harmonic is twice the frequency of the fundamental—an octave up. The third harmonic is three times the frequency of the fundamental—an octave plus a fifth.
Let’s Get Physical
Understanding this requires a detour into the physics of vibrating strings. When you pluck a string, its vibration creates a wide range of frequencies. But soon after the note is struck, all that remain are the fundamental and harmonic frequencies. When you pluck the string while touching the 12th-fret harmonic, you are effectively “cutting the string in half.” This eliminates the fundamental and any odd-numbered harmonics.
A node is a point on a string at which the string doesn’t move. The guitar has nodes at the nut and the bridge (see image), much like a playground jump rope has nodes where the kids hold the rope (ignoring the fact that the kids have to move a bit as they add energy to the rope). A 12th-fret harmonic forces a node in the middle of the string—like stepping on the middle of the jump rope.
Octaves are a way of describing factors of two. The fundamental frequency of the low E on a guitar is about 82 Hz. The low E on a bass guitar is an octave lower, or around 41 Hz. Notes on the 12th fret are an octave above the open string—twice the frequency. The harmonic that is twice the frequency of the fundamental is called the second harmonic. (That makes the fundamental the first harmonic, though you rarely hear it referred to that way—we usually just say fundamental.)
Higher and Higher
What about harmonics on other frets? The 7th fret is one-third the distance from the nut to the bridge. This makes a harmonic struck above this fret three times the frequency of the fundamental. (Extra credit for finding the other fret that creates the same harmonic as the 7th fret.) The 5th fret is one-quarter the distance from the nut to the bridge, and a harmonic struck there is two octaves above the open string.
You’ve probably noticed that it gets quite a bit harder to produce harmonics below the 5th fret. That’s because it becomes increasingly difficult for the string to vibrate in smaller sections. (This is where a real string and an idealized physical model start to diverge. A theoretical “ideal string” has an unlimited number of harmonics.)
To understand why a piano string sounds different from a nylon guitar string, or why your tone changes when you switch between 1st strings gauged .009 and .011, we need a few more facts about string physics.
The Tension Mounts
When we tighten a string with a tuner, pull up on the whammy bar, or bend a note, we increase string tension. Pitch increases as the square root of the tension. Another factor for an ideal string is the linear density, or mass per unit of length. A heavy string at a given tension vibrates at a lower frequency than a lighter string at the same tension. Conversely, a heavy string tuned to a particular pitch is under greater tension than a thinner string tuned to the same pitch. (You may have noticed that your truss rod and vibrato springs needed tightening when the ’80s ended, you ditched the spandex, and you switched from .009s to .011s.)
The higher the tension, the brighter the string sounds. If we want high tension and low frequency, then we need a long length, which is why a grand piano has such long strings. The difference in the tone of strings is in the balance of the fundamental and harmonics. Brighter-sounding strings have louder harmonics than mellow-sounding strings.
The way the fundamental and harmonics decay over time also determines the character of a string. Energy gets put in the string when we pluck it, and that energy decays as it vibrates the air and the instrument body. The materials of the string and instrument body determine the rate at which varying frequencies decay.
A guitar’s body has various resonances, depending on its shape, wood type, and finish. When a string frequency matches one of the body’s resonant frequencies, the body vibrates and sucks energy out of the string. This makes the note decay more quickly as it absorbs the string’s energy. (The body’s resonance actually decreases the string’s sustain. But if we’re playing through an amplifier, the guitar’s body absorbs energy from the sound waves produced by the amp, and sustain increases as energy is transferred back to the string.)What about harmonic distortion? We’ll look into distortion and clipping in more detail next time.
Looking for more great gear for the guitar player in your life (yourself included!)? Check out this year's Holiday Gear Finds!
D'Addario XPND Pedalboard
DR-05X Stereo Handheld Recorder
Wampler Pedals Ratsbane
Created in collaboration with legendary guitarist George Lynch of Dokken and Lynch Mob fame, the Mr.Scary Mod adds an adjustable tube gain stage and an onboard Deep control, which together are designed to enable an amp to have increased sustain while still retaining note definition and dynamics.
LegendaryTones, LLC today announced production availability of its new Mr. Scary Mod, a 100% pure tube module designed to instantly and easily expand the capabilities of many classic amplifiers with additional gain and tone shaping. Created in collaboration with legendary guitarist George Lynch of Dokken and Lynch Mob fame, the Mr.Scary Mod adds an adjustable tube gain stage and an onboard Deep control, which together are designed to enable an amp to have increased sustain while still retaining note definition and dynamics.
Originally released as the Lynch Mod in February 2021, the updated Mr. Scary Mod features the same core circuit as the Lynch Mod but is now equipped with a revised tube mix combo per George’s preference as well as a facelift in a newly redesigned electro-galvanized steel enclosure. As with the Lynch Mod, each run will be limited and the first run in Pumpkin Orange with Black hardware is limited to just 150 pieces worldwide.
The Mr. Scary Mod adds an adjustable tube gain stage on top of the cathode follower position, keeping note definition and articulation while further increasing sustain. Each Mr. Scary mod is meticulously built by hand in the USA, one at a time, and tuned using high-grade components. Equipped with a single ECC81 (12AT7) in the first position and ECC83 (12AX7) in the second, the Mr. Scary Mod can clean up beautifully when rolling down your guitar’s volume, and still adds scorching gain when you roll it back up. This is a gain stage that’s been tuned and approved by the ears of the maestro George Lynch himself.
“The Mr. Scary Mod excels with dynamics and is incredibly touch-responsive, allowing me to shift from playing clear, lightly compressed cleans to full-out aggressive sustain and distortion –and control it all simply by varying my guitar’s volume control and picking,” said GeorgeLynch. “In many ways, it’s an old-school approach, but it’s also so much more natural and expressive in addition to being musically fulfilling when you can play both the guitar and amp dynamically together this way.”
The Mr. Scary Mod installs in minutes, is safe and effective to use, and requires no special tools or re-biasing of the amplifier. Simply insert the module into the cathode follower preamp position of compatible amplifiers (includes Marshall 2203/2204/1959/1987 circuits) and
immediately get the benefit of enjoying a hot-rodded amp that delivers all the pure harmonic character that comes with an added pure tube gain stage. The handmade in the USA Mr. Scary Mod is now available to order for $319.
For more information, please visit legendarytones.com.
October Audio has miniaturized their NVMBR Gain pedal to create two mini versions of this beautifully organic-sounding circuit – including an always-on gain device.
The NVMBR Gain is a nonlinear amp that transitions gracefully from clean boost to overdriven tones. Volume increases from just over unity to about 10db before soft-clipping drive appears for another 5db of boost. Its extraordinary ease of use is matched by outstanding versatility: you can use it as a clean boost, push a stubborn amp into overdrive or create a just-breaking-up sound at any amp volume.
October Audio’s new family of mini NVMBR Gain pedals includes a switchable version that allows you to bypass the effect: one option features brand logo pedal graphics, while the other sports a fun “Witch Finger” graphic with a Davies knob as the“fingernail”.
The second version in the new lineup is an always-on device featuring the Witch Finger graphic and Davies knob, with the same NVMBR Gain circuit that lies at the core of the switchable version.
- Knob controls gain and clipping simultaneously
- Stunning silver hammertone finish
- Switchable versions are true-bypass, available with classic or witch finger graphics
- Authentic Davies knobs, including the “fingernail”
- 9V center negative power supply required
- Dimensions: 3.63 x 1.50 x 1.88 in
Witch Finger (always on NVMBR Gain) demo
All October Audio pedals are assembled in Richmond, VA, and available for purchase directly through the online shop. Street price is $109 for NVMBR Gain footswitch versions and $89 for the always-on device.
For more information, please visit octoberaudio.com.