Interested in exploring the history of scales and temperaments? J. Murray Barbour’s classic Tuning and Temperament: A Historical Survey examines the various systems that have been used across the centuries.
Do you remember the first time you felt intonation? I was in junior high, taking my second guitar lesson. My teacher, Mike Hoover, hit a 5th-fret E harmonic on the 6th string and then struck the 7th-fret E harmonic on the A string. As he slowly turned a tuner, I felt the fast pulse of the discord begin to slow down and eventually stop as the two notes became one. I could almost see the sine waves line up. Like so many guitarists, that was the moment I began a quest to achieve perfect intonation. Regrettably, this isn’t as simple as that early harmonic lesson led me to believe.

Duke Ellington said he only really understood music when he grasped the difference between G# and Ab. The Duke never did explain his cryptic quote, but he was probably talking about tonal context and enharmonics. G# and Ab are “enharmonic,” which means they are tones that have the same pitch, but different letter names. (Which name you use depends on the scale association.) Though they’re literally the same note on the piano and guitar, if you mathematically work out the frequencies, there actually isa difference: G# is 41 cents lower.

Quibbling purists talk this way to make dumb guitar schmoes like me feel inferior. However, there is scientific truth to this sharp and flat distinction, and whether you know it or not, you’ve probably been unconsciously adjusting for it. According to the laws of physics, intervals change with keys. But the modern, equal-temperament tuning system we use in Western music makes a few fudgy concessions to deal with the limitations of set-tuned instruments like guitar.

The math behind tuning looks like the calculus-class chalkboard in the movie A Beautiful Mind, but in a nutshell, it works like this: With equal temperament, the octave is divided into 12 half-steps, and each adjacent interval has an identical frequency ratio. But—here’s the rub—except for octaves, no intervals have exact ratios.

Harmony is order in chaos. Pythagorean tuning found harmony in fifths, but perfect fifths produce out-of-tune octaves and thirds. A slew of mathematicians have suggested meantone temperament could remedy the Pythagorean shortcomings by narrowing all fifths, except for one. The problem? Meantone tuning produces more than 12 notes in an octave. Renaissance instrument builders produced keyboards with split accidental keys—D# and Eb, G# and Ab, and others.

J.S. Bach popularized wohl temperiert tuning, a scheme that grew into the system used on modern keyboards. This employs built-in dissonance that sounds right(ish) in context. Hit a middle C on a piano, then the highest and lowest C notes. You’ll hear imperfect intervals, but it’s close enough for rock and roll ... or Bach.

Because masterfula cappella groups and string ensembles aren’t bound by frets, their members can individually adjust their intonation in real time. This allows them to produce incredibly sweet harmony. About 15 years ago, the Beach Boys did an album in Nashville with country artists. I was lucky enough to play in the house band for one of their Nashville shows. We did our soundcheck, then Brian Wilson, Mike Love, Al Jardine, Bruce Johnson, and Carl Wilson sanga cappellato ring in their monitors. Though I’d never been a Beach Boys fan before, I can honestly say I’d never heard anything so extraordinary. Without our instruments cluttering up the sonic landscape with questionable tuning, those voices produced pure harmony.

Though our static fretboard rules out such pitch flexibility, there are ways we can improve our intonation. Most good players do this, though often unconsciously. Ever notice how when you play songs, you avoid certain strings or chord voicings because they just don’t sound right? That’s you adjusting for a glitch in the system.

Another example is our beloved big, dumb power chords. They always sound great because removing that pesky third gives you closer intonation and a fun ambiguity. (Is it major? Is it minor?) Add a little distortion, and tuning becomes even less of an issue. Ever notice how gently manipulating a whammy bar or adding a bit of chorus or Leslie simulation can make a guitar sit well in a mix? As sound swirls around, intonation becomes less pronounced. The fine art of vibrato and bending probably originated in an attempt to adjust intonation.

The intonation quest can become an unhealthy obsession, but a heightened awareness will improve your playing. How far you take it depends on whether you are a “God is in the details” or a “don’t sweat the small stuff ” player. I’m a bit of both. If I’m tracking a song in the key of G, I start by tuning flat to the tuner, but then retune by ear with my fingers hitting a G on both E strings. I let my ear and gear guide me and just try to feel something. I’ve found that sometimes the heavy overtones humbuckers generate seem to jack with intonation when I’m utilizing all six strings in a chord. But other times, for big dumb rock or dark jazzy stuff, those delicious humbuckers fatten up the closer triads, power chords, or single lines that would sound anemic in single-coil land.

If you ever find yourself preoccupied with tuning and worrying about how you can sound right with an instrument that will not physically play in tune, listen to brother Duane Allman’s slide on the end of “Layla,” or Jimmy Page in “Heartbreaker,” or Keith Richards in “Sympathy for the Devil.” They may be out of tune with the Western scale, but they are all perfectly in tune with the song’s emotion. The ambiguity of intonation is part of the beauty, sadness, and tension in music. Hearing that, I see the hand of the divine and sense the mystery of it all.

John Bohlingeris a Nashville multi-instrumentalist best know for his work in television, having lead the band for all six season of NBC's hit programNashville Star, the 2011, 2010 and 2009 CMT Music Awards, as well as many specials for GAC, PBS, CMT, USA and HDTV.

John's music compositions and playing can be heard in several major label albums, motion pictures, over one hundred television spots and Muzak... (yes, Muzak does play some cool stuff.) Visit him check out his new band,The Tennessee Hot Damns.