Tuning With Harmonics - It Doesn't Work.
by Larry P. Schrof, Copyright 2003

As guitarists, we've all been there.  You've just finished one of your
songs at a gig, and a couple of your strings are noticeably out of
tune.  You've only got about 10 seconds of dead air before the crowd
gets antsy.  (Not to mention the drummer will probably start muttering
obscenities normally reserved for practice sessions.)

No problem!  Just pluck the 5th fret harmonic of your lowest string and
the 7th fret harmonic of the next string.  Adjust the second string
until its harmonic is in tune with the first, and move on to the next
pair.  It's quick and effective, right?

WRONG.  Tuning the guitar using harmonics is probably one of the most
common mistakes guitarists today make.  Yes, I know - everybody does it.
You've probably been doing it for years, and it seems to work.  Why,
even books and web list it as one of the common methods of tuning
a guitar.

In this article, I'll explain why tuning with harmonics is not
reliable.  You'll need to put on your thinking cap for a bit.  I'll try
to keep the math to a minimum.  It won't hurt too much, I promise.

First, we need to start with some basic facts about string acoustics
and the open-string notes.  When you play a 5th-fret harmonic, it
produces a frequency four times (exactly two octaves) higher than the
open string note.  When you play a 7th-fret harmonic, it produces a
frequency exactly three times higher than the open string note.  (Even
though this harmonic SOUNDS like a perfect fifth, it is not, and
THAT makes all the difference. More on this in a minute...)

Next, we need a list of the frequencies that a perfectly tuned set of
guitar strings will produce.  Assuming equal temperament using
A-440, we get:

Open Note  Frequency
Low E:      82.41
A          110.00
D          146.83
G          196.00
B          246.94
E          329.62

Using this information, you can now determine the frequencies produced
by the 5th and 7th-fret harmonics on every string.  For example, since
the A string rings open at 110 Hz, its 7th-fret harmonic will be at
330 Hz, and its 5th-fret harmonic will be at 440 Hz.

OK. Now that the groundwork is laid, let's see why tuning with
harmonics doesn't work.  We'll walk through an example.  Assume that
your low E and A strings are in perfect tune, but you want to
double-check them.  According to the chart above, your low E string will
produce a tone at 82.41 Hz.  Using the method you all know and love,
you'll pluck its 5th-fret harmonic.  This gives an E two octaves
higher, at 329.64 Hz.  Then, you pluck the 7th-fret A-string harmonic
and get a 330 Hz tone!

Ah hah... do you see the problem?  The 330 Hz harmonic of the
*PERFECTLY TUNED* A string will sound sharp to you, and you'll detune
it to match the E-string harmonic.  What you're actually doing,
though, is tuning the A string flatter than it should be by about 0.12
Hz!  Doesn't sound like much, does it?  Well, the A string is now almost
two cents flat.  That's not good news, and the problem gets worse.

You are now going to be tuning the next string off of a string that's
already flat.  Let's see what happens.  Our now-flat A string is ringing
open at 109.88 Hz.  You pluck the A-string 5th fret harmonic, then
adjust the D-string 7th fret harmonic to match.  When the harmonics
align, the D string will now ring open at 146.51 Hz.  Take a look at
the chart above.  We're 0.32 Hz too low.  The D string is now almost
FOUR cents flat.  Notice how the error becomes larger.

Continuing in this manner, the G string will end up almost 6 cents
flat.  Now THAT'S a noticeable difference.  Some people like to match
the D-string's 9th fret harmonic to the B-string's 5th fret harmonic,
but that won't work either.

In general, tuning strings to any harmonics besides octaves of the
open string notes will yield flawed results.  Of course, this all begs
the question - how should one tune?  Ideally, you should use an
electric tuner on each string.  If using a tuner is not an option, tune
your high E string to a known correct pitch such as another
(already-tuned) instrument.  Play the 5th fret of your B and match it
up to the high E.  Proceed the same way down all the strings, tuning
your low E string last.

If you're like me, you found all of this a bit surprising at first,
but hopefully a little enlightening.  (I personally had been using
harmonics to tune for years.)  Needless to say, playing an out-of-tune
guitar not only sounds harsh, it sounds unprofessional and amateurish.
So let's get the credit we deserve as players and stop using harmonics
to tune!

Practice hard,
- Larold