Someone showed you the trick
years ago,
and it felt like real musicianship.
No tuner.
Touch the low E
over the fifth fret,
touch the A
over the seventh,
and listen.
Two chiming notes,
and a slow wobble between them.
Turn the peg
until the wobble stops.
Then the next pair,
and the next,
across the neck.
Every pair
sounded perfect.
Then you played an E chord,
open,
and the top string
was sour against the bottom one.
You had tuned it twice.
Here is what the wobble was.
Two notes
that are almost the same pitch
beat against each other.
When the beating stops,
the two harmonics match exactly.
And that makes the strings
a perfect fourth apart,
a ratio of four to three.
Your guitar is not built
for perfect fourths.
The frets are spaced
in equal temperament,
twelve equal steps to the octave,
so every key sounds the same.
In that system
a fourth is slightly wider
than the pure one.
Five hundred cents,
against about four hundred and ninety eight.
Two cents.
Nobody hears two cents.
But you did not tune one pair.
You tuned a chain,
each string built
on the one before.
Two cents,
four,
six.
Then the G and B,
the one pair that is a major third.
The usual harmonics for that pair
make a pure third,
five to four,
and the pure third
is almost fourteen cents
smaller than the fretted one.
By the time you reach
the top E
the errors have stacked
to more than twenty cents.
A fifth of a semitone,
flat,
against the string
it should match
two octaves down.
Every step was perfect.
The total was wrong.
So use the trick
only where it is safe.
Octaves and unisons
are pure in every tuning system.
The harmonic at the twelfth fret
against the fretted note,
or the harmonic on the low E
at the fifth fret
against the open top string,
which is the same E.
Tune every string
to one reference,
not to its neighbour.
Or use the tuner,
and keep your ear
for checking chords.
When small errors
are passed from hand to hand,
nobody sees them
until the last one.
– Serguey Asael Shinder
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