TENSION AND TUNING
by Ian Noyce
Previously published in Sonics Oct-Dec 1982
THE VARIOUS relationships between string length,
string mass per unit length (usually given in kg per metre)
and resultant pitch (or 'frequency' as our technical brethren
call it) are fundamental - sorry! - to understanding why various
string length is taken as the length between the nut and the
PITCH depends on string length and string tension.
- If the string's mass per unit length remains constant,
the longer the string, the higher the tension required to
achieve the desired pitch.
- If the string's length remains constant, the higher the
string's mass per unit length, i.e. the heavier the string,
the higher the tension required to achieve the desired pitch.
This formula may look pretty formidable: just take it for
granted (it's actually derived from the fact that the note
produced by a string is proportional to the speed that sound
travels in the string, and that speed in turn depends on how
tense and how heavy the string is.)
By cutting up a new set of Dean Markley regular gauge electric
strings, weighing a measured length (640mm) on an electronic
balance to get the "mass per unit length", and doing
the number juggling on my calculator till I nearly wore out
the battery, I came up with the results in fig 2.
The formula actually produces answers in units of force called
"Newtons", and since you might be happier thinking
about "kilograms", I simply divided the formula
by 9.81, because there happens to be 9.81 Newtons in a kilogram
of force. So the results for T in Fig 2 are actually obtained
by plugging the appropriate figures into the formula:
2. Relationship between pitch, mass and tension for Dean Markley
strings of 640mm length. 640mm is in fact a midway between
a Les Paul and a Strat scale length and is the scale length
we use on most Noyce Guitars.
As may be seen from the measurements set out in Fig 2. the
tension required to achieve the correct pitch is reasonably
similar for all strings (or at least it will be in a balanced
set). This is of course necessary to avoid unequal stress
being inflicted on the body of the instrument. It's also the
reason why all your strings end up feeling much the same to
- Wound strings are no exception in this relationship, because
in these, the tension is applied primarily to the core,
with almost none at all to the winding.
- We should at this point also introduce the concept of
"stress". When we exert a force across a section
of something such as a guitar string, stress is produced,
in that section. When the forces pull on that string, the
result is called tension (as distinct from when they push,
which creates compression.). So if we pull the string, we
increase the tension, thus increasing the stress, and it
the stress becomes excessive the string breaks. It will
break earlier if it is a thinner string (i.e. having less
- Since a heavier string would require greater tension to
achieve a particular pitch, this increased tension would
make the string "stiffer". Now, since a stiffer
string enhances the upper modes of vibration (harmonics),
with less movement in the lower, if you were after a "tighter",
brighter sound, you might use a light top, heavy bottom
- Acoustic guitars with medium strings carry almost double
the tension of electrics with .010"-.046" strings: 80-90kg (180-200 lbs) depending on the the scale and gauge
of the strings.
- Putting .009"-.046" strings on a Gibson Les
Paul, as the Les Paul's shorter scale reduces tension about
6% compared to Fender's longer scale, just as going down
a step in string gauge gives a proportional decrease in
Editor's note. Just thought we'd let you know that we
checked out these relationships practically in a rather novel
(and rather gross) way. Hanging a B-string from a nail over
our managing editor's door, we clamped it at the free end
approximately 640 mm from the nail and hung one of our our
mail bags off the clamp: Filling the mailbags with (wait for
it!) Sonics 1982 Yearbooks to a total weight of approximately
8kg, we proceeded to pluck the string and lo and behold a
sound not too far from a B was heard.
Ain't that groovy! Try it yourself (if you've got enough
HOW DOES IT FEEL?
Every guitar has its own feel and amount of 'give' under
the hands when bending strings, etc. Although many aspects
of this 'feel' relate to properties of the instrument and
the hardware on it, it is also greatly influenced by what
goes on between the bridge and tailpiece.
Example 1: If you look at the length of a string on
a Strat between high E machine and the nut, and that between
the saddle and the back of the body, it represents 30% of
the effective string length (i.e. from nut to bridge saddle).
The same observation on a Les Paul represents 15% of scale
length. This is a very significant factor in the string-bending
feel of each guitar. To simplify this, let's look at a more
Fig 3a and 3b show two strings identical in everything except
overall length, but mounted such that the length between
the nut and the bridge is the same for each. Since for tuning
purposes this is the critical length, both strings can be
seen as identical as far as what is needed to tune them to
the same pitch is concerned - and will thus require equal
tension. However, the string in Fig 3a will be much easier
to deflect (bend) than the one in Fig 3b, as the increase
in tension that happens when you deflect the string is to
some extent distributed over the entire length of the string.
Example 2: The string break, or down bearing at the
nut and bridge saddles also affects ease of fretting and bending.
A Strat without string trees feels looser and sounds "looser"
- with less attack - than one with string trees pulling the
string down sharply past the nut, just as a Les Paul with
the tailpiece set high feels looser than the same guitar with
the tailpiece screwed right down.
It's all a matter of how firmly the string is pulled over
the nut and saddle and how much length of string there is
past these points. (The Strat and Les Paul have been used
here as convenient examples. There are many variations applicable
to other guitars)
3. Effect on "Bending Feel" of the distance
between machine and nut, and bridge and tailpiece. 3a
is easier to deflect than 3b.
For Experimental guitarists
To get a better feel for the forces involved in string movement,
get a friend and a towrope or similar and hold one end firmly
whilst the friend jiggles the rope to stimulate the modes
of vibration shown in Fig 1. You'll soon get an impression
of how violent the forces at the end of the string are, and
how they change according to the mode you're simulating. (Try
holding the rope against your chest and singing a note whilst
performing the above experiment.)
Strength of Strings
By clamping a string at each end in a machine (called an
extensiometer) and subjecting it to increasing tension until
it broke while measuring how much is stretched, I was able
to plot a graph for a Dean Markley .026" wound string
(see Fig 4).
The main point of interest here is that guitar strings are
bloody strong!! Also it has become quite clear that guitar
strings break during play due to mechanical damage (i.e. wear
at the nut, a particularly vicious stroke of the pick or whatever,
rather than due to over-tensioning).
Tension vs extension of a guitar string.
A: Normal tension in regular gauge electric strings;
B: Normal tension in medium gauge acoustic strings;
Tension in regular gauge electric string when held by
interval of a fourth (five fret bend);
Limit of elasticity (yield point);
Breaking point (ultimate Strength).
Summing up and Settling in
Although all of the above
facts and figures are basically true, there are numerous deviations
from theoretical behaviour in practical situations, and numerous
assumptions involved in doing practical tests. For example,
when a string is stretched, it must decrease in diameter but
it is assumed that the diameter remains constant.
Temperature and moisture also have their parts to play. One
significant deviation from the ideal elastic behavior is the
settling in process a string goes through when new. Even when
a string is pulled up to normal tension and pitch and fixed
firmly at each end point, it will stretch and detune a little
when pulled, until, after a number of pulls, it settles in
and remains fairly faithful in tune despite further plucking
and pulling. This phenomenon is known as 'work hardening'
and is experienced by every guitarist 'stretching in' a new
string or set of strings.
Also, as the bridge and nut are not frictionless carriages
for the string, tension can get 'stored up' in the lengths
of string between nut and machine and bridge and tailpiece
and, with playing, this stored tension in the vibrating length
and thus the pitch. That's another reason why 'playing in'
new strings is important.
Well, now you'll be thoroughly clued up on what your Dean
Markleys are doing when you produce your next Hendrix-inspired
wail, and you'll understand why your guitar feels a little
odd when someone strings it with the top E where the bottom
E should be. Ain't physics wonderful!