< Back to Calculating String Diameters
Maximum String Length / How Strings Vibrate - Part 3
By Daniel Larson
The Three Major Considerations for Strings
Length
Tension
Pitch
And these are all related and must be in balance for the string to work correctly. In this article we will consider the string parameter that is most commonly exceeded and that is length.
When the string length is too long for a given pitch some problems develop. In extreme cases, if the pitch is very much too high for the length, the string will break. Most often though, problems develop because the string length is just a little too long for a given pitch and the result is that the string is very thin, resulting in a weak string in tone. Also, the string is fragile and breaks frequently and unexpectedly.
There is a theory that, historically, gut strings were stronger than modern strings and could be tuned higher at longer lengths. It may be that in the old days the serosa material was superior to that of today, or there was some secret formula that was used to create super strings. In order for this to be true the gut would also have to have been lighter than today, or players had to have used more tension than we suspect today, as it is unlikely that the laws of physics have changed over the last three hundred years. Whatever the case may be, what we have to work with is the materials we have today and it is incumbent upon us to make the instruments work for musicians today regardless of what may or may not have been the case historically. Therefore, for the convenience of modern musicians it is important that string lengths do not get so long that strings are fragile and break at the target pitch.
Of course this is of most concern for the top string of the instrument. This is because this is the highest pitched string on the instrument and the most frequently used. Therefore, it is important that this string be reliable and stable so the musician may have confidence in the instrument.
Toward this end, I have compiled a table of common pitches used on top strings and the recommended lengths for string stability at that pitch. At the far right there is the longest recommended pitch and longer than that almost assures a string that will break when tuned up to pitch.
Keep in mind the quality of tone that you like in an instrument as well. Longer strings have a tendency to sound thin and reedy and if this is a tonal aesthetic you are looking for, then you may want to favor a longer length. Shorter strings need thicker strings and consequently the tone tends toward being coarse and raspy. What we are looking for is the Goldilocks length that is neither too long, nor too short — and the mean of the recommended lengths in the table below is just right, as the famous little girl said.
Pitch of String |
Frequency |
Recommended Length in cm |
Longest recommended Length in cm |
|
|
|
|
e" |
659.26 |
31 - 33 |
34 |
d#" |
622.26 |
33 - 34 |
36 |
d" (Soprano) |
587.33 |
34 - 36 |
39 |
c# |
554.37 |
36 - 38 |
40 |
c" |
523.50 |
38 - 41 |
45 |
b' |
493.88 |
42 - 44 |
46 |
Bb' |
466.16 |
45 - 47 |
48 |
a' (Alto) |
440 |
48 - 50 |
52 |
g# |
415 |
51 - 52 |
56 |
g' (Alto / Tenor) |
392 |
53 - 54 |
59 |
f#' |
369.99 |
55 - 58 |
62 |
f' |
349.23 |
62 - 64 |
67 |
e' (Bass) |
329.63 |
65 - 67 |
68 |
d' |
311.13 |
64 - 65 |
72 |
eb' |
293.66 |
65 - 68 |
76 |
c#' |
277.18 |
68 - 72 |
80 |
c" |
261.63 |
76 - 78 |
82 |
#
Hand-made in the USA by Gamut Music, Inc., a leader in the revival of early music strings and instruments. Gut strings are not intended to be used with fine tuners or string adjusters, and those devices should be removed before installing the gut string on the instrument.
All Gamut Academie strings (pure gut and gut/metal-wound) are made with beef serosa unless they specifically say "Sheep Gut." All pure gut Tricolore violin and viola strings are made with sheep gut; gut/metal-wound Tricolore and all Red Diamond strings are made with beef serosa.
Gamut gut string gauges are approximate (≈) diameter. Meaning, that while a ≈0.60mm string is polished in the workshop to a diameter of 0.60mm, changes in ambient humidity, temperature, shipping, and storage conditions can cause to string to expand or contract slightly.
Gimped gut strings and custom gauged equal tension strings are gauged with the equivalent-gauge (=) system. This means that the gauge listed, such as =1.50mm, indicates that the string is approximately equal in weight to a plain gut string of that diameter. Of course, because the wire is much heavier than gut, the string will be much thinner than a plain gut string.
More information about Gamut gut strings, string types, gauges, and string tensions can be found on our FAQ/Articles page. Not finding an answer to your question? Please contact us directly: support@gamutmusic.com.