Optimum Tension

The consensus among early commentators seems to have been that in order for a string to sound its best, to produce the optimum tone quality, it should be as taut as possible.[1] A number of theoretical treatises explain that to tune stringed instruments such as the lute[2] or the crwth[3] the small (treble) string should be brought to near breaking point and the other strings tuned from there.[4]

The situation is probably best summed up in this Leckingfield proverb, c.1518.

A slac strynge in a Virgynall soundithe not aright.[5]

Of course it would not be practical to have the strings of a harp tuned beyond their elastic limit let alone close to their breaking point, a certain safety factor must be applied to accommodate daily tuning or to compensate for changes in temperature. According to modern writers the size of the safety factor traditionally employed in stringed keyboard instrument design is somewhere in the order of one to three semitones below breaking point.[6]

As the tension on a string is increased its pitch will rise. The yield strength of a material represents the point where the rise in pitch slows down as the tension is increased and the string begins to stretch permanently, the point where Hooke’s law no longer applies.[7] In copper–based alloys the breaking point or the ‘ultimate tensile strength’ can be considerably higher than the yield strength of the material depending on hardness or temper. Typically the yield strength of softer alloys is much lower than their ultimate tensile strength, as much as 50% lower in some cases and lower than 40% for fully annealed wire.

It should be noted that the relationship between the tension on a string and its elastic limit (yield strength) does not of itself define the quality of a string tone. Although conventional wisdom does suggest that for best results a string should be tuned as high as possible, using weaker materials and tuning the string close to its elastic limit does not guarantee any improvement in tone quality. Tolerances for different string materials can differ greatly.

Many other factors besides tension contribute to the qualities of a string tone: elasticity, the string's proportions (length/diameter ratio), internal friction or damping to name but a few. The second section of the calculator (Strength) is mainly designed to show what is possible in terms length>frequency>tension for different string materials. A particular string may not sound better than another when tuned close to its elastic limit but it won’t sound at all if tuned any higher than this!

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[1] For example, ‘...take an instrument, as a Lute Orpharion, Pandora, or such like, being in naturall pitch, and set it a tone or two lower, it wil go much heauier and duller and far from that spirit it had before.’ Thomas Morley, A Plain and Easie Introduction to Practicall Musicke, (London: 1597), 166.

[2] Most early lute tutors with the exception of Dowland and Mace.

[3] Edward Jones, Musical and Poetical relicks of the Welsh Bards, (London: 1784) from a MS copied from Lewis Morris, footnote p.115.

[4] H. Panum, Stringed Instruments of the Middle Ages, (London: William Reeves, 1940), 411.

[5] William R. Thomas and J.J.K. Rhodes, ‘The String Scales of Italian Keyboard Instruments,’ Galpin Society Journal, 20 (1967), 58.

[6] Thomas Donahue, ‘Evaluating Historical Stringing Information’ in Early Keyboard Journal Vol. 25/26 (2008), 125–151 at 145–6.

[7] Hooke’s law states the elongation (strain) is proportional to the tension (stress) applied to an elastic string.

Submitted by Paul Dooley, 21 March, 2013. © 2004-2013 Paul Dooley

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