String Tension Comparison
Estimate how the same string’s tension changes with tuning or scale length. Get a ratio without guessing its construction, or add a known reference tension for a force estimate.
Both lengths use the selected unit. Notes are sounding pitches in 12-tone equal temperament at A4 = 440 Hz: low guitar E is E2, not its usual written E3. Leave reference tension blank if it is unknown. No force unit conversion is performed.
Compare one string under two conditions
The ratio is useful when a player wants to estimate the effect of lowering a string or moving an identical string specification to a different-scale instrument. It does not pick a gauge. Enter the original and new vibrating lengths in the same unit. Enter sounding pitches such as E2 and D2, or measured frequencies. The string-tension guide gives examples and explains where the model stops.
A manufacturer tension value is useful only when its original tuning and scale length match your reference inputs. Leave the optional force field empty if you do not have a suitable reference. The ratio still works. When a reference is supplied in newtons, the estimate is in newtons; when it is in pounds-force, the estimate is in pounds-force. Changing the label does not convert a number already entered.
The square-law relationship
An ideal flexible string follows f = √(T/μ) / (2L). Rearranging gives T = μ(2Lf)². For the same linear mass density μ, the comparison becomes T₂/T₁ = (L₂/L₁)² × (f₂/f₁)². The UNSW explanation of string vibration gives the underlying relationship.
At the same scale length, E2 to D2 is two equal-tempered semitones down. The frequency ratio is 2^(−2/12), so the tension ratio is 2^(−4/12), about 0.7937. The string retains about 79.37% of its original tension, a decrease of 20.63%. The “change” value is a percentage change, not the percentage remaining.
A note name needs an octave
E2 is about 82.407 Hz; E3 is twice that frequency. An accidental octave error multiplies this model’s tension by four. The scientific pitch notation guide explains the numbering. B♯3 and C4 yield the same equal-tempered frequency; spelling does not change the physical calculation.
The fretboard helps locate pitches, while the chromatic tuner estimates a live pitch. Neither determines a string’s breaking load. A capo shortens the sounding length and raises pitch without being equivalent to tightening an open string; do not use capo fret distance as a new retuned scale length.
What the model leaves out
The calculation holds linear density fixed. A real string stretches, has stiffness and can change its effective vibrating length at the nut and saddle. Fretting pressure and setup affect feel. Different wound strings with the same outside diameter can have different mass per length. For product-specific data, use the manufacturer’s published specifications; D’Addario explains where its tension charts appear.
Exporting records the original and new lengths, pitches, frequencies, ratio and any supplied force reference. Treat it as a documented comparison, not permission to raise a string beyond the instrument’s intended setup.
Questions
Can I compare different gauges or brands?
Not with this model. It assumes the same linear mass density. Winding, core size and material change that density, so gauge alone cannot establish the new tension.
Does the result tell me a retuning is safe?
No. The model does not know the instrument, string breaking strength, bridge, neck, nut, age or setup. Use manufacturer guidance or a qualified technician when deciding whether a setup is appropriate.
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