Violin String Tension Calculator
Computes tension in newtons needed on a violin string to produce a fundamental frequency from vibrating length and linear mass density.
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Violin string tension from linear mass: formula and example
Mersenne's law gives us T = 4 · L² · f² · μ. A 4/4 violin tunes in fifths (G3 = 196 Hz, D4 = 293.66 Hz, A4 = 440 Hz, E5 = 659.25 Hz) over a vibrating length of about L ≈ 0.325 m. Take a typical A4 string with μ ≈ 0.00045 kg/m and the tension comes out near 55 N, or roughly 5.6 kgf. Add up all four and the full set pulls roughly 25-30 kgf (~245-295 N) against the top, with the soundpost and bass bar carrying that load. The bow itself holds about 150-200 strands of horse hair, 6-7 g worth, tensioned by the screw and rosined with cake rosin.
Context and applications
Luthiers nudge the soundpost (alma) around to balance tension against tone. Shift it 1 mm toward the bridge and the E brightens while the G goes darker. String size matters for students too. A 3/4 violin runs L ≈ 0.30 m and a 1/2 runs L ≈ 0.27 m, so the same notes need lower tension and lighter strings. Synthetic-core sets like Dominant or Evah Pirazzi land near 23-26 kgf total; pure-gut sets sit lower, around 18-20 kgf, and feel softer under the bow.
FAQ
Why is the E string steel and not gut? At 659 Hz over 0.325 m, gut would have to be so thin it snaps under tension. A plain steel E (μ ≈ 0.00025 kg/m) holds about 80 N, roughly 8.2 kgf, without drama.
Does tuning to A=442 change tension much? Tension scales with f², so going from 440 to 442 Hz adds about 0.9%. That's tiny on a single string, but across the whole set it works out to roughly 250 g of extra pull, and the bridge feels it over time.
How tight should the bow hair be? Tight enough that the stick keeps a slight concave camber while you play. A pencil's width of gap between hair and stick at the middle is the usual rule of thumb. Crank it past that and you warp the stick for good.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.