The highest pitch a string can reach is set by its breaking load and its mass per metre: f max = (1 ÷ 2L) × √(T break ÷ μ), so weigh a metre of the string, hang weights from a sample until it breaks, and compute the limit before tuning. A string that breaks at 200 N with a mass of 1.0 g per metre on a 0.35 m length could theoretically reach 639 Hz, and should be kept to about 452 Hz to leave a margin. Gut, sinew and hair are animal materials that must come from animals of known health, because untreated hide and hair can carry anthrax.
Part of Music & Simple Instrument Making
Gut, sinew, plant fibre, hair and wire as instrument strings, and a home test that replaces guessing at strength.
The Limit Is Set By The Material, Not The Thickness
For a string of length L, tension T and mass per metre μ, the pitch is f = (1 ÷ 2L) × √(T ÷ μ), and the stress in the string at that pitch is σ = ρ × (2Lf)² (derived in One-String Diddley Bow). So a material of breaking stress σ_b and density ρ cannot be tuned above
f max = (1 ÷ 2L) × √(σ_b ÷ ρ)
whatever its thickness. A thicker string breaks at a larger force but at the same stress. The ratio √(σ_b ÷ ρ) is a speed, the fastest wave the material can carry before it breaks; compare materials by it.
You do not need to know σ_b or ρ if you can measure T_break and μ for a sample, which is what the test below does.
Method: Break Test A Sample
This replaces recalled strength figures with measurement. Use a sample cut from the same batch as the string.
Step 1: Weigh a known length. Weigh 5 m or 10 m of string on the best balance you have (e.g. a counterweight beam). μ = mass ÷ length. Example: 10 m weighing 10 g gives μ = 0.010 kg ÷ 10 m = 1.0 × 10⁻³ kg/m, which is 1.0 g per metre.
Step 2: Hang a load. Secure one end to a sound beam above head height, tie the sample in a knot you will use on the instrument, and hang a container from it. Add water or sand in small steps and weigh the container. Stand clear and wear eye protection.
Step 3: Record the load at which it fails in kilograms, then convert to newtons: T_break = mass × 9.81. A 20.4 kg load is 20.4 × 9.81 = 200 N. (A kilogram is a mass, not a force; multiplying by 9.81 gives the force.) Repeat on several samples and use the lowest, since the weakest sample governs.
Step 4: Test the knot, not just the cord. Knots usually fail first; the test must include the knot or the result is optimistic. See Rope Strength Testing for the corpus’s own testing method and its safety factors.
Step 5: Compute the limit.
Worked Example
A sample with μ = 1.0 × 10⁻³ kg/m that breaks at T_break = 200 N, on a lyre string of L = 0.35 m (hypothetical numbers for illustration; no sample was tested):
- √(T_break ÷ μ) = √(200 ÷ 1.0 × 10⁻³) = √(200,000) = 447 m/s
- f max = 447 ÷ (2 × 0.35) = 639 Hz
Never run a string at its breaking load. If you choose to work at half that load, a choice not a derived figure, the allowed pitch falls to f max × √0.5 = 639 × 0.707 = 452 Hz. Repeated loading, knots, moisture and age all weaken natural fibres, so leave a margin and recheck strings that have been under tension for weeks.
What The Materials Are Like
- Animal gut. Traditionally the best natural string. Gut strings are made from the intestines of animals, classically sheep, which are scraped clean, twisted and dried under tension. The process is long and I am describing the general craft, not a procedure. The tissue is raw slaughter waste: use only intestines from an animal you saw healthy at slaughter, process them promptly because they spoil in hours in warm weather, and wash hands thoroughly after.
- Sinew. Tendon, dried, pounded into fibres and twisted; strong in tension, less resonant than gut, and sensitive to moisture.
- Plant fibre. Linen, hemp or nettle fibre twisted into cord; see Flax Processing, Hemp Processing and Nettle Fiber. For the cordage method see Two-Ply Twist. Plant cord suits low pitches and low tension.
- Hair. Horsehair or human hair, bundled; low volume.
- Wire. Iron and steel carry the highest stress; copper is soft and stretches. See Iron Wire and Wire Drawing.
Natural strings stretch under load (creep) and change length with humidity, so they go flat in damp weather and need retuning more often than wire.
Common Mistakes
- Trusting the string’s thickness. Thickness changes force, not stress.
- Testing without the knot. Knots are the weak point.
- Ignoring a margin. A new string at 80% of its break load fails after a week.
- Mixing kilograms and newtons. A 20.4 kg weight is 200 N.
Safety
Animal materials and failing strings
Hide, hair, gut and sinew from animals of unknown history can carry anthrax spores, which survive in hide and hair for very long periods, and gut handling spreads other infections from raw tissue. Source only from animals you know, cover cuts, wash after handling and never process material from a carcass that died suddenly with blood from its orifices. See Zoonotic Diseases and Pressure Sterilization, which notes that boiling does not kill spores. During the break test and when tuning, a failing string or hanging load can strike: wear eye protection and keep out from under the load.
What’s Next
- Learn next: Simple Lyre (3-5 strings) — where these limits decide the design
- Combine with: Laying Rope — a related way to make strong twisted cord