A stretched string sounds higher when it is shorter, tighter or lighter, and halving its length raises the note one octave. Start with a one-string diddley bow, then a lyre of three to five strings, and expect the hard parts to be a string strong enough for the pitch you want and a frame that will not give under the pull. Wear eye protection when tuning, because a snapping string whips.
Part of Music & Simple Instrument Making
Plucked and strummed string instruments, the rule linking pitch to length, tension and weight, and what a first build costs in effort.
Three Things Set The Pitch
For a string fixed at both ends, the lowest frequency is f = (1 ÷ 2L) × √(T ÷ μ), where L is the vibrating length in metres, T the tension in newtons and μ the mass per metre in kilograms per metre. In words:
- Shorter is higher. Frequency is inversely proportional to L, so halving the length doubles the frequency, one octave up.
- Tighter is higher. Frequency rises as the square root of tension, so four times the tension gives twice the frequency.
- Lighter is higher. A thinner string of the same material has a smaller μ and sounds higher at the same tension.
A kilogram is a mass and a newton a force. A weight of 1 kg pulls with 9.81 N, so to convert a hanging mass in kilograms to the tension in newtons multiply by 9.81. A tension of 47.7 N is therefore a pull of 47.7 ÷ 9.81 = 4.9 kg hanging from the string, which is more than most people expect from a thin wire.
Instruments In Order Of Effort
- One-string diddley bow — a string over a board with a slide; the quickest build. See One-String Diddley Bow.
- Lyre of 3-5 strings — a frame, a crossbar and a sound box. See Simple Lyre (3-5 strings).
- Strings themselves are the hard part: gut, sinew, plant fibre, hair or wire. See String Materials.
What You Need
- A board or frame that will not bow under the string’s pull
- A string whose strength you have tested
- Pegs or tuners that hold under tension; see Material Selection
- A resonator (gourd, box, bowl) to make the sound audible
Method: Plan Before You Build
Step 1: Choose the speaking length L from the instrument you can build.
Step 2: Choose the pitch from the voices or other instruments it will join.
Step 3: Compute the tension the string needs, T = μ × (2Lf)², and then the stress in the string, T divided by its cross-section. If the stress is more than the string can carry, shorten L, lower f or use a stronger string. The worked example is in One-String Diddley Bow.
Step 4: Build, then tune up in small steps, stopping well short of the break.
Common Mistakes
- Tuning to a pitch the string cannot reach. The string breaks.
- Light frame. A frame that bends lowers the tension and the pitch.
- Forgetting the resonator. A bare string is nearly silent.
Safety
Snapping strings and animal materials
A wire or gut string that breaks under tension can whip back into the face; wear eye protection and keep your face out of the line of the string while tuning. Gut, sinew and hair strings come from animals and carry infection risks if the animal’s health is unknown; see String Materials.
What’s Next
- Learn next: One-String Diddley Bow — the first build
- Combine with: Rhythm Training — a string for rhythm as well as tune