A simple lyre is a Y-shaped frame with 3-5 strings running from a crossbar to a sound box, and on strings of equal length the stress in each string rises with the square of its pitch. For a five-note scale whose top note is 5/3 of the bottom, the top string is stressed (5/3)² = 2.78 times as much as the lowest. Either shorten the high strings, which also helps them sit on a Y-shaped frame, or use a stronger material for them, and test every string to find its breaking load before tuning.
Part of Music & Simple Instrument Making
A Y-frame lyre with three to five strings: frame, tuning, and how string stress sets the highest note you can safely tune.
String Stress Follows Pitch Squared
For a string of length L, density ρ and pitch f, the stress is σ = ρ × (2Lf)². On a lyre, strings of the same material and length differ in stress only through f². The ratio between two strings is the ratio of their frequencies squared.
Worked example. Take L = 0.35 m, gut with a density I recalled as about 1,300 kg/m³ (not verified; weigh a piece), and a major pentatonic scale in just ratios 1, 9/8, 5/4, 3/2, 5/3 above 196 Hz (the G below middle C). Stress is ρ × (2Lf)²:
| Note | Frequency (Hz) | Wave speed 2Lf (m/s) | Stress (MPa) |
|---|---|---|---|
| 1 | 196.0 | 137.2 | 24.5 |
| 9/8 | 220.5 | 154.3 | 31.0 |
| 5/4 | 245.0 | 171.5 | 38.2 |
| 3/2 | 294.0 | 205.8 | 55.1 |
| 5/3 | 326.7 | 228.7 | 68.0 |
The top string at 68.0 MPa carries 68.0 ÷ 24.5 = 2.78 times the stress of the lowest string, which equals (326.7 ÷ 196)² = (5/3)² = 2.78. If the lowest string is safely inside what the material can bear, the top one may not be. I have no sourced breaking strength for gut or other cords, so measure it using the test in String Materials.
Equal stress by varying length. The stress is the same on every string if L is proportional to 1 ÷ f, which on a Y-frame suits the arms: the lowest string longest (0.350 m) and the highest shortest. For the five notes the lengths are 0.350, 0.311, 0.280, 0.233 and 0.210 m. A crossbar set at a slant gives exactly this effect without any calculation.
Load on the crossbar. Using 1 mm gut (μ = ρ × π × d² ÷ 4 = 1,300 × π × (0.001)² ÷ 4 = 1.02 × 10⁻³ kg/m) the tensions are T = μ × v²: 19.2, 24.3, 30.0, 43.2 and 53.4 N, a total of 170 N, which is 170 ÷ 9.81 = 17 kilograms-force pulling the crossbar toward the sound box. The frame and joints must carry that without bending, and as the crossbar bends the pitch drops.
What You Need
- A Y-shaped branch or two branches lashed to a crossbar; the parent article gives an opening of about 30-40 cm
- A strong crossbar that spans the arms
- A sound box — tortoise shell, gourd half or wooden box; a gourd or box is better than taking a tortoise, which breeds slowly
- 3-5 strings — see String Materials
- Tuning wraps: the parent article winds strings around the crossbar, which can be loosened and tightened by turning and wedging
Method: Build And Tune
Step 1: Lash the frame and check it is rigid. Pull on the crossbar by hand before stringing.
Step 2: Fit the sound box to the base of the Y and fix a bridge across it to carry the strings.
Step 3: Tie strings to a tailpiece at the sound box and wrap each around the crossbar.
Step 4: Tune low to high, raising each string slowly to pitch, a note at a time; stop if any string creaks or the crossbar bends.
Step 5: Choose a scale by ear. A five-note pentatonic scale (no semitones) is forgiving; singers can pick it up quickly.
Common Mistakes
- Equal strings, wide pitch range. The top string is stressed 2.78 times the bottom and breaks first.
- Weak crossbar. The frame bows and the instrument drifts out of tune.
- Poor lashings. The frame twists under tension.
Safety
Strings under load and animal materials
Total pull of about 170 N on this design can break a weak joint suddenly, and a snapped string can whip into the eye; wear eye protection when tuning. Gut and sinew come from animals and can carry infection if sourced from animals of unknown health; see String Materials.
What’s Next
- Learn next: String Materials — choosing and testing the string
- Combine with: Group Singing Without Instruments — a lyre accompanying a song