Most players have noticed this while tuning: turn the pegs of different strings by the same angle and the pitch changes by different amounts.
Some strings feel easy to tune “precisely”, while on others a tiny twist sends the pitch far off.
What is the principle behind this? Try it yourself with the mini tool below.
A tuning peg changes the string’s frequency by changing its tension.
Cents convert a frequency ratio into an interval: 1200 × log₂(f₂/f₁). Predicting pitch from a peg angle also requires a mechanical model of winding, string stiffness and tension; equal temperament alone cannot provide that mapping.
Modern guitar tuner design should also take tuning precision and practicality fully into account.
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Tuning-Peg Rotation and Pitch Simulator · About the tool
This page embeds a tuning-peg simulator that shows the physical relationship between peg rotation and pitch change more intuitively. Turning a peg changes the string tension through the string post; the tension change alters the string’s vibration frequency, which you hear as the pitch rising or falling.
What the tool does
Drag the peg rotation angle to see how each string’s pitch changes. The tool accepts a rotation angle (the default example is 180 degrees), compares the pitch change of every string in cents, and lists the detailed results: each string’s new frequency, tension change and pitch change.
Adjustable parameters
String parameters can be set individually for each string. Global physical parameters include scale length, string-post radius, total string length and Young’s modulus, in metres and gigapascals respectively. Results update in real time as you change them, so you can compare how strings of different gauges respond to the same rotation.
Why different strings change pitch by different amounts
For a fixed nut-to-saddle length, peg rotation mainly changes string tension rather than scale length. Pitch sensitivity depends on effective stiffness, initial tension, post radius and friction. A bass string is not necessarily more sensitive than a treble string.
Relation to real-world tuning
Real tuning is also affected by nut friction, string age, the number of wraps and the post radius, so the simulation is an approximation under ideal conditions. Treat it as an aid for understanding the principle and developing a feel. When tuning, approach the target note from below: get close first, then fine-tune, rather than going back and forth across the target.
Further reading
To learn how string vibration and overtones are formed, see our String Vibration Visualiser and Sound Synthesis tool; to learn how pressing force relates to string action, see the Total Pressing-Force Physical Model and Calculator.
Reading the tuning simulation
Compare one setting at a time: keep the initial string and tension settings, change the peg angle, and note the resulting pitch interval in cents. A frequency ratio describes the interval; the winding and tension model determines how much a peg turn changes the string.
For the physical background, see UNSW on strings and harmonics. Return to Kepma guitar tools for listening and tuning practice.
