๐ต String Harmonics Calculator
The nth harmonic's frequency = fundamental ร n. Nodes sit at k/n of the string length (k = 1 to n-1).
Enter a string's fundamental (open-string) frequency and a harmonic number (2nd, 3rd harmonic, etc.) to calculate the pitch produced by that harmonic and the positions of its "nodes" โ the points along the string that don't vibrate. Useful for understanding harmonics (artificial/natural harmonics) on stringed instruments.
How to use
- Enter the string's fundamental (open-string) frequency (Hz).
- Select a harmonic number (2nd through 8th harmonic).
- The resulting frequency and node positions are shown in the diagram.
FAQ
What is a "node"?
A node is a point on a vibrating string where the amplitude stays at zero. For the nth harmonic, nodes appear at points dividing the string into n equal parts (excluding the two ends). The red dots in the diagram mark the node positions.
What's the formula?
The nth harmonic's frequency is n times the fundamental (f = n ร fโ). Node positions sit at k/n of the string's length (k = 1, 2, ..., n-1). For example, the 3rd harmonic has nodes at 1/3 and 2/3 of the string.
How does this relate to playing harmonics on a guitar?
Lightly touching a string at a node position while plucking produces just that harmonic's pitch โ this is how "harmonics" are played. Touching at the 12th fret (the string's midpoint, a node of the 2nd harmonic) sounds an octave up; touching near the 7th or 19th fret (nodes of the 3rd harmonic) sounds an octave plus a perfect fifth up.