Inharmonicity

Inharmonicity, in acoustics and music, refers to the deviation of the overtones (harmonics) of a musical instrument from a perfectly harmonic series. In an ideal harmonic series, the frequencies of overtones are whole-number multiples of the fundamental frequency. However, in many real-world instruments, particularly those with stiff strings or vibrating plates, the overtones are not perfectly harmonic, resulting in a slightly 'out of tune' or complex sound. This deviation is due to factors like string stiffness, the physical dimensions of the instrument, and the material properties of the vibrating elements. The degree of inharmonicity varies across different instruments and is a significant factor in their unique timbral qualities.

Inharmonicity meaning with examples

• The piano's characteristic sound is partly due to its inherent inharmonicity; the steel strings are stiff, causing higher partials to deviate from the perfect harmonic series. This contributes to the richness and complexity of the instrument's sound, making each note subtly unique. Even slight variations add depth, a quality often described as a 'warmth' to the piano's tone.
• Guitar strings, especially those with higher tension or shorter lengths, often exhibit noticeable inharmonicity. This is due to their relative stiffness and the influence of the fretboard on the vibrating length. This deviation adds to the perceived complexity and character of the instrument, adding slightly 'off' harmonics to the overall sound of chords and notes played on the guitar.
• The imperfections caused by inharmonicity on the struck strings of a hammered dulcimer give it a uniquely 'shimmering' quality. The metallic strings, vibrating freely, produce rich overtones which provide a distinct sonic signature. The effect helps provide the unique and appealing sound of this particular instrument adding depth and complexity to the music.
• Synthesizers and digital instruments can be designed to model inharmonicity, adding a realistic, complex, and organic sound to simulated instrument sounds. This allows sound designers to create textures that are evocative of acoustic instruments, thus adding a richness and nuance. This can give depth and perceived character.