Anharmonischen

Anharmonischen, in acoustics and music theory, refers to tones whose overtone spectrum is not a purely harmonic series. In a harmonic sound, overtones occur at integer multiples of the fundamental frequency. Inharmonic tones have partials that deviate from these integer multiples, producing a timbre that can sound brighter or more metallic and affecting pitch perception and chord perception.

The primary causes are physical properties and construction. The stiffness of strings and plates, nonuniform geometries, and boundary conditions shift the frequencies of higher modes away from exact multiples of the fundamental. Instruments such as bells, cymbals, and some percussion exhibits strong inharmonicity due to their complex shapes and materials. Inharmonicity is typically modest in many wind and string instruments, but can be pronounced in bells and other rigid, nonuniform bodies. Room acoustics and nonlinear effects can further color the perceived spectrum in some contexts.

Modeling and measurement often use an inharmonicity coefficient. A common approximation expresses the nth partial as f_n ≈ n f1 sqrt(1 + B n^2), where f1 is the fundamental and B measures the degree of inharmonicity. For pianos, the high tension of tightly wound strings yields positive B values, causing higher partials to lie above the corresponding harmonic series and leading to a commonly observed octave-stretch in tuning. For bells and similar instruments, larger B values produce distinctly non-harmonic spectra.

Perception and application: inharmonics influence timbre and the perception of consonance, complicating the blending of notes in chords. Instrument makers and tuners account for inharmonicity through design choices or tuning adjustments; digital synthesis and physical modeling likewise incorporate anharmonics to recreate realistic sounds. In physics, the term also appears in the broader concept of anharmonicity, describing nonlinear deviations from simple harmonic motion.