Harmonische

Harmonische is a term used in several Germanic languages to denote relations to harmony and harmonic phenomena. In science and art it appears in various fields, notably music theory, acoustics, and mathematics. The term's usage is often context dependent and translates to "harmonic" or "harmony" in English.

In music and acoustics, harmonische relates to the harmonic series and overtones that accompany a vibrating tone. The fundamental frequency is accompanied by higher partials whose frequencies are integer multiples of the fundamental, shaping timbre and perceived consonance. The study of how these relations form chords, scales, and tonal structure is sometimes referred to as harmonische Funktion or harmonic analysis in German.

In mathematics and physics, harmonische Funktionen are solutions of Laplace's equation, central to potential theory and complex analysis in two dimensions. Harmonic motion, or harmonische Schwingung, describes oscillations with constant amplitude where displacement follows a sinusoid. Harmonic analysis concerns representing functions or signals as sums of basic waves, a framework that includes Fourier series and transforms. The term harmonische Reihe denotes the harmonic series, the sum 1 + 1/2 + 1/3 + ..., which diverges.

Etymology: from Latin harmonia via Greek harmonia; in German and Dutch, the adjective harmonisch/harmonische regularly conveys the idea of harmony or harmonic relations. The word appears in many technical phrases as well as everyday language to describe things that are in proportion or agreeable.