harmonical

Harmonical is an adjective derived from harmony or harmonics. In modern English, the form harmonical is uncommon and usually superseded by harmonic or harmony; it is most often encountered in older texts, regional usage, or when translating from languages with a similar form. The word can describe things pertaining to harmony, or to the overtones and harmonic series that arise from vibrating musical objects.

In music theory, harmonical is sometimes found in historical or theoretical writings to emphasize relationships among pitches within the harmonic series or between chords. Today, scholars typically refer to harmonic analysis, harmonic progression, and harmonic function rather than harmonical analysis, but rare instances still appear in discussions of tonal structure. The use of harmonical to denote overtones aligns with the broader concept of harmonics in music.

In mathematics and physics, harmonical appears in older literature as a variant spelling or translation of harmonic, especially in the phrase harmonical function, instead of the standard harmonic function. Contemporary mathematical writing favors harmonic function, harmonic conjugate, and harmonic analysis. Despite its limited present-day usage, harmonical can be found in some dictionaries and philological texts as a historical or etymological form.

See also: harmonic, harmony, harmonics, harmonic function, harmonic series.