A topic in the Open Knowledge Graph — a free, open map of 15,290 topics and the order to learn them in.
Extended harmony moves beyond tertian (third-based) sonorities. Clusters are compressed groups of adjacent pitches; microtonality subdivides the semitone; spectral harmony derives from instrumental overtones. Each creates distinct timbral and harmonic identities that redefine what a 'chord' can be.
You already know how to construct extended chords built in thirds — ninths, elevenths, and thirteenths stack interval by interval above a root, and you've encountered just intonation and the natural overtone series as an acoustic basis for harmony. Now consider what happens when composers push past these tertian structures entirely. The traditions covered here — clusters, microtonality, and spectral harmony — each represent a different way of asking: what is a chord, fundamentally? Is it a functional unit in a key? A particular interval stack? Or simply any simultaneous collection of sounds with a coherent sonic identity?
A pitch cluster is a dense grouping of adjacent pitches — semitones, whole tones, or chromatic runs played simultaneously. Clusters appear prominently in the piano music of Henry Cowell, who literally instructed performers to press entire forearm-lengths of keys. A cluster is not intended to be heard as individual pitches but as a timbral mass — a sound object with a particular density and register, rather than a functional harmony. This is a fundamental reconception: instead of identifying a chord by its root and quality, you identify it by its color and spatial distribution. Understanding clusters requires accepting that simultaneous pitches don't have to form individually distinguishable intervals to constitute a meaningful harmonic gesture.
Microtonality subdivides the semitone — the smallest step in standard Western equal temperament — into smaller intervals: quarter tones, sixth tones, or arbitrary fractions. Your study of just intonation has already shown you that the 12-tone equal temperament is a compromise; many naturally-occurring overtone relationships fall between the cracks of the twelve pitches. Microtonal systems such as 24-tone equal temperament (quarter tones), the 31-tone system, or the flexible just-intonation tunings of composers like Harry Partch allow these "in-between" pitches to be used deliberately. The result is a harmonic vocabulary of finer gradations — chords that can express subtle inflections of tension and release unavailable in 12-tone tuning.
Spectral harmony goes further still, deriving chord content directly from the overtone series of a specific fundamental pitch. When a string or wind instrument plays a note, it produces not just the fundamental frequency but a stack of harmonics at integer multiples (the 2nd, 3rd, 4th partial, etc.). Spectral composers like Gérard Grisey and Tristan Murail analyzed these overtone profiles with electronic tools and used them as compositional material. A "chord" in spectral music might represent the literally-measured partials of a trombone F2, scaled and approximated for a chamber ensemble. The harmony is no longer abstract pitch logic — it is a sonic portrait of physical vibration, reconnecting musical structure to the acoustics you studied in just intonation, now used as a primary compositional engine.
Topics in reflective domains aren't scored by quiz answers. Read, reflect, and mark when you've thought it through.