Limit (music)

In music theory, limit or harmonic limit is a way of characterizing the harmony found in a piece or genre of music, or the harmonies that can be made using a particular scale. The term limit was introduced by Harry Partch, who used it to give an upper bound on the complexity of harmony; hence the name. "Roughly speaking, the larger the limit number, the more harmonically complex and potentially dissonant will the intervals of the tuning be perceived." "A scale belonging to a particular prime limit has a distinctive hue that makes it aurally distinguishable from scales with other limits."

Harry Partch, Ivor Darreg, and Ralph David Hill are among the many microtonalists to suggest that music has been slowly evolving to employ higher and higher harmonics in its constructs (see emancipation of the dissonance). In medieval music, only chords made of octaves and perfect fifths (involving relationships among the first 3 harmonics) were considered consonant. In the West, triadic harmony arose (Contenance Angloise) around the time of the Renaissance, and triads quickly became the fundamental building blocks of Western music. The major and minor thirds of these triads invoke relationships among the first 5 harmonics.

Around the turn of the 20th century, tetrads debuted as fundamental building blocks in African-American music. In conventional music theory pedagogy, these seventh chords are usually explained as chains of major and minor thirds. However, they can also be explained as coming directly from harmonics greater than 5. For example, the dominant 7th chord in 12-ET approximates 4:5:6:7, while the major 7th chord approximates 8:10:12:15.

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