Limit (music)
mathematical characterization of the harmonic complexity of music; way of characterizing the harmony found in a piece or genre of music, or the harmonies that can be made using a particular scale
A limit is the highest prime or odd factor used in the ratios of any musical tuning system. The term was devised by Harry Partch.
History
The idea of a limit to the prime numbers that could be used to generate intervals originated with Harry Partch. The essential limit of equal temperament is 5, which allows for all the basic triads. By increasing the limit, more complex chords could be created. In his music, Partch capped the prime factor at 11. His goal was to expand tonality.
In medieval music, only chords made of octaves and perfect fifths (involving relationships among the first three 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 five harmonics.
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This entry incorporates text from “Limit (music)” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.