page_title: Set (music)
section_title: Non-serial
hierarchical_section_title: Set (music) / Non-serial
caption_attribution_description: English: Minor seventh on C. 1000 cents. Created by Hyacinth (talk) 06:29, 7 December 2010 using Sibelius 5.
context_page_description: A set in music theory, as in mathematics and general parlance, is a collection of objects. In musical contexts the term is traditionally applied most often to collections of pitches or pitch-classes, but theorists have extended its use to other types of musical entities, so that one may speak of sets of durations or timbres, for example.
  A set by itself does not necessarily possess any additional structure, such as an ordering or permutation. Nevertheless, it is often musically important to consider sets that are equipped with an order relation; in such contexts, bare sets are often referred to as "unordered", for the sake of emphasis.
  Two-element sets are called dyads, three-element sets trichords. Sets of higher cardinalities are called tetrachords, pentachords, hexachords, heptachords, octachords, nonachords, decachords, undecachords, and, finally, the dodecachord.
  A time-point set is a duration set where the distance in time units between attack points, or time-points, is the distance in semitones between pitch classes.
context_section_description: The fundamental concept of a non-serial set is that it is an unordered collection of pitch classes.
  The normal form of a set is the most compact ordering of the pitches in a set. Tomlin defines the "most compact" ordering as the one where, "the largest of the intervals between any two consecutive pitches is between the first and last pitch listed". For example, the set (0,2) (a major second) is in normal form while the set (0,10) (a minor seventh, the inversion of a major second) is not, its normal form being (10,0).
  Rather than the "original" (untransposed, uninverted) form of the set the prime form may be considered either the normal form of the set or the normal form of its inversion, whichever is more tightly packed. Forte (1973) and Rahn (1980) both list the prime forms of a set as the most left-packed possible version of the set. Forte packs from the left and Rahn packs from the right ("making the small numbers smaller," versus making, "the larger numbers ... smaller"). For many years it was accepted that there were only five instances in which the two algorithms differ . However in 2017, music theorist Ian Ring discovered that there is a sixth set class where Forte and Rahn's algorithms arrive at different prime forms. Ian Ring also established a much simpler algorithm for computing the prime form of a set, which produces the same results as the more complicated algorithm previously published by John Rahn.
caption: Minor seventh on C About this soundPlay (help·info).
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