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This is a list of set classes, by Forte number. In , where (in base-ten) X = 12 – 2C, where C is the smaller set's cardinality. In nearly all cases, complements of unsymmetrical sets are related by inversion—i.e., the complement of an "A" version of a set of cardinality C is (usually) the "B" version of the respective set of cardinality 12 – C. The most significant exceptions are the sets 4-14/8-14, 5-11/7-11, and 6-14, which are all closely related in terms of subset/superset structure.
Pitch Class Set Calculator
from Mount Allison University
Chord Analyzer
on ''Lamadeguido.com'' Online lists * Solomon, Larry (2005).
, ''SolomonsMusic.net''. * Tucker, Gary (2001).
, ''A Brief Introduction to Pitch-Class Set Analysis''. * Nelson, Paul (2004).
, ''ComposerTools.com''. {{Set theory (music) Musical set theory Music theory lists, Pitch class sets
This is a list of set classes, by Forte number. In music theory
Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory": The first is the "Elements of music, ...
, a ''set class'' (an abbreviation of ''pitch-class-set class'') is an ascending collection of pitch classes, transposed to begin at zero. For a list of ordered collections, see this list of tone rows and series.
Sets are listed with links to their complements. For unsymmetrical sets, the prime form is marked with "A" and the inversion with "B"; sets without either are symmetrical. Sets marked with a "Z" refer to a pair of different set classes with identical interval class content unrelated by inversion, with one of each pair listed at the end of the respective list when they occur. ("Z" is derived from the prefix ''zygo-'', from Ancient Greek ''ζυγόν'', "yoke". Hence: zygosets.) "T" and "E" are conventionally used in sets to notate ten and eleven, respectively, as single characters. The ordering of sets in the lists is based on the string of numerals in the interval vector treated as an integer, decreasing in value, following the strategy used by Forte in constructing his numbering system.
There are two slightly different methods of obtaining the prime form—an earlier one by Allen Forte and a later but now generally more popular one by John Rahn—both often confusingly described as "most packed to the left". However, a more precise description of the Rahn spelling is to select the version most dispersed from the right, whereas the precise description of the Forte spelling is to select the version most packed to the left within the smallest span. In the lists here, the Rahn spelling is used for the 17 out of 352 set classes where the two methods yield different results; the alternative Forte spellings are listed in the footnotes.
Before either (1960–67), Elliott Carter
Elliott Cook Carter Jr. (December 11, 1908 – November 5, 2012) was an American modernist composer who was one of the most respected composers of the second half of the 20th century. He combined elements of European modernism and American " ...
had produced a numbered listing of pitch class sets, or "chords", as Carter referred to them, for his own use. Donald Martino
Donald James Martino (May 16, 1931 – December 8, 2005) was a Pulitzer Prize winning American composer.
Biography
Born in Plainfield, New Jersey, Martino attended Plainfield High School. He began as a clarinetist, playing jazz for fun and ...
had produced tables of hexachord
In music, a hexachord (also hexachordon) is a six- note series, as exhibited in a scale ( hexatonic or hexad) or tone row. The term was adopted in this sense during the Middle Ages and adapted in the 20th century in Milton Babbitt's serial t ...
s, tetrachord
In music theory, a tetrachord (; ) is a series of four notes separated by three interval (music), intervals. In traditional music theory, a tetrachord always spanned the interval of a perfect fourth, a 4:3 frequency proportion (approx. 498 cent (m ...
s, trichords, and pentachords for combinatoriality in his 1961 article, "The Source Set and its Aggregate Formations".Schuijer, Michael (2008). ''Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts'', p.97. University of Rochester. .
The difference between the interval vectors of a set and its complement is List
, , rowspan="2" , , , rowspan="2" , , , , , ''Ryukyu '' scale , , 7-20B , - style="background:white;" , , , } , , , , ''Hirajōshi'' scale, ''in'' scale, ''iwato'' scale , , 7-20A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-21B , - style="background:white;" , , , , , , , ... , , 7-21A , - style="background:white;" , , , , , , , , , , , ... , , 7-22 , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-23B , - style="background:white;" , , , , , , , ... , , 7-23A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-24B , - style="background:white;" , , , , , , , ... , , 7-24A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , , , , , Half-diminished minor ninth chord , , 7-25B , - style="background:white;" , , , , , , , Seven six chord , , 7-25A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , , , , , Half-diminished ninth chord , , 7-26A , - style="background:white;" , , , , , , , Augmented major ninth chord , , 7-26B , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , , , , , Major ninth chord , , 7-27B , - style="background:white;" , , , , , , , Minor ninth chord , , 7-27A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-28A , - style="background:white;" , , , , , , , ... , , 7-28B , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-29B , - style="background:white;" , , , , , , , ''Insen'' scale, minor sixth ninth chord , , 7-29A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-30B , - style="background:white;" , , , , , , , Jazz sus chord, Lydian augmented chord , , 7-30A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , , , , , Beta chord, diminished minor ninth chord , , 7-31B , - style="background:white;" , , , , , , , Diminished ninth chord, dominant minor ninth chord , , 7-31A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , , , , , Dominant seventh sharp ninth chord , , 7-32B , - style="background:white;" , , , } , , , , ''Elektra'' chord, gamma chord , , 7-32A , - style="background:white;" , , , , , , , , , , , Augmented dominant ninth chord, ninth augmented fifth chord, ninth flat fifth chord , , 7-33 , - style="background:white;" , , , , , , , , , , , Dominant ninth chord , , 7-34 , - style="background:white;" , , , , , , , , , , , Major pentatonic scale , , 7-35 , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-Z36B , - style="background:white;" , , , , , , , ... , , 7-Z36A , - style="background:white;" , , , , , , , , , , , ... , , 7-Z37 , - , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-Z38B , - style="background:white;" , , , , , , , ... , , 7-Z38A , - , , , , , , , 4 , , , , Chromatic hexachord , , 6-1 , - , , , , , rowspan="2" , , , rowspan="2" , 19 , , , , ... , , 6-2B , - , , , , , , , ... , , 6-2A , - , , , , , rowspan="2" , , , rowspan="2" , 49 , , , , ... , , 6-Z36B , - , , , , , , , ... , , 6-Z36A , - , , , , , , , 24 , , , , ... , , 6-Z37 , - , , , , , rowspan="2" , , , rowspan="2" , 16 , , , , ... , , 6-5B , - , , , , , , , ... , , 6-5A , - , , , , , , , 33 , , , , ... , , 6-Z38 , - , , , , , , , 7 , , , , Two-semitone tritone scale , , 6-7 , - , , , , , , , 5 , , , , ... , , 6-8 , - , , , , , rowspan="2" , , , rowspan="2" , 20 , , , , ... , , 6-9B , - , , , , , , , ... , , 6-9A , - , , , , , rowspan="2" , , , rowspan="2" , 42 , , , , ... , , 6-Z39A , - , , , , , , , ... , , 6-Z39B , - , , , , , rowspan="2" , , , rowspan="2" , 47 , , , , ... , , 6-Z40B , - , , , , , , , Sacher hexachord , , 6-Z40A , - , , , , , rowspan="2" , , , rowspan="2" , 46 , , , , ... , , 6-Z41B , - , , , , , , , ... , , 6-Z41A , - , , , , , , , 29 , , , , Istrian scale , , 6-Z42 , - , , , , , rowspan="2" , , , rowspan="2" , 3 , , , , ... , , 6-14A , - , , , , , , , ... , , 6-14B , - , , , , , rowspan="2" , , , rowspan="2" , 13 , , , , ... , , 6-15B , - , , , , , , , ... , , 6-15A , - , , , , , rowspan="2" , , , rowspan="2" , 11 , , , , ... , , 6-16B , - , , , , , , , ... , , 6-16A , - , , , , , rowspan="2" , , , rowspan="2" , 35 , , , , All-trichord hexachord , , 6-Z43B , - , , , , , , , ... , , 6-Z43A , - , , , , , rowspan="2" , , , rowspan="2" , 17 , , , , ... , , 6-18B , - , , , , , , , ... , , 6-18A , - , , , , , rowspan="2" , , , rowspan="2" , 37 , , , , ... , , 6-Z44B , - , , , , , , , ... , , 6-Z44A , - , , , , , , , 2 , , , , Augmented scale, "Ode-to-Napoleon" hexachord , , 6-20 , - , , , , , rowspan="2" , , , rowspan="2" , 12 , , , , ... , , 6-21B , - , , , , , , , ... , , 6-21A , - , , , , , rowspan="2" , , , rowspan="2" , 10 , , , , ... , , 6-22B , - , , , , , , , ... , , 6-22A , - , , , , , , , 27 , , , , ... , , 6-Z45 , - , , , , , rowspan="2" , , , rowspan="2" , 39 , , , , Minor major eleventh chord , , 6-Z46B , - , , , , , , , Half-diminished eleventh chord , , 6-Z46A , - , , , , , rowspan="2" , , , rowspan="2" , 43 , , , , Major eleventh chord , , 6-Z47B , - , , , , , , , ... , , 6-Z47A , - , , , , , , , 26 , , , , Major ninth sharp eleventh chord , , 6-Z48 , - , , , , , rowspan="2" , , , rowspan="2" , 14 , , , , ... , , 6-27B , - , , , , , , , Diminished eleventh chord , , 6-27A , - , , , , , , , 21 , , , , Augmented major eleventh chord , , 6-Z49 , - , , , } , , , , 32 , , , , Bridge chord , , 6-Z50 , - , , , , , rowspan="2" , , , rowspan="2" , 15 , , , , ... , , 6-30B , - , , , , , , , Petrushka chord, tritone scale , , 6-30A , - , , , } , , rowspan="2" , , , rowspan="2" , 8 , , , , ... , , 6-31B , - , , , } , , , , ... , , 6-31A , - , , , , , , , 6 , , , , Diatonic hexachord, minor eleventh chord , , 6-32 , - , , , , , rowspan="2" , , , rowspan="2" , 18 , , , , ... , , 6-33B , - , , , , , , , Dominant eleventh chord , , 6-33A , - , , , , , rowspan="2" , , , rowspan="2" , 9 , , , , Mystic chord , , 6-34B , - , , , , , , , Augmented eleventh chord, dominant sharp eleventh chord, '' Prélude'' chord , , 6-34A , - , , , , , , , 1 , , , , Whole tone scale , , 6-35 , - , , , , , rowspan="2" , , , rowspan="2" , 50 , , , , ... , , 6-Z3B , - , , , , , , , ... , , 6-Z3A , - , , , , , , , 23 , , , , ... , , 6-Z4 , - , , , , , , , 34 , , , , ... , , 6-Z6 , - , , , , , rowspan="2" , , , rowspan="2" , 41 , , , , ... , , 6-Z10A , - , , , , , , , ... , , 6-Z10B , - , , , , , rowspan="2" , , , rowspan="2" , 48 , , , , ... , , 6-Z11B , - , , , , , , , ... , , 6-Z11A , - , , , , , rowspan="2" , , , rowspan="2" , 45 , , , , ... , , 6-Z12B , - , , , , , , , ... , , 6-Z12A , - , , , , , , , 30 , , , , ... , , 6-Z13 , - , , , , , rowspan="2" , , , rowspan="2" , 36 , , , , ... , , 6-Z17B , - , , , , , , , ... , , 6-Z17A , - , , , , , rowspan="2" , , , rowspan="2" , 38 , , , , Schoenberg hexachord , , 6-Z19B , - , , , } , , , , ... , , 6-Z19A , - , , , , , , , 28 , , , , ... , , 6-Z23 , - , , , , , rowspan="2" , , , rowspan="2" , 40 , , , , Scale of harmonics , , 6-Z24B , - , , , , , , , ... , , 6-Z24A , - , , , , , rowspan="2" , , , rowspan="2" , 44 , , , , ... , , 6-Z25B , - , , , , , , , Blues scale , , 6-Z25A , - , , , , , , , 25 , , , , ... , , 6-Z26 , - , , , , , , , 22 , , , , ... , , 6-Z28 , - , , , , , , , 31 , , , , ... , , 6-Z29 , - style="background:white;" , , , , , , , 1 , , , , ... , , 5-1 , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 11 , , , , ... , , 5-2B , - style="background:white;" , , , , , , , ... , , 5-2A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 14 , , , , ... , , 5-3B , - style="background:white;" , , , , , , , ... , , 5-3A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 12 , , , , ... , , 5-4B , - style="background:white;" , , , , , , , ... , , 5-4A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 13 , , , , ... , , 5-5B , - style="background:white;" , , , , , , , ... , , 5-5A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 27 , , , , ... , , 5-6B , - style="background:white;" , , , , , , , ... , , 5-6A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 30 , , , , ... , , 5-7B , - style="background:white;" , , , , , , , ... , , 5-7A , - style="background:white;" , , , , , , , 2 , , , , ... , , 5-8 , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 15 , , , , ... , , 5-9B , - style="background:white;" , , , , , , , ... , , 5-9A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 19 , , , , ... , , 5-10B , - style="background:white;" , , , , , , , ... , , 5-10A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 18 , , , , ... , , 5-11A , - style="background:white;" , , , , , , , ... , , 5-11B , - style="background:white;" , , , , , , , 5 , , , , ... , , 5-Z12 , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 17 , , , , ... , , 5-13B , - style="background:white;" , , , , , , , ... , , 5-13A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 28 , , , , Natural minor scale , , 5-14B , - style="background:white;" , , , , , , , ... , , 5-14A , - style="background:white;" , , , , , , , 4 , , , , ... , , 5-15 , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 20 , , , , ... , , 5-16B , - style="background:white;" , , , , , , , ... , , 5-16A , - style="background:white;" , , , , , , , 10 , , , , ... , , 5-Z17 , - style="background:white;" , , , } , , rowspan="2" , , , rowspan="2" , 35 , , , , ... , , 5-Z18B , - style="background:white;" , , , }, , , , ... , , 5-Z18A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 31 , , , , ... , , 5-19B , - style="background:white;" , , , , , , , ... , , 5-19A , - style="background:white;" , , , } , , rowspan="2" , , , rowspan="2" , 34 , , , , Persian scale , , 5-20B , - style="background:white;" , , , } , , , , ... , , 5-20A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 21 , , , , ... , , 5-21B , - style="background:white;" , , , , , , , ... , , 5-21A , - style="background:white;" , , , , , , , 8 , , , , Double harmonic scale, Hungarian minor scale , , 5-22 , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 25 , , , , ... , , 5-23B , - style="background:white;" , , , , , , , ... , , 5-23A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 22 , , , , ... , , 5-24B , - style="background:white;" , , , , , , , Enigmatic scale , , 5-24A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 24 , , , , ... , , 5-25B , - style="background:white;" , , , , , , , ... , , 5-25A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 26 , , , , ... , , 5-26A , - style="background:white;" , , , , , , , ... , , 5-26B , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 23 , , , , ... , , 5-27B , - style="background:white;" , , , , , , , ... , , 5-27A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 36 , , , , ... , , 5-28A , - style="background:white;" , , , , , , , ... , , 5-28B , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 32 , , , , ... , , 5-29B , - style="background:white;" , , , , , , , ... , , 5-29A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 37 , , , , Augmented thirteenth chord, minor Neapolitan scale , , 5-30B , - style="background:white;" , , , , , , , ... , , 5-30A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 38 , , , , Hungarian major scale , , 5-31B , - style="background:white;" , , , , , , , Romanian major scale , , 5-31A , - style="background:white;" , , , , , rowspan="2" , , , rowspan="2" , 33 , , , , Augmented major thirteenth chord,harmonic minor scale
The harmonic minor scale (or Aeolian ♮7 scale) is a Scale (music), musical scale derived from the natural minor scale, with the minor seventh degree raised by one semitone to a major seventh, creating an augmented second between the sixth and ...
, Ukrainian Dorian scale , , 5-32B
, - style="background:white;"
, , , , , , , Half-diminished thirteenth chord, harmonic major scale , , 5-32A
, - style="background:white;"
, , , , , , , 6 , , , , Major Locrian scale, major Neapolitan scale , , 5-33
, - style="background:white;"
, , , , , , , 9 , , , , Acoustic scale, altered scale, minor major thirteenth chord , , 5-34
, - style="background:white;"
, , , , , , , 7 , , , , Diatonic scale
In music theory a diatonic scale is a heptatonic scale, heptatonic (seven-note) scale that includes five whole steps (whole tones) and two half steps (semitones) in each octave, in which the two half steps are separated from each other by eith ...
, major thirteenth chord, minor thirteenth chord , , 5-35
, - style="background:white;"
, , , , , rowspan="2" , , , rowspan="2" , 16 , , , , ... , , 5-Z36B
, - style="background:white;"
, , , , , , , ... , , 5-Z36A
, - style="background:white;"
, , , , , , , 3 , , , , ... , , 5-Z37
, - style="background:white;"
, , , , , rowspan="2" , , , rowspan="2" , 29 , , , , ... , , 5-Z38B
, - style="background:white;"
, , , , , , , ... , , 5-Z38A
, -
, , , , , , , , , , , ... , , 4-1
, -
, , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 4-2B
, -
, , , , , , , ... , , 4-2A
, -
, , , , , , , , , , , ... , , 4-3
, -
, , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 4-4B
, -
, , , , , , , ... , , 4-4A
, -
, , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 4-5B
, -
, , , , , , , ... , , 4-5A
, -
, , , , , , , , , , , ... , , 4-6
, -
, , , , , , , , , , , ... , , 4-7
, -
, , , , , , , , , , , ... , , 4-8
, -
, , , , , , , , , , , ... , , 4-9
, -
, , , , , , , , , , , ... , , 4-10
, -
, , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 4-11B
, -
, , , , , , , ... , , 4-11A
, -
, , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 4-12A
, -
, , , , , , , ... , , 4-12B
, -
, , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 4-13B
, -
, , , , , , , ... , , 4-13A
, -
, , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 4-14A
, -
, , , , , , , ... , , 4-14B
, -
, , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 4-Z15B
, -
, , , , , , , ... , , 4-Z15A
, -
, , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 4-16B
, -
, , , , , , , ... , , 4-16A
, -
, , , , , , , , , , , ... , , 4-17
, -
, , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 4-18B
, -
, , , , , , , ... , , 4-18A
, -
, , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 4-19B
, -
, , , , , , , ... , , 4-19A
, -
, , , , , , , , , , , ... , , 4-20
, -
, , , , , , , , , , , ... , , 4-21
, -
, , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 4-22B
, -
, , , } , , , , ... , , 4-22A
, -
, , , , , , , , , , , Bebop dominant scale, bebop major scale , , 4-23
, -
, , , , , , , , , , , ... , , 4-24
, -
, , , , , , , , , , , Seventh flat five diminished scale , , 4-25
, -
, , , } , , , , , , , , Bebop harmonic minor scale , , 4-26
, -
, , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 4-27B
, -
, , , } , , , , Bebop melodic minor scale , , 4-27A
, -
, , , , , , , , , , , Octatonic scale , , 4-28
, -
, , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 4-Z29B
, -
, , , , , , , ... , , 4-Z29A
, - style="background:white;"
, , , , , , , , , , , ... , , 3-1
, - style="background:white;"
, , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 3-2B
, - style="background:white;"
, , , , , , , ... , , 3-2A
, - style="background:white;"
, , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 3-3B
, - style="background:white;"
, , , , , , , ... , , 3-3A
, - style="background:white;"
, , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 3-4B
, - style="background:white;"
, , , , , , , ... , , 3-4A
, - style="background:white;"
, , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 3-5B
, - style="background:white;"
, , , , , , , ... , , 3-5A
, - style="background:white;"
, , , , , , , , , , , ... , , 3-6
, - style="background:white;"
, , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 3-7B
, - style="background:white;"
, , , } , , , , ... , , 3-7A
, - style="background:white;"
, , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 3-8B
, - style="background:white;"
, , , } , , , , ... , , 3-8A
, - style="background:white;"
, , , , , , , , , , , Blues scale , , 3-9
, - style="background:white;"
, , , , , , , , , , , ... , , 3-10
, - style="background:white;"
, , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , #3-11B, 3-11B
, - style="background:white;"
, , , } , , , , ... , , #3-11A, 3-11A
, - style="background:white;"
, , , , , , , , , , , ... , , #3-12, 3-12
, -
, , , , , , , , , , , ... , , #2-1, 2-1
, -
, , , , , , , , , , , ... , , #2-2, 2-2
, -
, , , , , , , , , , , ... , , #2-3, 2-3
, -
, , , , , , , , , , , ... , , #2-4, 2-4
, -
, , , , , , , , , , , ... , , #2-5, 2-5
, -
, , , , , , , , , , , ... , , #2-6, 2-6
, - style="background:white;"
, , , , , , , , , , , Northern lights chord , , #1-1, 1-1
, -
, , , , , , , , , , , aggregate (music), Aggregate, all-interval twelve-tone row , , #0-1, 0-1
There is an anomaly in Allen Forte's book concerning the numbering of the pair of hexachords 6-Z28, [013569], and 6-Z49, [013479], where adjacency intervals are shown here by subscripts. They both have the same span, with a minor-third at the right. But, within that span, the hexachord [0,1,3,4,7,9] is "more packed to the left" than [0,1,3,5,6,9], as seen by inspecting the left-hand adjacency-interval sequences, and therefore, according to Forte's own rule, the set [0,1,3,4,7,9] should have been assigned the lower number 6-Z28, with [0,1,3,5,6,9] given the higher number 6-Z49.
See also
* Interval vector * List of chords * Z-relationReferences
Notes
Sources
External links
Pitch Class Set Calculator
from Mount Allison University
Chord Analyzer
on ''Lamadeguido.com'' Online lists * Solomon, Larry (2005).
, ''SolomonsMusic.net''. * Tucker, Gary (2001).
, ''A Brief Introduction to Pitch-Class Set Analysis''. * Nelson, Paul (2004).
, ''ComposerTools.com''. {{Set theory (music) Musical set theory Music theory lists, Pitch class sets