This is a list of set classes by

Forte number In musical set theory, a Forte number is the pair of numbers Allen Forte assigned to the prime form of each pitch class set of three or more members in ''The Structure of Atonal Music'' (1973, ). The first number indicates the number of pitch ...

. For a list of ordered collections, see: list of tone rows and series. Sets are listed next to their complements. Inversions are marked "B" (sets not marked "A" or "B" are

symmetrical Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definit ...

). "T" and "E" are conventionally used in sets to notate 10 and 11, respectively, as single characters. There are two slightly different methods of obtaining a normal form. This results in two different normal form sets for the same Forte number in a few cases. The alternative notation for those chords are listed in the footnotes.

Elliott Carter Elliott Cook Carter Jr. (December 11, 1908 – November 5, 2012) was an American modernism (music), modernist composer. One of the most respected composers of the second half of the 20th century, he combined elements of European modernism a ...

had earlier (1960–67) 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 theor ...

tetrachord In music theory, a tetrachord ( el, τετράχορδoν; lat, tetrachordum) is a series of four notes separated by three intervals. In traditional music theory, a tetrachord always spanned the interval of a perfect fourth, a 4:3 frequency pr ...

trichord In music theory, a trichord () is a group of three different pitch classes found within a larger group. A trichord is a contiguous three-note set from a musical scale or a twelve-tone row. In musical set theory there are twelve trichords g ...

s, and

pentachord A pentachord in music theory may be either of two things. In pitch-class set theory, a pentachord is defined as any five pitch classes, regarded as an unordered collection . In other contexts, a pentachord may be any consecutive five-note sectio ...

s for

combinatoriality In music using the twelve tone technique, combinatoriality is a quality shared by twelve-tone tone rows whereby each section of a row and a proportionate number of its transformations combine to form aggregates (all twelve tones). Whittall, Arnold ...

in his article, "The Source Set and its Aggregate Formations" (1961).Schuijer, Michael (2008). ''Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts'', p.97. University of Rochester. .

List

, , , , , , , , ... , - , , , , , rowspan="2" , , , rowspan="2" , 29 , , , ,

Half-diminished seventh chord In music theory, the half-diminished seventh chord (also known as a half-diminished chord or a minor seventh flat five chord) is a seventh chord composed of a root note, together with a minor third, a diminished fifth, and a minor seventh (1,&nb ...

, , 8-27B , , , , rowspan="2" , , , rowspan="2" , , , , , ... , - , 4-27B , , , , , , dominant 7th chord , , , , , , , , ... , - , , , , , , , 5 , , , , dim. 7th chord , , , , , , , , , , , ,

octatonic scale An octatonic scale is any eight- note musical scale. However, the term most often refers to the symmetric scale composed of alternating whole and half steps, as shown at right. In classical theory (in contrast to jazz theory), this symmetrica ...

, - , , , , , rowspan="2" , , , rowspan="2" , 23 , , , , all-interval tetrachord , , 8-z29B , , , , rowspan="2" , , , rowspan="2" , , , , , ... , - , 4-z29B , , , , , , all-interval tetrachord, , , , , , , , ... , - style="background:#F5F5F5;" , , , , , , , , , , , ... , , , , , , , , 1 , , , , ... , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-2B , , , , rowspan="2" , , , rowspan="2" , 11 , , , , ... , - style="background:#F5F5F5;" , 5-2B , , , , , , ... , , , , , , , , ... , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-3B , , , , rowspan="2" , , , rowspan="2" , 14 , , , , ... , - style="background:#F5F5F5;" , 5-3B , , , , , , ... , , , , , , , , ... , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-4B , , , , rowspan="2" , , , rowspan="2" , 12 , , , , ... , - style="background:#F5F5F5;" , 5-4B , , , , , , ... , , , , , , , , ... , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-5B , , , , rowspan="2" , , , rowspan="2" , 13 , , , , ... , - style="background:#F5F5F5;" , 5-5B , , , , , , ... , , , , , , , , ... , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-6B , , , , rowspan="2" , , , rowspan="2" , 27 , , , , ... , - style="background:#F5F5F5;" , 5-6B , , , , , , ... , , , , , , , , ... , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-7B , , , , rowspan="2" , , , rowspan="2" , 30 , , , , ... , - style="background:#F5F5F5;" , 5-7B , , , , , , ... , , , , , , , , ... , - style="background:#F5F5F5;" , , , , , , , , , , , ... , , , , , , , , 2 , , , , ... , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-9B , , , , rowspan="2" , , , rowspan="2" , 15 , , , , ... , - style="background:#F5F5F5;" , 5-9B , , , , , , ... , , , , , , , , ... , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-10B , , , , rowspan="2" , , , rowspan="2" , 19 , , , , ... , - style="background:#F5F5F5;" , 5-10B , , , , , , ... , , , , , , , , ... , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-11B , , , , rowspan="2" , , , rowspan="2" , 18 , , , , ... , - style="background:#F5F5F5;" , 5-11B , , , , , , ... , , , , , , , , ... , - style="background:#F5F5F5;" , , , , , , , , , , , ... , , , , , , , , 5 , , , , ... , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-13B , , , , rowspan="2" , , , rowspan="2" , 17 , , , , ... , - style="background:#F5F5F5;" , 5-13B , , , , , , ... , , , , , , , , ... , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-14B , , , , rowspan="2" , , , rowspan="2" , 28 , , , , ... , - style="background:#F5F5F5;" , 5-14B , , , , , , ... , , , , , , , , ... , - style="background:#F5F5F5;" , , , , , , , , , , , ... , , , , , , , , 4 , , , , ... , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-16B , , , , rowspan="2" , , , rowspan="2" , 20 , , , , ... , - style="background:#F5F5F5;" , 5-16B , , , , , , ... , , , , , , , , ... , - style="background:#F5F5F5;" , , , , , , , , , , ,

Farben chord In music, the Farben chord is a chord, in ascending order C–G–B–E–A, named after its use in ''Five Pieces for Orchestra'', Op.16, No. 3, "Farben" (German: "colors") by Arnold Schoenberg. Its unordered pitch-class content in normal form is ...

, , , , , , , , 10 , , , , ... , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , , , } , , rowspan="2" , , , rowspan="2" , 35 , , , , ... , - style="background:#F5F5F5;" , 5-z18B , , , , , , ... , , 7-z18B , , , , , , ... , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-19B , , , , rowspan="2" , , , rowspan="2" , 31 , , , , ... , - style="background:#F5F5F5;" , 5-19B , , , , , , ... , , , , , , , , ... , - style="background:#F5F5F5;" , , , } , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-20B , , , , rowspan="2" , , , rowspan="2" , 34 , , , , ... , - style="background:#F5F5F5;" , 5-20B , , , , , ,

In scale The ''in'' scale (also known as the ''Sakura'' pentatonic scale due to its use in the well-known folk song '' Sakura Sakura'') is, according to a traditional theory, one of two pentatonic scales used in much Japanese music, excluding ''gagaku'' and ...

, , , , } , , , , Persian scale , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-21B , , , , rowspan="2" , , , rowspan="2" , 21 , , , , ... , - style="background:#F5F5F5;" , 5-21B , , , , , , ... , , , , , , , , ... , - style="background:#F5F5F5;" , , , , , , , , , , , ... , , , , , , , , 8 , , , ,

double harmonic scale In music, the double harmonic major scaleStetina, Troy (1999). ''The Ultimate Scale Book'', p. 59. . is a scale whose gaps may sound unfamiliar to Western listeners. This is also known as Mayamalavagowla, Bhairav Raga, Byzantine scale, Arabic (Hi ...

, - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-23B , , , , rowspan="2" , , , rowspan="2" , 25 , , , , ... , - style="background:#F5F5F5;" , 5-23B , , , , , , ... , , , , , , , , ... , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-24B , , , , rowspan="2" , , , rowspan="2" , 22 , , , ,

enigmatic scale The enigmatic scale ( it, scala enigmatica) is an unusual musical scale, with elements of both major and minor scales, as well as the whole-tone scale. It was originally published in a Milan journal as a musical challenge, with an invitation t ...

, - style="background:#F5F5F5;" , 5-24B , , , , , , ... , , , , , , , , ... , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , Seven six chord , , 7-25B , , , , rowspan="2" , , , rowspan="2" , 24 , , , , ... , - style="background:#F5F5F5;" , 5-25B , , , , , , ... , , , , , , , , ... , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , , , , , rowspan="2" , , , rowspan="2" , 26 , , , , ... , - style="background:#F5F5F5;" , 5-26B , , , , , , ... , , 7-26B , , , , , , ... , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-27B , , , , rowspan="2" , , , rowspan="2" , 23 , , , , ... , - style="background:#F5F5F5;" , 5-27B , , , , , , ... , , , , , , , , ... , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , , , , , rowspan="2" , , , rowspan="2" , 36 , , , , ... , - style="background:#F5F5F5;" , 5-28B , , , , , , ... , , 7-28B , , , , , , ... , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-29B , , , , rowspan="2" , , , rowspan="2" , 32 , , , , ... , - style="background:#F5F5F5;" , 5-29B , , , , , , ... , , , , , , , , ... , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-30B , , , , rowspan="2" , , , rowspan="2" , 37 , , , , ... , - style="background:#F5F5F5;" , 5-30B , , , , , , ... , , , , , , , , minor Neapolitan scale , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , beta chord , , 7-31B , , , , rowspan="2" , , , rowspan="2" , 38 , , , , ... , - style="background:#F5F5F5;" , 5-31B , , , , , , Dominant minor ninth chord , , , , , , , ,

Hungarian major scale The Hungarian major scale is an ancohemitonic, heptatonic scale with the following interval structure in semitones: 3, 1, 2, 1, 2, 1, 2, giving it the notes C D E F G A B in the key of C.

, - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-32B , , , , rowspan="2" , , , rowspan="2" , 33 , , , , harmonic major scale , - style="background:#F5F5F5;" , 5-32B , , , , , ,

Elektra chord The ''Elektra'' chord is a "complexly dissonant signature-chord"Lawrence Kramer. "Fin-de-siècle Fantasies: ''Elektra'', Degeneration and Sexual Science", ''Cambridge Opera Journal'', Vol. 5, No. 2. (Jul., 1993), pp. 141-165. and motivic elabor ...

gamma chord An octatonic scale is any eight-note musical scale. However, the term most often refers to the symmetric scale composed of alternating whole and half steps, as shown at right. In classical theory (in contrast to jazz theory), this symmetrical ...

, , , , , , , ,

harmonic minor scale In music theory, the minor scale is three scale patterns – the natural minor scale (or Aeolian mode), the harmonic minor scale, and the melodic minor scale (ascending or descending) – rather than just two as with the major scale, which als ...

, - style="background:#F5F5F5;" , , , , , , , , , , , ... , , , , , , , , 6 , , , , M Locrian scale , - style="background:#F5F5F5;" , , , , , , , , , , ,

Dominant ninth chord In music theory, a ninth chord is a chord that encompasses the interval of a ninth when arranged in close position with the root in the bass. Heinrich Schenker and also Nikolai Rimsky-Korsakov allowed the substitution of the dominant seventh ...

, , , , , , , , 9 , , , ,

altered scale In jazz, the altered scale, altered dominant scale, Palamidian Scale, or Super Locrian scale is a seven-note scale that is a dominant scale where all non-essential tones have been altered. This means that it comprises the three irreducibly essen ...

, - style="background:#F5F5F5;" , , , , , , , , , , , M pentatonic scale , , , , , , , , 7 , , , ,

diatonic scale In music theory, a diatonic scale is any heptatonic 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 either two or three whole st ...

, - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-z36B , , , , rowspan="2" , , , rowspan="2" , 16 , , , , ... , - style="background:#F5F5F5;" , 5-z36B , , , , , , ... , , , , , , , , ... , - style="background:#F5F5F5;" , , , , , , , , , , , ... , , , , , , , , 3 , , , , ... , - style="background:#F5F5F5;" , , , , , rowspan="2" , , , rowspan="2" , , , , , ... , , 7-z38B , , , , rowspan="2" , , , rowspan="2" , 29 , , , , ... , - style="background:#F5F5F5;" , 5-z38B , , , , , , ... , , , , , , , , ... , - , , , , , , , 4 , , , ,

chromatic hexachord In music theory, the chromatic hexachord is the hexachord consisting of a consecutive six-note segment of the chromatic scale. It is the first hexachord as ordered by Forte number, and its complement is the chromatic hexachord at the tritone. Fo ...

, , colspan="6" rowspan="3", , - , , , , , rowspan="2" , , , rowspan="2" , 19 , , , , ... , - , 6-2B , , , , , , ... , - , , , , , rowspan="2" , , , rowspan="2" , 49 , , , , ... , , 6-z36B , , , , rowspan="2" , , , rowspan="2" , 50 , , , , ... , - , 6-z3B , , , , , , ... , , , , , , , , ... , - , , , , , , , 24 , , , , ... , , , , , , , , 23 , , , , ... , - , , , , , rowspan="2" , , , rowspan="2" , 16 , , , , ... , , colspan="6" rowspan="2", , - , 6-5B , , , , , , ... , - , , , , , , , 33 , , , , ... , , , , , , , , 34 , , , , ... , - , , , , , , , 7 , , , , ... , , colspan="6" rowspan="4", , - , , , , , , , 5 , , , , ... , - , , , , , rowspan="2" , , , rowspan="2" , 20 , , , , ... , - , 6-9B , , , , , , ... , - , , , , , rowspan="2" , , , rowspan="2" , 42 , , , , ... , , 6-z39B , , , , rowspan="2" , , , rowspan="2" , 41 , , , , ... , - , 6-z10B , , , , , , ... , , , , , , , , ... , - , , , , , rowspan="2" , , , rowspan="2" , 47 , , , , ... , , 6-z40B , , , , rowspan="2" , , , rowspan="2" , 48 , , , , ... , - , 6-z11B , , , , , ,

Sacher hexachord The Sacher hexachord (6-Z11, musical cryptogram on the name of Swiss conductor Paul Sacher) is a hexachord notable for its use in a set of twelve compositions (''12 Hommages à Paul Sacher'') created at the invitation of Mstislav Rostropovich fo ...

, , , , , , , , ... , - , , , , , rowspan="2" , , , rowspan="2" , 46 , , , , ... , , 6-z41B , , , , rowspan="2" , , , rowspan="2" , 45 , , , , ... , - , 6-z12B , , , , , , ... , , , , , , , , ... , - , , , , , , , 29 , , , , ... , , , , , , , , 30 , , , , ... , - , , , , , rowspan="2" , , , rowspan="2" , 3 , , , , ... , , colspan="6" rowspan="6", , - , 6-14B , , , , , , ... , - , , , , , rowspan="2" , , , rowspan="2" , 13 , , , , ... , - , 6-15B , , , , , , ... , - , , , , , rowspan="2" , , , rowspan="2" , 11 , , , , ... , - , 6-16B , , , , , , ... , - , , , , , rowspan="2" , , , rowspan="2" , 35 , , , , all-trichord hexachord , , 6-z43B , , , , rowspan="2" , , , rowspan="2" , 36 , , , , ... , - , 6-z17B , , , , , , ... , , , , , , , , ... , - , , , , , rowspan="2" , , , rowspan="2" , 17 , , , , ... , , colspan="6" rowspan="2", , - , 6-18B , , , , , , ... , - , , , , , rowspan="2" , , , rowspan="2" , 37 , , , , ... , , 6-z44B , , , , rowspan="2" , , , rowspan="2" , 38 , , , , ... , - , 6-z19B , , , , , , ... , , , , , , , ,

Schoenberg hexachord 6-Z44 (012569), known as the Schoenberg hexachord, is Arnold Schoenberg's signature hexachord, as one transposition contains the pitches Es, C, H, B, E, G (A. Schoenberg), E, B, and B being Es, H, and B in German.Friedmann, Michael L. (1990) ...

, - , , , , , , , 2 , , , , "Ode-to-Napoleon" hexachord , , colspan="6" rowspan="5", , - , , , , , rowspan="2" , , , rowspan="2" , 12 , , , , ... , - , 6-21B , , , , , , ... , - , , , , , rowspan="2" , , , rowspan="2" , 10 , , , , ... , - , 6-22B , , , , , , ... , - , , , , , , , 27 , , , , ... , , , , , , , , 28 , , , , ... , - , , , , , rowspan="2" , , , rowspan="2" , 39 , , , , ... , , 6-z46B , , , , rowspan="2" , , , rowspan="2" , 40 , , , , ... , - , 6-z24B , , , , , , ... , , , , , , , , ... , - , , , , , rowspan="2" , , , rowspan="2" , 43 , , , ,

Major eleventh chord In music theory, an eleventh chord is a chord (music), chord that contains the tertian extended chord, extension of the eleventh. Typically found in jazz, an eleventh chord also usually includes the seventh (chord), seventh and ninth, and elements ...

, , 6-z47B , , , , rowspan="2" , , , rowspan="2" , 44 , , , ,

blues scale Blues is a music genre and musical form which originated in the Deep South of the United States around the 1860s. Blues incorporated spiritual (music), spirituals, work songs, field hollers, Ring shout, shouts, chants, and rhymed simple narra ...

, - , 6-z25B , , , , , , ... , , , , , , , , ... , - , , , , , , , 26 , , , , ... , , , , , , , , 25 , , , , ... , - , , , , , rowspan="2" , , , rowspan="2" , 14 , , , , ... , , colspan="6" rowspan="2", , - , 6-27B , , , , , , ... , - , , , , , , , 21 , , , , ... , , , , , , , , 22 , , , , ... , - , , , } , , , , 32 , , , , Bridge chord , , , , , , , , 31 , , , , ... , - , , , , , rowspan="2" , , , rowspan="2" , 15 , , , , ... , , colspan="6" rowspan="10", , - , 6-30B , , , , , ,

Petrushka chord The Petrushka chord is a recurring polytonal device used in Igor Stravinsky's ballet '' Petrushka'' and in later music. These two major triads, C major and F major – a tritone apart – clash, "horribly with each other", when sounded together ...

, - , , , } , , rowspan="2" , , , rowspan="2" , 8 , , , , ... , - , 6-31B , , } , , , , ... , - , , , , , , , 6 , , , , diatonic hexachord , - , , , , , rowspan="2" , , , rowspan="2" , 18 , , , , ... , - , 6-33B , , , , , , Dominant eleventh chord , - , , , , , rowspan="2" , , , rowspan="2" , 9 , , , ,

mystic chord In music, the mystic chord or Prometheus chord is a six-note synthetic chord and its associated scale, or pitch collection; which loosely serves as the harmonic and melodic basis for some of the later pieces by Russian composer Alexander Scriabi ...

, - , 6-34B , , , , , , ... , - , , , , , , , 1 , , , ,

whole tone scale In music, a whole-tone scale is a scale in which each note is separated from its neighbors by the interval of a whole tone. In twelve-tone equal temperament, there are only two complementary whole-tone scales, both six-note or '' hexatonic'' ...

Notes

References

External links

*Solomon, Larry (2005).
The Table of Pitch Class Sets
, ''SolomonsMusic.net''. *Tucker, Gary (2001).

, ''A Brief Introduction to Pitch-Class Set Analysis''. *Nelson, Paul (2004).

, ''ComposerTools.com''.

, ''MtA.Ca''.

{{Set theory (music) Musical set theory Pitch class sets

List

See also

Notes

References

External links