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 Viennese trichord (also known as Viennese fourth chord and tritone-fourth chordDeLone, Richard, et al (1975). ''Aspects of 20th Century Music'', p. 348. Englewood Cliffs, New Jersey: Prentice-Hall .), named for the

Second Viennese School The Second Viennese School () was the group of composers that comprised Arnold Schoenberg and his pupils, particularly Alban Berg and Anton Webern, and close associates in early 20th-century Vienna. Their music was initially characterized by late ...

, is a pitch set with

prime form In algebraic geometry, the Schottky–Klein prime form ''E''(''x'',''y'') of a compact Riemann surface ''X'' depends on two elements ''x'' and ''y'' of ''X'', and vanishes if and only if ''x'' = ''y''. The prime form ''E'' is not quite ...

(0,1,6). Its

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 cl ...

is 3-5. The sets C–D–G and C–F–G are both examples of Viennese trichords, though they may be

voiced Voice or voicing is a term used in phonetics and phonology to characterize speech sounds (usually consonants). Speech sounds can be described as either voiceless (otherwise known as ''unvoiced'') or voiced. The term, however, is used to refe ...

in many ways. According to Henry Martin, " mposers such as

Webern Anton Webern (; 3 December 1883 – 15 September 1945) was an Austrian composer, conductor, and musicologist. His music was among the most radical of its milieu in its lyric poetry, lyrical, poetic concision and use of then novel atonality, aton ...

... are partial to 016

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 given ...

s, given their 'more dissonant' inclusion of ics 1 and 6."Martin, Henry (Winter, 2000). "Seven Steps to Heaven: A Species Approach to Twentieth-Century Analysis and Composition", p. 149, ''

Perspectives of New Music ''Perspectives of New Music'' (PNM) is a peer-reviewed academic journal specializing in music theory Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. ''The Oxford Companion to Musi ...

'', vol. 38, no. 1, pp. 129–168. In

jazz Jazz is a music genre that originated in the African-American communities of New Orleans, Louisiana, in the late 19th and early 20th centuries. Its roots are in blues, ragtime, European harmony, African rhythmic rituals, spirituals, h ...

and

popular music Popular music is music with wide appeal that is typically distributed to large audiences through the music industry. These forms and styles can be enjoyed and performed by people with little or no musical training.Popular Music. (2015). ''Fun ...

, the chord formed by the inversion of the set usually has a dominant

function Function or functionality may refer to: Computing * Function key, a type of key on computer keyboards * Function model, a structured representation of processes in a system * Function object or functor or functionoid, a concept of object-orie ...

, being the

third Third or 3rd may refer to: Numbers * 3rd, the ordinal form of the cardinal number 3 * , a fraction of one third * 1⁄60 of a ''second'', i.e., the third in a series of fractional parts in a sexagesimal number system Places * 3rd Street (di ...

, seventh, and added fourth/eleventh of a

dominant chord In music, the dominant is the fifth scale degree () of the diatonic scale. It is called the ''dominant'' because it is second in importance to the first scale degree, the tonic. In the movable do solfège system, the dominant note is sung as "So ...

with elided

root In vascular plants, the roots are the plant organ, organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They are most often bel ...

Forte, Allen (2000). "Harmonic Relations: American Popular Harmonies (1925–1950) and Their European Kin", pp. 5–36, ''Traditions, Institutions, and American Popular Music'' (''Contemporary Music Review'', vol. 19, part 1), p. 7. Routledge. Covach, John and Everett, Walter; eds. . (and fifth, see

jazz chord Jazz chords are chords, chord voicings and chord symbols that jazz musicians commonly use in composition, improvisation, and harmony. In jazz chords and theory, most triads that appear in lead sheets or fake books can have sevenths added to t ...

). For example, the Viennese trichord of C-F#-G could be considered a D11/C: D (elided) - F# - A (elided) - C - G.

References

External links

*Jay Tomlin
"All About Set Theory"
''Java Set Theory Machine''.
"More on Set Theory"
''Flexistentialism''. {{Pitch segments Chords Tritones Musical set theory