music theory Music theory is the study of the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory". The first is the "rudiments", that are needed to understand music notation (ke ...

, a Viennese trichord (also 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 (german: Zweite Wiener Schule, Neue Wiener Schule) 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. ...

, 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 cla ...

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 refer ...

in many ways. Bill Evans's

According to Henry Martin, " mposers such as

Webern Anton Friedrich Wilhelm von Webern (3 December 188315 September 1945), better known as Anton Webern (), was an Austrian composer and conductor whose music was among the most radical of its milieu in its sheer concision, even aphorism, and stead ...

... 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 In music, consonance and dissonance are categorizations of simultaneous or successive Sound, sounds. Within the Western tradition, some listeners associate consonance with sweetness, pleasantness, and acceptability, and dissonance with harshness ...

' 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 and analysis. It was established in 1962 by Arthur Berger and Benjamin Boretz (who were its initial editors-in-chief). ''Perspectives'' was first ...

'', 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, with its roots in blues and ragtime. Since the 1920s Jazz Age, it has been recognized as a major ...

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 Inversion or inversions may refer to: Arts * , a French gay magazine (1924/1925) * ''Inversion'' (artwork), a 2005 temporary sculpture in Houston, Texas * Inversion (music), a term with various meanings in music theory and musical set theory * ...

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-oriente ...

, being the

third Third or 3rd may refer to: Numbers * 3rd, the ordinal form of the cardinal number 3 * , a fraction of one third * Second#Sexagesimal divisions of calendar time and day, 1⁄60 of a ''second'', or 1⁄3600 of a ''minute'' Places * 3rd Street (d ...

seventh Seventh is the ordinal form of the number seven. Seventh may refer to: * Seventh Amendment to the United States Constitution * A fraction (mathematics), , equal to one of seven equal parts Film and television *"The Seventh", a second-season e ...

, 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 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 below the sur ...

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 them ...

). 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