Editing Béla Bartók (section)

==Musical analysis==
[[File:Bartok Bela Baja.jpg|thumb|right|Béla Bartók memorial plaque in [[Baja, Hungary]]]]
[[Paul Wilson (music theorist)|Paul Wilson]] lists as the most prominent characteristics of Bartók's music from late 1920s onwards the influence of the [[Carpathian basin]] and European art music, and his changing attitude toward (and use of) tonality, but without the use of the traditional [[Diatonic functionality|harmonic functions]] associated with major and minor scales.{{sfn|Wilson|1992|pp=2–4}}

Although Bartók claimed in his writings that his music was always tonal, he rarely used the chords or scales normally associated with tonality, and so the descriptive resources of tonal theory are of limited use. [[George Perle|George]] {{harvtxt|Perle|1955}} and Elliott {{harvtxt|Antokoletz|1984}} focus on his alternative methods of signaling tonal centers, via axes of [[Inversion (music)#Inversional equivalency|inversional symmetry]]. Others view Bartók's axes of symmetry in terms of atonal analytic protocols. [[Richard Cohn|Richard]] {{harvtxt|Cohn|1988}} argues that inversional symmetry is often a byproduct of another atonal procedure, the formation of chords from transpositionally related dyads. Atonal pitch-class theory also furnishes resources for exploring [[polymodal chromaticism]], [[projected set]]s, [[privileged pattern]]s, and large set types used as source sets such as the equal tempered twelve tone [[tone row#total chromatic|aggregate]], [[octatonic scale]] (and [[alpha chord]]), the diatonic and ''heptatonia secunda'' seven-note scales, and less often the whole tone scale and the primary pentatonic collection.{{sfn|Wilson|1992|pp=24–29}}

He rarely used the simple aggregate actively to shape musical structure, though there are notable examples such as the second theme from the first movement of his [[Violin Concerto No. 2 (Bartók)|Second Violin Concerto]], of which he commented that he "wanted to show [[Arnold Schoenberg|Schoenberg]] that one can use all twelve tones and still remain tonal".{{sfn|Gillies|1990|p=185}} More thoroughly, in the first eight measures of the last movement of his Second Quartet, all notes gradually gather with the twelfth (G{{music|♭}}) sounding for the first time on the last beat of measure 8, marking the end of the first section. The aggregate is partitioned in the opening of the Third String Quartet with C{{music|♯}}–D–D{{music|♯}}–E in the accompaniment (strings) while the remaining pitch classes are used in the melody (violin 1) and more often as 7–35 (diatonic or "white-key" collection) and 5–35 (pentatonic or "black-key" collection) such as in no. 6 of the ''Eight Improvisations''. There, the primary theme is on the black keys in the left hand, while the right accompanies with triads from the white keys. In measures 50–51 in the third movement of the Fourth Quartet, the first violin and cello play black-key chords, while the second violin and viola play stepwise diatonic lines.{{sfn|Wilson|1992|p=25}} On the other hand, from as early as the Suite for piano, Op. 14 (1914), he occasionally employed a form of [[serialism]] based on compound interval cycles, some of which are maximally distributed, multi-aggregate cycles.{{sfn|Martins|2006}}{{sfn|Gollin|2007}} [[Ernő Lendvai]] analyses Bartók's works as being based on two opposing tonal systems, that of the [[acoustic scale]] and the [[axis system]], as well as using the [[golden ratio|golden section]] as a structural principle.{{sfn|Lendvai|1971}}

[[Milton Babbitt]], in his 1949 review of Bartók's string quartets, criticized Bartók for using tonality and non-tonal methods unique to each piece. Babbitt noted that "Bartók's solution was a specific one, it cannot be duplicated".{{sfn|Babbitt|1949|p=385}} Bartók's use of "two organizational principles"—tonality for large scale relationships and the piece-specific method for moment to moment thematic elements—was a problem for Babbitt, who worried that the "highly attenuated tonality" requires extreme non-harmonic methods to create a feeling of closure.{{sfn|Babbitt|1949|pp=377–378}}