Piazzolla's nuevo tango was distinct from the traditional tango in its incorporation of elements of jazz, its use of extended harmonies and dissonance, its use of counterpoint, and its ventures into extended compositional forms. As Argentine psychoanalyst Carlos Kuri has pointed out, Piazzolla's fusion of tango with this wide range of other recognizable Western musical elements was so successful that it produced a new individual style transcending these influences. It is precisely this success, and individuality, that makes it hard to pin down where particular influences reside in his compositions, but some aspects are clear. The use of the passacaglia technique of a circulating bass line and harmonic sequence, invented and much used in 17th and 18th century baroque music but also central to the idea of jazz "changes", predominates in most of Piazzolla's mature compositions. Another clear reference to the baroque is the often complex and virtuosic counterpoint that sometimes follows strict fugal behavior but more often simply allows each performer in the group to assert his voice. A further technique that emphasises this sense of democracy and freedom among the musicians is improvisation that is borrowed from jazz in concept, but in practice involves a different vocabulary of scales and rhythms that stay within the parameters of the established tango sound-world. Pablo Ziegler has been particularly responsible for developing this aspect of the style both within Piazzolla's groups and since the composer's death.
With the composition of Adios Nonino in 1959, Piazzolla established a standard structural pattern for his compositions, involving a formal pattern of fast-slow-fast-slow-coda, with the fast sections emphasizing gritty tango rhythms and harsh, angular melodic figures, and the slower sections usually making use of the string instrument in the group and/or Piazzolla's own bandoneÃ³n as lyrical soloists. The piano tends to be used throughout as a percussive rhythmic backbone, while the electric guitar either joins in this role or spins filigree improvisations; the double bass parts are usually of little interest, but provide an indispensable rugged thickness to the sound of the ensemble. The quintet of bandoneÃ³n, violin, piano, electric guitar and double bass was Piazzolla's preferred setup on two extended occasions during his career, and most critics consider it to be the most successful instrumentation for his works. This is due partly to its great efficiency in terms of sound it covers or imitates most sections of a symphony orchestra, including the percussion, which is improvised by all players on the bodies of their instruments and the strong expressive identity it permits each individual musician. With a style that is both rugged and intricate, such a setup augments the compositions' inherent characteristics.
Despite the prevalence of the quintet formation and the ABABC compositional structure, Piazzolla consistently experimented with other musical forms and instrumental combinations. In 1965 an album was released containing collaborations between Piazzolla and Jorge Luis Borges where Borges's poetry was narrated over very avant-garde music by Piazzolla including the use of dodecaphonic (twelve-tone) rows, free non-melodic improvisation on all instruments, and modal harmonies and scales. In 1968 Piazzolla wrote and produced an "operita", MarÃa de Buenos Aires, that employed a larger ensemble including flute, percussion, multiple strings and three vocalists, and juxtaposed movements in Piazzolla's own style with several pastiche numbers ranging from waltz and hurdy-gurdy to a piano/narrator bar-room scena straight out of Casablanca.
By the 1970s Piazzolla was living in Rome, managed by the Italian agent Aldo Pagani, and exploring a leaner, more fluid musical style drawing on more jazz influence, and with simpler, more continuous forms. Pieces that exemplify this new direction include Libertango and most of the Suite Troileana, written in memory of the late AnÃbal Troilo. In the 1980s Piazzolla was wealthy enough, for the first time, to become relatively autonomous artistically, and wrote some of his most ambitious multi-movement works. These included Tango Suite for the virtuoso guitar duo Sergio and Odair Assad; Histoire du Tango, where a flutist and guitarist tell the history of tango in four chunks of music styled at thirty-year intervals; and La Camorra, a suite in three ten-minute movements, inspired by the Neapolitan crime family and exploring symphonic concepts of large-scale form, thematic development, contrasts of texture and massive accumulations of ensemble sound. After making three albums in New York with the second quintet and producer Kip Hanrahan, two of which he described on separate occasions as "the greatest thing I've done", he disbanded the quintet, formed a sextet with an extra bandoneÃ³n, cello, bass, electric guitar, and piano, and wrote music for this ensemble that was even more adventurous harmonically and structurally than any of his previous works (Preludio y Fuga; Sex-tet). Had he not suffered an incapacitating stroke on the way to Notre Dame mass in 1990, it is likely that he would have continued to use his popularity as a performer of his own works to experiment in relative safety with even more audacious musical techniques, while possibly responding to the surging popularity of non-Western musics by finding ways to incorporate new styles into his own. In his musical professionalism and open-minded attitude to existing styles he held the mindset of an 18th century composing performer such as Handel or Mozart, who were anxious to assimilate all national "flavors" of their day into their own compositions, and who always wrote with both first-hand performing experience and a sense of direct social relationship with their audiences. This may have resulted in a backlash amongst conservative tango aficionados in Argentina, but in the rest of the West it was the key to his extremely sympathetic reception among classical and jazz musicians, both seeing some of the best aspects of their musical practices reflected in his work.