Twelve-tone music illustrates many characteristics relative with those of conventional tonal form, though works are based on a different composition method. The fundamental question of twelve-tone music arises in debate on terminology between tonal and atonal as well as methodology of musical analysis. Certain theorists try to approach twelve-tone music by traditional harmonic views rather than by pitch-class set theory. Conventional harmonic aspects arise from the fact that both tonal and twelve-tone music share similar narrative strategies. This point is explored in examining Anton Webern's Quartet for Violin, Clarinet, Tenor-Saxophone and Piano, Op. 22, which displays connection to tonal music. The present study seeks to examine certain features of the composer's working in pitch materials; i.e., the dispositions of pitch classes and the characteristics of the matching dyads, and thereby to disclose the connection between twelve-tone methods and conventional harmony.