The Usage of Pitch-class Set in Atonal Music

Developing new methods to direct music sounds differing from those remained from classic and romantic era in old systems has always been the main concern of the 20th century composers. Efforts to achieve a new sounding for expressing issues that descended in this century led to establishing new systems and using them in creating pieces by composers. Some of those methods have received more expanded anticipation by music composers and listeners. One of the methods that was first prevailed in the beginning of the 20th century and after the Second World War received attention again, has been establishing structures of sounds based on creating sound sets. By this system, the music composer experiences an extensive freedom in action to express his thoughts in form of a music piece. The present paper tries to study the structure rules of sets in a simple language. Efforts to establish a theoretic framework named sets structure has been an effort to analyze works that could not be possible by tonal or Cyril 12-note systems. Composition of those works started in the first half of the 20th century and generally, without being carefully studied, they were considered superficially and became classified under a general title; Atonal”. This type of works could be seen from the music composers of Second Vienna School to their contemporary composers such as Stravinsky or Ives. Scriabin. In continuation, efforts have been made to know the concept of sets and understanding the relationship among sets for opening a better path to understand those pieces.With respects to the subjects discussed in this paper, it is evident what an open hand music composers have in selecting sounds and directing them. Music composer knows how to work with this knowledge and form in music to fulfill what he considered. The re-approach of music composers to this system in post-second world war shows that the notes sets have high capacities for creating pieces. Extensive use of sets techniques could be seen in the works of great composers such as Briton, Shostakovich, schnittkeand lutoslawski. Preparing new sounds as one of the most important materials of composition is what this method provides for the music composer in a good way. of pitch-class sets, namely, 220. Each of these pitch class sets has been assigned a name consisting of the cardinal number of the set followed by hyphen followed by a number that gives the position of the set on a list of sets, the ordinal number. The set may also include the character Z, which indicates that the set so designated has a counterpart of a particular nature. For example 4-Z15, this name indicates that the set contains 4 elements that it is item 15 on the list of 4-elementpitch-class sets. The interval between two notated pitches is measured by counting the number of half steps that separate them. The distance from C to E is 4 half steps. Specifically, the interval between two any notated pitches as represented by pitch-class integers can be reduced to one of the interval classes represented by the integers 1-6.There is, however, one basic from associated with each pitch-class set type, and this basic form is called the prime form. It is also possible to define relations of similarity between pitch class sets of the same cardinal number based upon pitch class similarity and upon interval class similarity. The notion of pitch class is implicit in ordinary musical language whenever we speak of 12 notes of the chromatic scale. That is, it is assumed that only 12 different pitches comprise the basic stock of the chromatic system. More precisely, this means that the 12 notes can be represented in a single octave by assuming octave equivalence and that a particular for a pitch is not unique by assuming enharmonic equivalence.