Editing John Cage (section)

===Early works, rhythmic structure, and new approaches to harmony===
Cage's first completed pieces have been lost. According to the composer, the earliest works were very short pieces for piano, composed using complex mathematical procedures and lacking in "sensual appeal and expressive power."{{sfn|Pritchett|1993|loc=6}} Cage then started producing pieces by improvising and writing down the results, until Richard Buhlig stressed to him the importance of structure. Most works from the early 1930s, such as ''[[Sonata for Clarinet (Cage)|Sonata for Clarinet]]'' (1933) and ''Composition for 3 Voices'' (1934), are highly [[Chromaticism|chromatic]] and betray Cage's interest in [[counterpoint]]. Around the same time, the composer also developed a type of a tone row technique with 25-note rows.{{sfn|Pritchett|1993|loc=7}} After studies with Schoenberg, who never taught [[dodecaphony]] to his students, Cage developed another tone row technique, in which the row was split into short motives, which would then be repeated and transposed according to a set of rules. This approach was first used in ''Two Pieces for Piano'' ({{circa|1935}}), and then, with modifications, in larger works such as ''Metamorphosis'' and ''Five Songs'' (both 1938).

[[File:Sonatas-interludes-sonata3graph.gif|upright=1.35|thumb|right|Rhythmic proportions in ''Sonata III'' of ''Sonatas and Interludes'' for prepared piano]]
Soon after Cage started writing percussion music and music for modern dance, he started using a technique that placed the rhythmic structure of the piece into the foreground. In ''[[Imaginary Landscape No. 1]]'' (1939) there are four large sections of 16, 17, 18, and 19 bars, and each section is divided into four subsections, the first three of which were all 5 bars long. ''[[Construction (Cage)|First Construction (in Metal)]]'' (1939) expands on the concept: there are five sections of 4, 3, 2, 3, and 4 units respectively. Each unit contains 16 bars, and is divided the same way: 4 bars, 3 bars, 2 bars, etc. Finally, the musical content of the piece is based on sixteen motives.{{sfn|Nicholls|2002|loc=71–74}} Such "nested proportions", as Cage called them, became a regular feature of his music throughout the 1940s. The technique was elevated to great complexity in later pieces such as ''Sonatas and Interludes'' for prepared piano (1946–48), in which many proportions used non-integer numbers (1¼, ¾, 1¼, ¾, 1½, and 1½ for ''Sonata I'', for example),{{sfn|Pritchett|1993|loc=29–33}} or ''[[A Flower]]'', a song for voice and closed piano, in which two sets of proportions are used simultaneously.<ref>Notes in the score: ''A Flower''. [[Edition Peters]] 6711 (1960)</ref>

In late 1940s, Cage started developing further methods of breaking away with traditional harmony. For instance, in ''String Quartet in Four Parts'' (1950) Cage first composed a number of ''gamuts'': chords with fixed instrumentation. The piece progresses from one ''gamut'' to another. In each instance the ''gamut'' was selected only based on whether it contains the note necessary for the melody, and so the rest of the notes do not form any directional harmony.<ref name="Pritchett, Grove"/> ''Concerto for prepared piano'' (1950–51) used a system of charts of durations, dynamics, melodies, etc., from which Cage would choose using simple geometric patterns.<ref name="Pritchett, Grove"/> The last movement of the concerto was a step towards using chance procedures, which Cage adopted soon afterwards.<ref>{{cite journal|last=Pritchett|first=James|date=Fall 1988|title=From Choice to Chance: John Cage's Concerto for Prepared Piano|journal=[[Perspectives of New Music]]|volume=26|number=1|pages=50–81|doi=10.2307/833316 |jstor=833316 }}</ref>