CHANCE – used by Cage to free composition from the expression of his own taste.  Cage developed a number of techniques which used chance operations to replace the composer's CHOICE as a means of determining the continuity and detail of a piece, thus fundamentally re-defining the role of the composer.  He came to express it thus:  “I decided that rather than making choices, I would ask questions.”  This approach frees sounds to express their own nature rather than the desire or will of the composer. The DUCHAMP TRAIN used in Two⁶ is one way of putting chance operations to use in the selection of pitches; simpler forms of chance were used to make selections from the GAMUT of natural harmonics used in One^lO. The MESOSTIC technique behind Eight Whiskus and the IMITATIONS found in the MATERIAL of Two⁶ use chance to transform pre-existing material.  Chance can be incorporated into the compositional process, left to the PERFORMER‘s discretion, or even incorporated into the material itself.  There is a certain amount of indeterminacy built into any sustained note on the violin; the harmonics which make up One^lO are especially susceptible to unpredictable fluctuations of tone. SILENCE, in a Cage work, is always populated by the chance occurrence of unintended sounds.

CHOICE – in conventional composition (such as Cage's early Nocturne), the composer's task is primarily one of making choices – choosing the right pitch, the right harmony, the right rhythm. In Six Melodies, Cage was still making choices, although after the initial decisions of rhythmic STRUCTURE and pitch GAMUT were made, the composer's options were considerably more restricted.  In later works, the act of composition becomes one of creating macro-structures which accept MATERIAL determined largely by CHANCE (through techniques such as IMITATION or the DUCHAMP TRAIN) or by choices made by the PERFORMER, as in the late NUMBER pieces.

DUCHAMP TRAIN – from the Erratum Musical (1913) of Marcel Duchamp, in which names of notes are written onto balls poured into a funnel.  The funnel empties out into the freight cars of a moving toy railroad train, where each car represents one measure of time.  For the composition of Two⁶, Cage adapted this process to his own ends: computerized CHANCE operations mimic the action of the funnel and train, and rather than measures of time, the train cars are taken as encompassing a range of pitches (seven chromatically adjacent notes in the violin, eleven in the piano).  From each car Cage's chance operations select a given number of pitches (one each for the violin and from zero to five for the piano). The result in each case is a total GAMUT of pitches which is given on separate unbound pages in the score.  From these pitch collections the PERFORMERS make selections which are then used to express the several TIME BRACKETS – by the violin as sustained double-stops, by the piano as slowly ASCENDING figures. In Duchamp’s original instructions, the artist specifies that the resulting music be performed on an instrument “where the virtuoso intermediary has been suppressed.” Cage's playing instructions for Two⁶ reflect this by requiring the pianist to play “pppp as softly as possible, giving no sense of periodicity (depress key silently until you feel the escapement clearing; knowing where that is, play the piano on the edge of audibility)”, and the violinist to play “pppp as softly as possible (nearly inaudible) using from the gamut of pitches given any two, using harmonics or not, but sustained with imperceptible bowing.”

GAMUT – the total fixed collection of single notes, intervals, chords and aggregates which constitute the MATERIAL of a composition. Selection from the elements of the gamut to create melodies, harmonies, or passagework can be made by the composer or the performer. Six Melodies is a “re-cycling” of fragments left over from the composer’s String Quartet in Four Parts, which employs a fairly extensive gamut (distributed here between the piano and violin).  In Two⁶, Cage offers a stack of eight pitches to the violinist, inviting the player to select and sustain any two to occupy any of several TIME BRACKETS, and offers long ASCENDING sequences of pitches for the pianist to excerpt.  The smaller, MODAL gamut of Eight Whiskus insures the music's folk song-like character.  The gamut for One^lO consists of all possible natural harmonics on the violin, giving the piece both a modal and a MICROTONAL flavor.

IMITATION – Cage developed several different techniques for deriving new MATERIAL from old.  When dealing with the written word, Cage would use MESOSTICS to fragment and re-combine phrases from earlier writing (his or others’) into new texts.  In the Extended Lullaby, which is used as part of the material for Two⁶, Cage retains the rhythm of Satie's piano piece Vexations but applies CHANCE operations to the pitches to create a new melody.  When arranging the Eight Whiskus for violin at Malcolm Goldstein's request, the composer added indications for the placement, speed, and pressure of the bow to each note in imitation (but not literal correspondence) of the syllables of the original vocal line.

MATERIAL – In Two⁶ the players share the material of SILENCE, which may be used to fill any of the given TIME BRACKETS.  In addition, each player is given material unique to his or her instrument. Some of this is derived from the DUCHAMP TRAIN (the piano’s slowly ASCENDING passages, the violin’s sustained double stops).  Inverting this relationship, the violin's MICROTONAL phrases ascend gradually from string to string over the course of the piece, while the correspondingly melodic material for the piano – IMITATIONS of Satie – remains in a fixed register.  In One^lO and Six Melodies the homogeneous material is derived from a single GAMUT for each piece.  The even simpler gamut of pitches for Eight Whiskus is varied through changes of bow speed and pressure.  In the more freely-written Nocturne, Cage frequently uses the same material for both violin and piano, unifying the sound of the two instruments.

MESOSTIC – a technique used by Cage for writing texts.  A new text is developed around the letters of a “key” text (a person's name, the subject of the text, or an opening phrase, such as, in the original vocal version of Eight Whiskus, “whistlin is did”), the letters of which are placed down a middle row and preceded and followed by either newly written text or (as in the Whiskus) fragments of the original source text which contain the key letter.  The syllables containing the key letter in Eight Whiskus are always set as an A natural.  (In the violin version, the whole melodic line has been transposed so that the key is expressed by an F natural.)  The other notes of the little melodies develop a limited GAMUT of MODALLY related pitches.

MICROTONAL – the violin’s microtonal slides which appear in Nocturne are early examples of Cage's interest in the pitches lying outside of the twelve-tone scale.  In Two⁶, the MATERIAL for the violinist includes passages written in a scale which divides the octave into eighty-four pitches, to be played on successively ASCENDING strings. One^lO, by using nothing but natural overtones of the violin’s open strings, deviates from the equal-tempered scale.

MODAL – the restricted GAMUT of Eight Whiskus, composed originally for voice and using a MESOSTIC technique to center the line around a single pitch, recalls a type of scale used in folk music which, while harmonically simple, avoids expressive chromaticism and the directional pull of tonality, both foreign to Cage's mature vocabulary.  Many of Cage's earlier compositions (such as Six Melodies) also have a somewhat modal feel due to the careful selection of pitches to be used in the gamut.  The modal flavor of One^lO comes from the exclusive use of natural harmonics of the violin's four strings, tuned traditionally in fifths.  The even earlier Nocturne, however, still lives in the harmonically more complex world of impressionistic chromaticism.

NUMBER – many of Cage’s late pieces are often referred to as the “number” pieces, stemming from their TITLES (Two⁶ is the sixth of the number pieces to employ two players).  “Do you need some numbers? I have lots of numbers,” Cage once asked this writer.  “John Cage loved numbers,” says Mark Swed in Cage and Counting – The Number Pieces.  The use of numbers was a crucial element in Cage’s CHANCE-based compositional techniques, dividing the ranges of the violin and the piano into equal segments, determining the size of TIME BRACKETS, and distributing equally the likelihood that any given element from a pre-determined GAMUT would occur.

PERFORMER – the role of the performer became ever more consequential over Cage's career.  While the early pieces call for the performer to fulfill the traditional role of expressive interpreter, in many of the later works he or she must exercise substantial CHOICES which affect the music STRUCTURALLY, determining for example the placement and duration of notes (or entire passages) within the given TIME BRACKETS.

SILENCE – the unwilled sounds of the environment, unmasked by composer's intention or performer's activity, are at the heart of each of Cage's compositions since even before the famous “silent” composition 4'33" of 1952.  Used expressively in Nocturne and rhythmically (if sparingly) in Six Melodies, silence becomes the ever-present backdrop to the isolated pitches of One^lO and phrases of Eight Whiskus, and is incorporated into the MATERIAL of Two⁶ from which the PERFORMER fills the TIME BRACKETS.

STRUCTURE – the division of the whole into parts.  The structure of Cage's early Nocturne is intuitive and improvisatory, guided by the composer's moment-to-moment CHOICES.  Soon afterwards Cage was to begin using a technique of rhythmic structure which allowed him to place MATERIAL selected from a GAMUT of sounds into a pre-formulated framework in which the proportions of the small parts which together make up each large part are reflected in the proportions of the large parts which make up the whole.  The Eight Whiskus each consist of several short phrases which pivot around a single pitch expressing the MESOSTIC key of the original vocal version. In the late NUMBER pieces, the structural parts are varied and flexible in length due to the use of TIME BRACKETS.

TIME BRACKETS – flexible time brackets surround each event in most of Cage’s NUMBER pieces, giving a range of possible beginning times, ending times, and (therefore) durations. In One^lO, time brackets surround single pitches taken from the GAMUT of all possible natural harmonics on the violin’s open strings.  In Two⁶ empty time brackets are used by the players to situate entire blocks of material, including SILENCE for both players, MICROTONAL passages for the violin (which ASCEND over the course of the piece), IMITATIONS of Erik Satie's Vexations for the piano, and GAMUTS of pitches derived from the DUCHAMP TRAIN (ascending in the case of the piano, but expressed statically as a sustained double stop in the violin).  Which material appears in which time bracket is determined by the CHOICE of the PERFORMER.

TITLE – many of Cage's titles are self-explanatory (such as Nocturne), or involve NUMBERS.  Others elide two words, such as Mureau (music/Thoreau) and Whiskus (whistlin/hauku – linking the first word of the source text (from which the MESOSTIC is derived) with the haiku-like series of short poems which resulted).  The Six Melodies are indeed melodies, six single lines split between the two instruments (although some single notes in those lines are made up of two or more pitches).