Tone Clock
The Tone Clock, and its related compositional theory Tone-Clock Theory, is a post-tonal music composition technique, developed by composers Peter Schat and Jenny McLeod. Music written using tone-clock theory features a high economy of musical intervals within a generally chromatic musical language. This is because tone-clock theory encourages the composer to generate all their harmonic and melodic material from a limited number of intervallic configurations (called 'Intervallic Prime Forms', or IPFs, in tone-clock terminology). Tone-clock theory is also concerned with the way that the three-note pitch-class sets (trichords or 'triads ' in tone-clock terminology) can be shown to underlie larger sets, and considers these triads as a fundamental unit in the harmonic world of any piece. Because there are twelve possible triadic prime forms, Schat called them the 'hours', and imagined them arrayed in a clock face, with the smallest hour (012 or 1-1 in IPF notation) in the 1 o'clock position, and the largest hour (048 or 4-4 in IPF notation) in the 12 o'clock position. A notable feature of Tone-Clock Theory is 'tone-clock steering': transposing and/or inverting hours so that each note of the  chromatic aggregate is generated once and once only. Relationship to pitch-class set theory and serialism. While Tone-Clock Theory displays many similarities to Allen Forte's pitch-class set theory, it places greater emphasis on the creation of pitch 'fields' from multiple transpositions and inversions of a single set-class, while also aiming to complete all twelve pitch-classes (the 'chromatic aggregate') with minimal, if any, repetition of pitch-classes. While the emphasis of Tone-Clock Theory is on creating the chromatic aggregate, it is not a serial technique, as the ordering of pitch-classes is not important. Having  said that, it bears a certain similarity to the technique of 'serial derivation', which was used by Anton Webern and Milton Babbitt amongst others, in which a row is constructed from only one or two set-classes. It also bears a similarity to Josef Hauer's system of 'tropes', albeit generalised to sets of any cardinality. Peter Schat. The term 'tone clock' ("toonklok" in Dutch) was originally coined by Dutch composer Peter Schat, in reference to a technique he had developed of creating twelve-note pitch 'fields' by transposing and inverting a trichord so that all twelve pitch-classes would  be created once and once only. Schat discovered that it was possible to achieve a trichordally partitioned aggregate from all twelve trichords, with the exception of the diminished triad (036 or 3-10 in Forte's pitch-class set theory). Schat called the 12 trichords the 'hours', and they became central to the harmonic organization in a number of his works. He created a 'zodiac' of the hours, which shows in graphical form the symmetrical patterns created by the tone-clock steerings of the hours. (Note that Hour X is substituted with its tetrachord, the diminished seventh, which can be  tone-clock steered). Jenny McLeod and Tone-Clock Theory. In her as-yet-unpublished monograph 'Chromatic Maps', New Zealand composer Jenny McLeod extended and expanded Schat's focus on trichords to encompass all 223 set-classes, thus becoming a true 'Tone-Clock Theory'. She also introduced new terminology in order to 'simplify' the labelling and categorization of the set-classes, and to draw attention to the specific transpositional properties within a field. The most succinct musical expression of the theory is in her "24 Tone Clock Pieces", written between 1988–2011. Each of these piano works explores different aspects of tone -clock theory. McLeod's terminology. The following terms are explained in McLeod's "Chromatic Maps I": Mathematical generalizations of 'tessellating' set-classes. New Zealand composer and music theorist Michael Norris has generalized the concept of 'tone-clock steering' into a theory of 'pitch-class tessellation', and has developed an algorithm that can provide tone-clock steerings in 24TET. He has also written about and analyzed Jenny McLeod's 'Tone Clock Pieces'.