Tone Clock

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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

Peter Schat's 'Zodiac of the Hours', which graphically represents the tone-clock steerings of the twelve hours. Note that X can only be steered as a diminished seventh tetrachord (hence, the only non-triangular shape). Each point of a shape represents a pitch-class on the chromatic circle, and each shape represents one transposition or inversion of an hour. Zodiac of the Hours.svg
Peter Schat's 'Zodiac of the Hours', which graphically represents the tone-clock steerings of the twelve hours. Note that X can only be steered as a diminished seventh tetrachord (hence, the only non-triangular shape). Each point of a shape represents a pitch-class on the chromatic circle, and each shape represents one transposition or inversion of an hour.

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. [1] 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'. [2] 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'. [3] [4]

Related Research Articles

In music theory, a diatonic scale is a heptatonic scale that includes five whole steps and two half steps (semitones) in each octave, in which the two half steps are separated from each other by either two or three whole steps, depending on their position in the scale. This pattern ensures that, in a diatonic scale spanning more than one octave, all the half steps are maximally separated from each other.

In music, a tone row or note row, also series or set, is a non-repetitive ordering of a set of pitch-classes, typically of the twelve notes in musical set theory of the chromatic scale, though both larger and smaller sets are sometimes found.

In music theory, a tetrachord is a series of four notes separated by three intervals. In traditional music theory, a tetrachord always spanned the interval of a perfect fourth, a 4:3 frequency proportion —but in modern use it means any four-note segment of a scale or tone row, not necessarily related to a particular tuning system.

Enharmonic (in modern musical notation and tuning) note, interval, or key signature that is equivalent to some other note, interval, or key signature but "spelled", or named differently

In modern musical notation and tuning, an enharmonic equivalent is a note, interval, or key signature that is equivalent to some other note, interval, or key signature but "spelled", or named differently. Thus, the enharmonic spelling of a written note, interval, or chord is an alternative way to write that note, interval, or chord. For example, in twelve-tone equal temperament, the notes C and D are enharmonic notes. Namely, they are the same key on a keyboard, and thus they are identical in pitch, although they have different names and different roles in harmony and chord progressions. Arbitrary amounts of accidentals can produce further enharmonic equivalents, such as B, although these are much rarer and have less practical use.

This is an alphabetical index of articles related to music.

Twelve-tone technique musical composition method using all 12 chromatic scale notes equally often & not in a key

The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and twelve-note composition—is a method of musical composition first devised by Austrian composer Josef Matthias Hauer, who published his "law of the twelve tones" in 1919. In 1923, Arnold Schoenberg (1874–1951) developed his own, better-known version of 12-tone technique, which became associated with the "Second Viennese School" composers, who were the primary users of the technique in the first decades of its existence. The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded as often as one another in a piece of music while preventing the emphasis of any one note through the use of tone rows, orderings of the 12 pitch classes. All 12 notes are thus given more or less equal importance, and the music avoids being in a key. Over time, the technique increased greatly in popularity and eventually became widely influential on 20th-century composers. Many important composers who had originally not subscribed to or even actively opposed the technique, such as Aaron Copland and Igor Stravinsky, eventually adopted it in their music.

Pitch class

In music, a pitch class (p.c. or pc) is a set of all pitches that are a whole number of octaves apart, e.g., the pitch class C consists of the Cs in all octaves. "The pitch class C stands for all possible Cs, in whatever octave position." Important to musical set theory, a pitch class is, "all pitches related to each other by octave, enharmonic equivalence, or both." Thus, using scientific pitch notation, the pitch class "C" is the set

Set theory (music) branch of music theory that categorizes musical objects and describes their relationships by using sets and permutations of pitches and pitch classes, rhythmic onsets, beat classes, etc.

Musical set theory provides concepts for categorizing musical objects and describing their relationships. Howard Hanson first elaborated many of the concepts for analyzing tonal music. Other theorists, such as Allen Forte, further developed the theory for analyzing atonal music, drawing on the twelve-tone theory of Milton Babbitt. The concepts of musical set theory are very general and can be applied to tonal and atonal styles in any equal temperament tuning system, and to some extent more generally than that.

In music theory, a trichord is a group of three different pitch classes found within a larger group. A trichord is a contiguous three-note set from a musical scale or a twelve-tone row.

In music using the twelve tone technique, combinatoriality is a quality shared by twelve-tone tone rows whereby each section of a row and a proportionate number of its transformations combine to form aggregates. Much as the pitches of an aggregate created by a tone row do not need to occur simultaneously, the pitches of a combinatorially created aggregate need not occur simultaneously. Arnold Schoenberg, creator of the twelve-tone technique, often combined P-0/I-5 to create "two aggregates, between the first hexachords of each, and the second hexachords of each, respectively."

Chromaticism is a compositional technique interspersing the primary diatonic pitches and chords with other pitches of the chromatic scale. Chromaticism is in contrast or addition to tonality or diatonicism and modality. Chromatic elements are considered, "elaborations of or substitutions for diatonic scale members".

Not only at the beginning of a composition but also in the midst of it, each scale-step [degree] manifests an irresistible urge to attain the value of the tonic for itself as that of the strongest scale-step. If the composer yields to this urge of the scale-step within the diatonic system of which this scale-step forms part, I call this process tonicalization and the phenomenon itself chromatic.

Chromaticism is almost by definition an alteration of, an interpolation in or deviation from this basic diatonic organization.

Throughout the nineteenth century, composers felt free to alter any or all chord members of a given tertian structure [chord built from thirds] according to their compositional needs and dictates. Pronounced or continuous chordal alteration [and 'extension'] resulted in chromaticism. Chromaticism, together with frequent modulations and an abundance of non-harmonicism [non-chord tones], initially effected an expansion of the tertian system; the overuse of the procedures late in the century forewarned the decline and near collapse [atonality] of the system [tonality].

Chromaticism is the name given to the use of tones outside the major or minor scales. Chromatic tones began to appear in music long before the common-practice period, and by the beginning of that period were an important part of its melodic and harmonic resources. Chromatic tones arise in music partly from inflection [alteration] of scale degrees in the major and minor modes, party from secondary dominant harmony, from a special vocabulary of altered chords, and from certain nonharmonic tones.... Notes outside the scale do not necessarily affect the tonality....tonality is established by the progression of roots and the tonal functions of the chords, even though the details of the music may contain all the tones of the chromatic scale.

Sometimes...a melody based on a regular diatonic scale is laced with many accidentals, and although all 12 tones of the chromatic scale may appear, the tonal characteristics of the diatonic scale are maintained. ... Chromaticism [is t]he introduction of some pitches of the chromatic scale into music that is basically diatonic in orientation, or music that is based on the chromatic scale instead of the diatonic scales.

Complement (music)

In music theory, complement refers to either traditional interval complementation, or the aggregate complementation of twelve-tone and serialism.

Genus is a term used in the Ancient Greek and Roman theory of music to describe certain classes of intonations of the two movable notes within a tetrachord. The tetrachordal system was inherited by the Latin medieval theory of scales and by the modal theory of Byzantine music; it may have been one source of the later theory of the jins of Arabic music. In addition, Aristoxenus calls some patterns of rhythm "genera".

Multiplication (music)

The mathematical operations of multiplication have several applications to music. Other than its application to the frequency ratios of intervals, it has been used in other ways for twelve-tone technique, and musical set theory. Additionally ring modulation is an electrical audio process involving multiplication that has been used for musical effect.

Set (music) collection of objects in music theory lily&jazz

A set in music theory, as in mathematics and general parlance, is a collection of objects. In musical contexts the term is traditionally applied most often to collections of pitches or pitch-classes, but theorists have extended its use to other types of musical entities, so that one may speak of sets of durations or timbres, for example.

Jennifer Helen McLeod, is a composer and former Professor of Music at Victoria University of Wellington, New Zealand.

An all-interval tetrachord is a tetrachord, a collection of four pitch classes, containing all six interval classes. There are only two possible all-interval tetrachords, when expressed in prime form. In set theory notation, these are [0,1,4,6] (4-Z15) and [0,1,3,7] (4-Z29). Their inversions are [0,2,5,6] (4-Z15b) and [0,4,6,7] (4-Z29b). The interval vector for all all-interval tetrachords is [1,1,1,1,1,1].

Diatonic and chromatic

Diatonic and chromatic are terms in music theory that are most often used to characterize scales, and are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair, especially when applied to contrasting features of the common practice music of the period 1600–1900.

All-trichord hexachord

In music, the all-trichord hexachord is a unique hexachord that contains all twelve trichords, or from which all twelve possible trichords may be derived. The prime form of this set class is {012478} and its Forte number is 6-Z17. Its complement is 6-Z43 and they share the interval vector of <3,2,2,3,3,2>.


  1. Schat, Peter (1993). Tone Clock (Contemporary Music Studies, vol. 7). Routledge.
  2. McLeod, Jenny (1994). "Chromatic Maps I & II".
  3. Norris, Michael (2006). "Tessellations and Enumerations: generalizing chromatic theories". CANZONA: The Yearbook of the Composers Association of New Zealand: 92–100.
  4. Norris, Michael (2006). "Crystalline Aphorisms: commentary and analysis of Jenny McLeod's Tone Clock Pieces I–VII". Canzona: The Yearbook of the Composers Association of New Zealand: 74–86.