Tone Clock · Aggregate Builder

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A 12-note field: each pitch-class used once.

Group colours

Single-hour aggregate

A/S: hour A steered by S. Reverse exchanges the two roles.

Hour (A)

Steering (S)

Path starts on

Steering form

Dual aggregate (2+2)

Dual tonality: two triads of hour A and two of hour B.

Hour A

Hour B

Tetrad aggregate

Three tetrads on a three-note path. A same-form tetrad fills the aggregate by transposition only when it tiles at period 4 (path XII), or when it is V⁴ (path VI). If it does not tile by transposition, inversion will not complete a same-form field — use a mixed 2+1 field instead.

Tetrad hour

Tetrad form

Steering

Path starts on

Steering form

Second hour (2+1)

Mixed-hour aggregate

3+1: three triads of A and one of B. 2+1+1: two of A and one each of B and C — a three-hour partition used in these tools. Choose A, then a viable partner.

Split

Hour A (majority)

Hour B

Hour C

All working combinations

Select a combination to load it above.

Dual pairs

Rows and columns are hours. A filled cell is a dual pair; the label is the column hour. A dash is the same hour; a dot has no pair.

About this tool

Build a complete 12-note field. Colours show which group each note belongs to.

A/S — hour A steered by S (S as tetrad). Eleven triad hours can form a 12-note tone-clock steering. X as a triad cannot: its residues mod 3 collide. X⁴ (diminished seventh) does tile, and is the classical T-path for I, IV, VI, IX, XII.
T vs TI — T means the field is built by transposition only. TI means inversion is required. A T-hour on a non-X path is still a TI field. Each result is labelled for the pair, not only the hour.
Reverse — swap A and S. A T pair has a full reverse field. A TI pair reverse-steers only part-way; the leftover centre is an anchor form (use Complement in the subset explorer).
Cluster-scale T-fields — three extra T-tiles that are not “hour / X⁴”: V⁴ (Bartók cell Z) by VI, III⁶ (hexatonic) by 2, and Mode 5 / IV-gemini by 3.
Dual 2+2 — two triads of each of two hours.
Mixed hours — 3+1 and 2+1+1 fields (three hours sharing the aggregate). Not part of Schat’s original steerings or McLeod’s dual pairs; added here as a working partition.
Tetrad — three STs of one hour on a 3-note path. Only I⁴, II^M⁴, V⁴, VII^m⁴, IX⁴ and X⁴ T-tile. Default path is XII (period 4). V⁴ also tiles by VI (Cell Z). X⁴ tiles by I, IV, VI, IX, XII. The other hours cannot form a same-form tetrad field — use a 2+1 mix instead.
Symmetrical hours (I, VI, X, XII): one form; m and M are the same. IX is 2+5 / 5+2.