2 3 4 5 / 6 7 8 9 t e when repeated immediately results in the following succession of two aggregates, in the middle of which is a new and complete aggregate beginning with the second hexachord: 0 1 2 3 4 5 / 6 7 8 9 t e / 0 1 2 3 4 5 / 6 7 8 9 t e secondary set: [6 7 8 9 t e / 0 1 2 3 4 5] A "weighted aggregate" is an aggregate in which the twelfth pitch does not appear until at least one pitch has appeared at least twice, supplied by segments of different set forms. It seems to have been first used in Milton Babbitt's String Quartet No. 4. An aggregate may be vertically or horizontally weighted. An "all-partition array" is created by combining a collection of hexachordally combinatorial arrays. Nonstandard tone rows Schoenberg specified many strict rules and desirable guidelines for the construction of tone rows such as number of notes and intervals to avoid. Tone rows that depart from these guidelines include the above tone row from Berg's Violin Concerto which contains triads and tonal emphasis, and the tone row below from Luciano Berio's Nones which contains a repeated note making it a 'thirteen-tone row': Igor Stravinsky used a five-tone row, chromatically filling out the space of a major third centered tonally on C (C–E), in one of his early serial compositions, In memoriam Dylan Thomas. In his twelve-tone practice, Stravinsky preferred the inverse-retrograde (IR) to the retrograde-inverse (RI), as for example in his Requiem Canticles: Ben Johnston uses a "just tone row" (see just intonation) in works including String Quartets Nos. 6 and 7. Each permutation contains a just chromatic scale, however, transformations (transposition and inversion) produce pitches outside of the primary row form, as already occurs in the inversion of P0. The pitches of each hexachord are drawn from different otonality or utonality on A+ utonality, C otonality and utonality, and E- otonality, outlining a diminished triad. See also Musical set theory Unified field Side-slipping Pitch interval List of tone rows and series References Sources Further reading External links Database on tone rows and tropes, Harald Fripertinger, Peter Lackner Twelve-tone technique Musical symmetry