Enders, Bernd / Stange-Elbe, Joachim (Hrsg.): Global Village - Global Brain - Global Music

Sequence 2 (Schubert)

Figure 3:

Sequence from Schuberts D-Minor String Quartet, D. 810, 4th movt. mm. 16–25 as simplified by Harrison ([4], p. 33)

Again we consider four Denotators of the Form PiMod₁₂Set denoting the 3rd and the 2nd chord of this sequence (a Major tonic triad t and a Minor¹⁴

14: According to the entire logic of this sequence we dogmatically assume the note A_b in the 2nd chord instead of A, see also [4] Footnote 21.

Subdominant s with respect to C-Tonality), as well as the union of 3rd and 4th chord (the “flattening” set b) and the union of the 2nd and 3rd chord (the plagal cadence set A)

“T” : P iM od12Set({0,4,7}) “s” : P iM od12Set({5,8}) “b” : P iM od12Set({0,3,4,7}) “P” : P iM od12Set({5,8,0,4,7})

PICT

The duality of these two sequences is expressed trough two facts:

The sequences are isomorphic as local as well as global compositions if suitably extended to the sides or glued to a circle of 24 overlapping maps (12 copys of # and 12 copys of A). Note that they are retrogrades of one another.
The pairings of # and b as well as A and P are dual: $“#/b ” : P iM od DualSets({0,3,4,7},{7,4,3,0}) “A/P ” : PiM o1d2DualSets({7,2,11,0,3},{0,5,8,7,4}) 12$