# The Vertical and The Horizontal



## millionrainbows (Jun 23, 2012)

In tonality, the vertical dimension is derived from consonance/dissonance of intervals in relation to "1" or tonic. These are expressed as "fractions" of that "1", falling within the octave (1:1). This is "ranked" by degree of increasing dissonance: 1:1, 2:3, 3:4, 4:5, 5:6, etc. These vertical intervals are then "projected" into the horizontal dimension as "functions:" I, ii, iii, IV, V, vi, vii.


In 12-tone rows, the order of the notes is already projecting the horizontal dimension; order equals time. So in serial rows, the vertical dimension "doesn't really exist" as a built-in concrete structural function, so any vertical relations must occur contrapuntally, as the result of simultaneously-sounding lines. So the 12-tone method took music back to a contrapuntal, "pre-function/pre-harmony" state.


The "harmony" which results from these intersections is wholly dependent on the row-order itself, structurally speaking.


This has always been the challenge in serial composition; this is why Milton Babbitt and George Perle showed such interest in "all-interval rows" which exhibited certain consistencies within the row itself, and when transposed, and when combined with certain other forms of the row. This was all in an attempt to control and define the vertical dimension.


Once again, serial music is not inherently, or structurally, tonal, or harmonically-based. 


Since our ears hear everything harmonically, serial music has harmonic effects, as all music does which uses sustained pitches. This harmonic dimension is not inherently part of its structural function, though. It occurs as a consequence of other factors.


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