Some interesting ideas were said in the recent discussions " 2d
inversion triads". Specifically Danny Shorr wrote:
"Schoenberg and Hindemith both characterized what LJS is saying here
as the
struggle for dominance between the lowest tone (and thus, it's
overtone
series) and the triad arrived at through spelling."
Let us consider stability of inversion chords. At first it is
necessary to determine what is stability in this case. As musicians
suppose that bass of the inversion chord must determine its
fundamental bass, then stability is its ability to perform this task
surely.
For first inversion the harmonic row E3,C4,G4 corresponds C1 as first
harmonic and its force in "struggle" with E3 for determination of
signal's period would be weak. By the way overtones of E3 may be
strong and im****tant. By such consideration E3 as fundamental bass
has OTS series 1:2:3:4 and triad E3,C4,G4 corresponds series 5:8:12
of its fundamental bass. Thus we can consider E3 es fundamental and
estimate the first inversion as relative stable.
For second inversion the harmonic row G3,C4,E4 corresponds C2 as
first harmonic, has harmonic series 3:4:5 and it harms estimation of
triad's bass G3 as fundamental essential more then in the case of
first inversion. Therefore bass note in 2d inversion chords must
usually be doubled and this inversion is used if it is possible from
composer's viewpoint.
Yuri Vilenkin
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