Octave invariance

Graham Breed writes:

>If you allow for the octave equivalence of intervals, all triadic
>inversions contain the same intervals.

How so? The way I larnt it, a simple C major triad in root position consists
of a minor third stacked on top of a major third. In first inversion, it
consists of a perfect fourth stacked on top of the minor third. In second
inversion it's that perfect fourth with the major third stacked above it.
From what perspective are those the same set of intervals?

> ... However, if you disallow octave
>equivalence of intervals, and you define harmony in terms of intervals,
>you must also reject the octave equivalence of harmony. Inversional
>invariance follows from octave invariance, unless you have a
>privileged root to lift the otonal/utonal degeneracy.

I don't quite follow all that, especially the "privileged root" part, with
which concept I am unfamiliar. Could you give an example?

> ... none of this
>implies that octave transpositions are harmonically negligible. Many
>people state this, and I believe it to be a result of sloppy thinking.

To my great surprise, I am increasingly inclined to agree with you on that.
After all, orchestrators and arrangers have known the importance of
appropriate "voicing," or spacing of intervals across octaves, for about as
long as there has been 4-part harmony.

David J. Finnamore

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