inversional relationships and symmetry


“I am also curious to learn how certain twelve-tone operations might be heard within a tonal context, and vise-versa. I may never be able to hear the diatonic collection exclusive of its tonal functionality. For example, I know the inversional relationship between {C, E, G} and {A, C, E}. However, I question whether I actually perceive that relationship. I hear these two trichords tonally, as major and minor triads (perhaps even as relatives of one another). This may outweigh my capacity to hear them as inversionally related. Should I look beyond my own limitations? Can I not use both interpretations simultaneously, so that multiple levels of listening and elucidation are possible? In such an imagined composition, I seek to manipulate the idea of a major/relative minor relationship on the surface, while on a deeper structural level move from T0 to T4I, or create two
large formal divisions that are related by T4I (Ic/e). This deeper level may not involve trichords at all, but may serve to establish a transformational relationship, which might exist on various levels, to varying degrees.”

So I like the major/minor inversional relationship found in tonal music. I find it gives my ear some relief. But what do I do when I have a harmonic collection that is symmetrical? Where is the relief?  When {CEG} becomes {ACE}, my ear hears the Major third “get smaller.” The effect is one of greater tension, and it “feels good,” musically speaking. But in my dance piece, I have a symmetrical collection, {BbDFACE}.  It’s inversion {BD#F#A#C#A#} is the SAME! Where is my relief? This does not feel so good. In thinking back to tonal music, I try and imagine the major triad extending to a seventh chord: {CEGB}.  Now, this collection is symmetrical, it’s inversion does not yield a minor 7th at all. So, for now, I am taking that as a cue. My original collection contains six pitch classes, only one of them is invisible (in the4 same way that a triad might suggest a 7th chord with a missing element, the 7th).  Now, {BbDFAC_} no longer appears to be symmetrical. Here, T7I gives me {FDbBbGbEb_}, and THIS, seems to give me some relief. I know the analogy is somewhat artificial, but I can not afford to spend too much time thinking about this, or I will not write a note. I want to write, not think!

Thoughts? Ideas? Help me!


6 thoughts on “inversional relationships and symmetry

  1. whoa, I was just asking myself many of those same questions! Where is my relief indeed!? I’d rather not think either…let me know when you get some real answers to these perplexing problems! xo

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