On 2/2/19, Dan Eble <d...@faithful.be> wrote:
> Isn’t the salient property of an inversion simply which note is lowest in
> pitch?  (It has been a long time since I studied music theory.)  If so, both
> of those fit, as does the chord resulting from lowering the e' by an octave.

David was more specifically referring to the 5th inversion of an 11th
chord, and I *think* I’m starting to get his point:

even if
<e' g' b' c'' d'' f''>
is acceptable, then you get to
<g' b' c'' d'' e'' f''>
and
<b' c'' d'' e'' f'' g''>
and this is where things start to get weird:
<c'' e'' e'' f'' g'' b''>
If the algorithm continues blindly by only taking into account the
previous state rather than the initial state, you then find yourself
with a so-called inversion where the bass note is actually the root
note again, i.e. not an inversion, and you’ll never get to a point
where either d'' or f'' can become the bass note.

Instead we should be aiming for something aikin to
<d'' e'' f'' g'' b'' c'''>
which means that the c'' has to be moved again. (IIUC, again.)

> Speaking as a software designer, if you have implemented a useful function
> that is more limited than the conventional musical concept of inversion,
> consider giving it a different name

Sure, but that’s not the point at all. We certainly do want proper
inversions here.

Thanks for the input, that was helpful! And I think I get David’s
point after all…

Cheers,
V.

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