like when using invertChords on a c:11 chord for the fifth inversion.
Oh. Then this becomes a whole other can of worms; what should be the
correct inversion of an 11th chord?
Should
<c' e' g' b' d'' f''>
become
<e' g' b' d'' f'' c'''> (as you seem to suggest)
or
<e' g' b' c'' d'' f''> (as the current code produces)?
If I understand correctly, the same problem already arises with c:9,
that is, as soon as the given chord voicing spans more than an octave.
But the problem is much more general: "inversion", when only applied to
chords given as stacks of thirds, is as artificial a concept as the
stacks-of-thirds themselves, for as you know, real chords (sets of
pitches) have an arbitrary distribution of their pitch classes to actual
pitches, including doublings of pitch classes (maybe even doublings of
actual pitches).
You might argue that this is not about real chords but about "idealized"
chord representations, but then it's not at all obvious *what* the
precise class of chord representations should be that a chord-inversion
function should operate on. ({Stacks-of-thirds}, {chords with range < 1
octave} etc. all do not work.)
Tbh, I'm not quite sure what the useful applications of a function
\invertChord might be, anyway, but I would expect that the two obvious
interpretations:
a) raising the lowest sounding pitch by one or more octaves in order to
become the new highest sounding pitch,
b) raising the lowest sounding pitch by exactly one octave
both might be sensible and should be supported - ideally using two
different functions (e.g. \invertChord, \invertChordII). (And this still
does not take into account the possibility of <c' c' e'> which is a
perfectly valid chord e.g. in a 3-part setting in homophonic notation.)
(Ceterum censeo: The whole concept of chord positions arising by
"inverting" a chord is not as useful as it is widespread, anyway,
because it leads to the frequent mis-conception that different chord
positions can't have the same upper voice. In my theory classes, chord
positions are always written either in a two-staff-piano system with a
clearly distinguished bass note, or in an abstract reduction "all pitch
classes mapped into the octave above the bass pitch" - for want of a
better term, I call it "compact voicing" with the convention that it
always be written in bass clef - that lends itself easily to being
encoded as bass figures[1]. And of course the same philippika might be
repeated from the point of view of melody notes instead of bass notes...)
Best
Lukas
[1] With the exception of bass figures > 8, of which only "9" is used
regularly.
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