Chord inversion (and voicing) naming

Question

I'm studying chord inversions and have bumped into naming problems. As an example I'll be using the C# minor (tri)chord and its pitch classes ordered in a list like [1, 4, 8], where a lower index denotes a lower note. In other words, the first pitch class in the list is the bass note; in this case it's the 1.

As far as I can see from literature this is how we call the inversions:

pitch class list            | name
----------------------------|----------------------------
[1, 4, 8]                   | root position
[4, 8, 1]                   | first inversion
[8, 1, 4]                   | second inversion

However, I'm unsure of the naming of the following:

pitch class list            | name
----------------------------|----------------------------
[1, 8, 4]                   | root position?
[4, 1, 8]                   | first inversion?
[8, 4, 1]                   | second inversion?

These last three pitch class lists share the same bass notes as the first three lists above, but the non-bass tones are reversed. If they share the same inversion names, as suggested in Correct terminology for chord inversions, what are they called? Does e.g. [8, 4, 1] then have a name like "second inversion with first voicing inversion"?

Answer 1

I suspect your numbering system is referring to the number of semitones between each note?

C# 1 - D 2 - D# 3 - E 4 - F 5 - F# 6 - G 7 - G# 8

Rockin Cowboy is right. When describing chord inversions, you typically refer to each note by their interval relative to the root note. For the C# minor triad (C# E G#) in root position it can be described as [1, 3, 5] (the root, a 3rd from the root and a 5th from the root). eg:

This is called a closed root position chord.

Tim is right as well. Inversions simply take note of the lowest note. In your last three examples I suspect you are trying to refer to inversions where the higher notes are more than an octave apart from the lowest note? eg:

This is an example of an open root position chord. It still has the same notes as the above closed inversion but the third of the chord is raised an octave. It still has the same inversion name since the lowest notes are the same, but it is referred to as an open inversion. This is the correct terminology to differentiate these inversions.