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Take the following example (I'm a guitar player, so I'm going to give a guitar-centric example):

Let's say you start by playing an A major triad using the C-shape. So you're fingering the 9th fret on the G string (E), the 11th fret on the D string (C#), and the 12th fret on the A string (A). You strum it. Mountains move. Angels sing. You know, the usual.

Now let's say you're feeling a little bold and instead you play that triad by playing the A string open, without fretting it. The other fingers stay right where they are. It's not an inversion (says the novice with far too much conviction) because the A continues to be the bass note. But it's a distinct voicing change.

Is there a name for this?

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    Yes: playing without a bass player ;-) – musicamante Jan 22 at 4:20
  • @musicamante Ooo I know of this phenomenon – Zelbinian Jan 22 at 4:24
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This is usually referred to as an open or spread voicing, it is a general term to indicate the voicing of the chord spans beyond regular stacking, or close voicing. You are right that it isn’t an inversion. The guitar lends itself to many different ways to voice the same chord. Depending on the chord sometimes the guitar will give you options for open strings even when playing high up the neck and those chords usually have an extra nice quality to them.

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    Maybe worth mentioning that the original voicing is closed, where all the notes are as close to each other as possible. +1. – Tim Jan 22 at 9:55
  • @Tim thanks, I worked that in. – John Belzaguy Jan 22 at 18:54
  • We've reached the stage of people editing 'closed' to 'close' in other people's answers, is it? – Judy N. Jan 23 at 1:51
  • @JohnBelzaguy No it was a edit by Aaron. Of course we had a whole question about what the correct "official" term was a few days ago.... – Judy N. Jan 23 at 1:53
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    @JudyN. I’ll check it out, I’ve seen and probably have used both over the years without even thinking about it. I see close more often although closed does make sense given the alternative... – John Belzaguy Jan 23 at 2:03
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Yes, but your question title and body describe two difference cases that bring up different terminology.

...A major triad using the C-shape...playing the A string open

In other words: x 12 11 9 x x becomes x 0 11 9 x x.

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When the tones of the chord are arranged without skips - basically within one octave for triads and seventh chords - it is called close voicing. When there are larger spaces between tones it is called open voicing.

As you point out this doesn't necessarily make a new inversion.

...dropping the bass note of a chord an octave...

I jazz there is something called drop voicing where the voices of a close voiced chord are labeled by number descending from the highest voice. SATB would be numbered as soprano=1, alto=2, tenor=3, and bass=4.

When one of those voices is dropped an octave it is called drop voicing. Drop the 2 voice and it is called drop 2 voicing, drop 2 and 4 and it is called drop 2-4 voicing, etc.

enter image description here

I have only seen drop voicing in the context of four tone seventh chords. Calling a root position triad with the bass dropped a "drop 3" chord would seem inappropriate.

I imagine you didn't mean to have a distinction between your title and question body, but you should know about the two cases.

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    I don't really see the distinction you're referring to. Is it simply that OP used "drop"? – Judy N. Jan 23 at 1:47
  • @JudyN. despite quoting the title I somehow thought "bass" wasn't in it. But clearly it was. My mistake. – Michael Curtis Jan 23 at 22:00

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