As the name implies, "Rootless" means there's no root in the chord.
Rootless chords are chords without the root present.
It is believed that every chord can be seen as a rootless form of another chord.
How do we locate the rootless form of a chord?
Let's try an example using a normal Cmajor triad as C-E-G
If you look deep you'll find out that its also a Rootless Amin7[A-C-E-G]
Did you see the Cmaj triad in the Amin7 chord as A/CEG which is A/Cmaj.
Another rootless chord will be Abmaj7#5 [Ab-C-E-G]
Which is simply Ab/C-E-G.
I believe you're following up?
I guess so:
Let's try another example using F minor triad as F-Ab-C
Look it at the triad very well you'll see a Dmin7b5[D-F-Ab-C] chord.
Your ability to locate chords makes this easy.
It can also be seen as a Rootless Dbmaj7 chord as Db-F-Ab-C.
Now you try this.
Find the Rootless form of the following chords
> D minor [D-F-A]
> F7 tetrad [F-A-C-Eb]
> G diminish triad [G-Bb-Db]
> C dim7[C-Eb-Gb-Bbb]
There are several principle for detecting a rootless chord.
Let me share just one today.
"Every Altered dominant chord has its Rootless form a tritone interval away from its root"
Let's try few example.
E7#5#9 as E-G#-B#-D-Fx [Enharmonically; E-G#-C-D-G] will have its rootless from a tritone away from the root which is E
So the tritone will be Bb.
Adding Bb to the chord we'll have
Bb + E-G#-C-D-G
Juxtaposing it in stack of 3rd, we'll have
Bb-D-Ab-C-E-G which is a Bb13#11 chord Harmonize from Bb Overtone scale [Bb-C-D-E-F-G-Ab
Also called Bb Lydian dominant scale or Bb Dominant #4 scale.
In modern music; Rootless chords had evolve from being a chord without the root note present.
Now you see a chord called rootless but the root is present in it but "Not in root position"
An example makes this better.
Cmaj7 in second inversion [EGBC] and third inversion [GBCE] can be termed Rootless.
Because the Root [C] is not the lowest note.