I understand the functionality of rootless chords in a band setting where there is a bass player, but rootless chords are supposedly used in solo piano as well (the Jazz Piano Book says this, and I think Bill Evans is a prime example).
However in solo piano what is the point of rootless chords? If a play rootless D-7, then I play F-A-C-E which is the same as Fmaj7, so why not notate the chord as Fmaj7 instead of D-7? In the same vein, what makes this rootless D-7 so special?
First thing which comes to my mind is that you get a (rootless) D-9 when you play FM7, so you add color to your chord (the 9th). And if you play the root in the melody, you don't "lose" a voice by doubling a note.
The second thing is that playing the rootless chords, especially when playing standards, change the feeling of the chord progression: playing FM7 / B-7♭5 / CM7 is a change from 'plain old' D-7 / G7 / CM7. It also gives you an opportunity to play with your left hand in a higher register and from time to time pop down the root in the lower register for an additional percussive effect.
Third thing is that you will get familiar with these voicings, which means that when you get to play with a bass, you can keep playing them without having to think about it and get the roots from the bass player.
In the end, it all boils down to a matter of style and how you wish to sound. My advice: try both on the same tune, and record yourself playing. Then listen back, and go for the one you prefer as your main style, keeping in mind that variety is the key. Being able to switch from rootless to non-rootless will bring more diversity to your playing which is always a good thing.
Depending on how much the audience is used to the type of music being played, it can "hear" the root although it's not there.
As if the player was saying "I don't play the root D there, but you know what I mean". The context helps pretending the root was there.
A bit like when someone is playing a very minimalistic version of a standard tune, if the audience knows the tune well enough it can hear chord changes that are not even played. Very few tones are needed to hear a blues progression, if you listen to a lot of blues.
It's a matter of voicing: many chord changes happen by just changing few notes slightly. If there is a dedicated bass note keeping track of the respective root, it tends to jump around a lot, not maintaining a melodic line of its own. Omitting such a bass line makes the resulting changes more subtle and work on their own, like reciting a poem without making a marked pause after each line and stressing each stress, or showing a comedy without queued laughter or not explaining a joke.
Of course, there are differences in rootiness: the bass line for a Silcher chorale is a lot more bland than one for Bach: with Bach, you tend to have a reasonably solid melodic line for the bass without losing its fundamental function.
For Jazz, a walking bass line is also frequent and it just does not make sense then to try continuously providing an additional root for the right hand chord voicings.
There are a number of cases where it's possible to think of chords from different perspectives. One example would be the way that a C major 6th chord and an A minor 7th chord have the same notes in, but in different contexts it might make more sense to think of the chord as one or the other. Another example would be when modulating, say using a common chord - The I chord in G major is also the IV chord in D major, so you have to think of it both ways.
The idea of rootless chords, too, is a question of 'how you're looking at the notes you're playing' - rather than seeing the chord as just identified by the struck notes, you're seeing it as part of a different chord for some reason - either because someone else is playing the root, or because the root has been sounded in a previous phrase, or some other reason.
Alternatively you could see the rootless chord as a substitution for the normal, 'rooted' chord.
There is a big difference between "adding" color to an existing chord via extension, and "subtracting" from a chord by dropping notes. In classical harmony theory the 5th of a chord is considered unnecessary, and is often dropped from the V7 chord and the root doubled. Not always but often enough for it to be mentioned in every harmony book I have.
The concept of "root-less" chord may be taken out of context in many places. In a nut shell the ROOT identifies the chord. So if the root is missing the chord should not be considered by the name of the root. In some cases when looking at the movement of notes the root is not that relevant to the sound of the movement. A classic (classical) example is, again, V7. In the cadence V7 --> I the root of the V chord is the "common tone". It doesn't move. That doesn't mean it is not important, but it does not contribute to the 7-->8, 4-->3 movement that defines the sound of completion. Removing it leaves one with the diminished triad on the vii degree of the Maj scale of the Key. The movement works and is called the Leading tone resolution, viii(o) --> I.
The point is that, strictly speaking, removing the root did not create a rootless V7 chord, it created a viii chord and that is how it would be notated in a classical chord analysis. In functional harmony one might consider the viii(o) and the V7 as functionally the same since they serve the same purpose when moving to I but that is only one point of view. Out of this context the V7 no root is simply NOT a V7 any more.
If one wants to think of the viii(o) as a rootless minimalist version of the V7 that's fine, no one could stop that. But that's not to say that some players wouldn't think "boy, a leading tone resolution would sound great here". Whether you think of it as a rootless V7 or a viii is in part, a matter of brain washing. It depends on the school of thought you were trained in and subscribe to.
When it comes to playing extended chords on guitar this is a very useful device since you only have 6 strings and 4 fingers and you WILL necessarily need to sacrifice notes. The issue there might be one of convenience rather than music theory. Can you get (1) closed harmony, (2) moving in small intervals, and (3) get your fingers where they need to be quickly. These are some of the things a guitarist needs to worry about. For this reason we drop roots often. BUT, and this is a big but, I am not sure we think of those as "rootless" chords rather than suitable substitutions.
My take on this is pretty simple, Bill Evans and other jazz pianists are aware of and hear the roots in their heads when they play chords where the bottom note is not the root. They have developed systems of voicing either one or two handed chords where the bottom note is either a 3rd, 6th or 7th in order to avoid clashes with the bassist. They sometimes like to improvise as if there is a bass player even when playing solo. It has a light, etherial quality. It doesn’t mean they’re changing the harmony, they’re just electing to leave out parts of it at times. When they play the melody at the beginning and end of the song they are much more likely to play the roots of the chords.
The fact is they are are just performing, and improvising, they are not thinking about having what they do analyzed and transcribed. If a pianist plays F-A-C-E bottom to top he’s probably thinking Dm9 and hearing the root in his head. It’s not special, it’s just the way he plays a Dm9.
