This is perhaps one of the hardest areas of jazz theory to understand for students coming from a classical background.
Student Question:
When you play a rootless voicings for Cmaj7, you played E-G-B-D which to me is E-7. How can E-7 be Cmaj7?
Hayden’s Answer:
On a lead sheet we see the chord symbol Cmaj7 and so as a jazz arranger, you need to decide how to play a Cmaj7 to produce a nice sophisticated jazzy sound.
You need to understand that whenever you voice a chord, you have the creative freedom to choose what notes to include, your options for major chords are root, 3rd, 5th, 7th, 9th, #11th & 13th (if you add another 3rd on top of the 13 you are back to the root so 13 is the highest extension)
Generally speaking, the higher the extension you include, the richer and ‘more complex’ the sound will be. Complex doesn’t always mean good, sometimes just the 3 and 7 will suffice, but rootless left hand voicings with added extensions and alterations (pioneered by Bill Evans) have become a staple sound of jazz piano.
As your ears develop to hear and appreciate the sound of extensions… you will understand they these voicings have more ‘texture’ and ‘colour’ than voicings made up exclusively of the primary chord tones.
The Benefits Of Rootless Voicings:
There are a number of key reasons why we play rootless voicings, and why leanring them is an important part of your musical development:
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You free up a finger for a more interesting note choice such as an extension or alteration
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Rootless voicings voice lead much more smoothly in a 251- it’s easy to play a rootless 251 without looking and so you can focus on your right hand lines.
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It gets you familiar with extensions and alterations, if you don’t practice rootless voicings, chances are you will be sticking to simple root position 7th chords. Practicing rootless voicings will give you a much greater appreciation of the extended and altered tones available to you.
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If you are playing in a jazz band, you will be required to play mostly rootless voicings, otherwise, you will clash with the bass player.
Stripping The Chord Down To The Essentials
One of the main things you need to understand here is that to play Cmaj7, all you really need is the 3 & 7 as these define the C major sound. Aside from that you can choose any of the other notes listed above (root, 3rd, 5th, 7th, 9th, #11th & 13th)… that’s the available notes you have.
3-5-7-9 or 3-6-7-9 would be my 'go to’ voicings… they have the essential chord tones which are defining the C Major sound, but also has extra texture from the 9th.
Solo Jazz Piano vs, Trio or Band Performance:
If you are playing solo jazz piano, you should include the root most of the time.
Left hand voicings are what you would play in a band where a bass player is present. However, I do stress in the lessons that these voicings are still very useful in a solo piano context but just not on every chord. When playing solo piano, you should be playing at least some of the roots to ground the harmony.
One Voicing Is Actually Many Different Voicings:
As you learn more voicings, you will find much overlap:
If you take the notes Gb - Bb - C & F
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This could be a rootless voicing for Ab13 - from bottom to top we have b7, 9, 3 & 13 (probably the chord that you associate this voicing with)
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It could also be a D7#5#9 - from bottom to top we have 3, #5, b7 & #9 (think tritone sub D7/Ab7)
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It could also be a C-11b5 - from bottom to top we have b5, b7, b3 & 11
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It could also be many other things.
This is where you need to understand that ‘intent’ is important.
Understand That “Intent” Is Important
If I see a Cmaj7, I could play just B (7), C (Root) & D (9). This is a cluster voicing.
From a classical standpoint, this voicing does not follow the rules of traditional harmony. There is no 3rd in the chord which from a classical standpoint makes no sense, but in jazz, if you play this in your left hand, it can sound very interesting. I wouldn’t use this voicing all the time for Cmaj7 but it can be nice to throw in a more ‘obscure’ voicing like from time to time.
Rootless Voicings In The Context Of A Band
If you are playing jazz in a band, you will likely be playing with a bass player.
The bass players job is to play the root of the chord.
If I played the Cmaj7 as C-E-G-B then I am doubling the root note that the bass player already has covered.
Whereas, if I play 3-5-7-9, then I have added in an extension which creates more interesting harmony and a more interesting sound overall coming from the band.
A Common Tripping Point
A common tripping point for students is analysing rootless voicings as a completely different chord which isn’t the case. It’s simply a rootless voicing.
It’s a hard area to grasp because in classical/traditional harmony, we are conditioned into analysing and naming chords in their root position.
Whereas in jazz this isn’t the case, there are lots and lots of ways to voice a chord and 1 voicing can actually function as many different chords as in the example highlighted above.
Complicated and confusing I know! But it makes sense with time.
Spend some time reading over the above and if you want me to clarify or elaborate on any of the points then copy and paste any particular sentence that doesn’t make sense and I will try my best to explain further 
… when I played something I didn’t intend on playing, but it sounded great.
