When you start ‘adding‘ or ‘extending‘ chords into a 2nd octave (other than duplicating a note from the first octave) a couple of problems become apparent pretty quickly. One, when notes in different octaves are separated by a single half-tone interval (m2), they tend to sound pretty nasty when played together. And two, unless you’re polydactyl or an alien of some sort, you’ll probably run out of fingers on a couple of the extended chord types. This is especially problematic for guitar players.
But fear not!
There is a solution in the form of drop, omit, avoid or skip notes.
Call them what you will, but they all refer to the same thing. If a “tension” note located in the 2nd octave occurs within a single half-step of a chord “tone” in the 1st octave, it’s going to sound dissonant (bad!) because it will naturally want to resolve to the next higher note. In cases like this, it’s normal to either drop the “tone” note and keep the tension note or sharpen the conflicting tension note. It takes a little bit of experimentation, but trust me, you’ll know it when you hear it.
As a rule of thumb, you’ll probably want to drop the 5th and keep the 3rd, 7th and highest tension notes since those notes tend to give the chord its flavor. The 3rd indicates the type of TRIAD (MAJOR, minor), the 7th indicates the type of 7th chord (MAJOR, minor, Dominant) and the highest tension note should be kind of obvious. But not always.
Take the following C MAJOR 11th for example. It’s made up of the 1, 3, 5, 7, 9, 11 scale degrees with 9 and 11 residing in the 2nd octave.
Normally, you wouldn’t drop the 3rd (e) because the chord would lose its MAJOR characteristics and if you dropped the 11th (F), it would simply revert to being a 9th. In cases such as this, it’s normal to raise the offending tension note in the second octave by a single half-tone. In this case, the F would become F#.
You can really hear the difference when it’s played on a piano.
Experiment until if fits and remember Occam’s Razor: given 2 choices, the simplest is usually right!