I'm referring to the upper structure triad use you mention here. Any triad can be used of course, whether major minor or diminished or augmented.

One way of dealing with them is to obtain a purposely limited palette or set of chords you can use with a similar sonority and interval spacing. It's a way of coming up with voicings, extensions and alterations methodically yet which you might not have thought of otherwise.

Employing just the root spelling of the triads you can opt to play these over a similar slash bass note (e.g. CMaj/Db, CMaj/D, Cmin/Db, Cmin/D etc..)

This particular group give you some interesting 'incomplete' voicings for familiar 7th and altered 7th suspended chords.

Cmaj/Db = DbmMaj7b5 ...........1 7 b3 b5
Cmaj/D = D9sus(no 5th)........1 b7 9 4
Cmin/Db = DbMaj9b5(no 3rd).....1 7 9 b5
Cmin/D = D7susb9 (no 5th).....1 b7 b9 4
Cdim/Db = Dbmaj9sus(no 5th)....1 7 9 4
Cdim/D = D7b9(no 5th).........1 b7 b9 3
Caug/Db = Dbmmaj9b5............1 7 b3 5
Caug/D = D9b5(no 3rd).........1 b7 9 b5

You may not like all of these voicings. I don't like Caug/Db in this context as it has the 3rd and 5th which seems to contradict the other chords and sounds out of place. But overall they work well together.
There's no reason why you wouldn't want to mix or alternate groups. Try combining/alternating chords from this set with slash chords using the 7th/b7th in the bass.


When I'm trying to reharmonize a melody however I like to use the slash chord approach in different ways. Firstly I think of an appropriate bass line that gives me a particular type of counterpoint or root movement; then I choose an appropriate inversion to go under the melody that gives a desired degree of tension at a particular point. Other times I might go the opposite route; start with the triads under the melody and then manipulate the bass line for root movement and tension.

Another way is to take an inventory of all the triad over alternate bass note possibilities and grade them for tension and/or implied functional possibilities. It's an interesting exercise to use tension chords like Emaj/C, Emaj/F or Edim/Ab as substitues for dominant functions even though strictly speaking they are not dominant 7th chords.

The more you get into this area of harmony the more natural it feels I think. Like everything else it's a matter of living with the material long enough to begin to 'feel' it as you rightly put it.
It helps of course if you happen to actually like the modern repertoire that makes use of this harmony. I'm thinking especially of ECM label jazz or related musics. Pianists such as Jarrett or Beirach. Composers such as Ralph towner or Kenny Wheeler.

In the end it depends on your willingness to experiment and do something slightly different from the usual. Again there's no need to feel this way if you're more comfortable dealing with the normal diatonic 7th chord spellings with chromatic alterations.

With the slash chord method however there's a tendency as Ralph Towner has stated to improvise melodic lines that are less tethered to the chord root and which gravitate more freely around the upper triad in a way that's very much in keeping with the music of Charlie Parker who was basically doing this long before anyone else and with obvious success.

Alan