Ear training is obviously an extremely important pursuit for improvising musicians. I spend a significant portion of my practice time on ear training activities, and try to find ways to incorporate an ear training aspect into all of my practicing.
One of the things that makes harmony so complex is that as you add notes, the complexity increasing in a combinatorial way, not an additive way. For example:
If you hear an E against a C, it's one piece of information: major 3rd.
If you hear an E and a G against a C it's 3 pieces of information: major 3rd between C and E, perfect 5th between C and G, and minor 3rd between E and G.
If you hear an E, G, and B, against a C, it's 6 pieces of information: major 3rd between C and E, perfect 5th between C and G, and minor 3rd between E and G, major 7th between C and B, perfect 5th between E and B, major 3rd between G and B.
If you hear EGBD against C, it's 10 pieces of information: major 3rd between C and E, perfect 5th between C and G, and minor 3rd between E and G, major 7th between C and B, perfect 5th between E and B, major 3rd between G and B, major 9th between C and D, minor 7th between E and D, perfect 5th between G and D, minor 3rd between B and D.
So in order to learn all the sounds, we need to give names to specific combinations, like triads, and ultimately triads with added notes (including 7ths).
I've made a set of audio files (mp3 format) based on an exercise suggested by Rufus Reid. Each file presents one of the four triads (Major, Minor, Augmented, or Diminished), and alternates with adding one of the twelve available tones to it. The idea is to learn to hear the sound of all the available notes over each type of chord.
Download file here.
I used triads because once you can identify the sound of the 6ths and 7ths over a triad, then hearing more complex chords is merely a matter of identifying the chord as (Maj, Min, Aug, or Dim) triad+(6, b7, or 7) + additional note(s).
There are more than 12 files for each chord, because I included some notes in more than one octave (specifically, the 2nds/9th, 3rds/10ths, 4ths/11ths, and 7ths). I did this because these notes can have some additional different characteristics when voiced close to the chord, and these differences can distract you from hearing the essential characteristics. For these notes, I suggest spending some time going back and forth between the lower and higher version in order to focus on part of the sound that doesn't depend on what octave you're in.
There's a lot here (76 33-second clips), but it's pretty manageable. There are a lot of ways to work with these files. Here are some suggested playlists:
All Major Triads
All Minor Triads
All Dim. Triads
All Aug. Triads
comparing 7ths close-voiced or spread
All 7ths (or any other interval) over Maj, Min, Aug, Dim triads
Compare min chord with added M3 with major chord with added b3: very interesting!
Compare maj chord with added b6 with augmented chord with added P5
Compare min chord with added #4 with dim chord with added P5
I hope this is helpful!
PS. There's tons of stuff out there written about ear training, but here are a few of my observations:
-Singing is extremely important.
-Singing over a drone is extremely helpful.
-Deliberately 'hearing' notes in your head before you sing them is very important. You can also use this to work on mentally 'hearing' more than one note at a time.
-Visualizing notes on your instrument as you mentally 'hear' them and/or sing them is very helpful. Visualizing a piano (if your main instrument is not piano) and written music are also helpful.
-Singing the root motion of chord progressions is great exercise. So is singing guide tone lines (3rds and 7ths)
-Intervals can be heard two ways: as harmonic events or as distances. Of the two, it's more important to hear the harmonic event (even when presented melodically). But it's helpful to learn to recognize the sound of a particular distance as well (some people argue that distance-hearing will actually impede your development, but I'm not convinced).
-Testing your ear is not necessarily the same as training it, though it can be helpful.
-One of the main ways we learn to distinguish similar things is through comparison.