You've been asking me over twitter what music theory a 15-16 year old should know. You'll have to forgive me here, because I don't know much about you. But I'm happy to answer your question. Though this isn't so much as what a 15-16 year old should know, but I think this is something every advancing student should know. So many musicians don't know beep about theory, and most are never taught it. Theory is often treated as this strange voodoo that is little understood and infrequently taught.
As I mentioned, playing bass or a rhythm section instrument kind of forces you to learn some theory. I learned song forms, chord structures and scale relationships before I even got to a theory "class". But there were a lot of gaps in what I knew.
In my first class, which was a high school elective and not offered to all students, we spent a great deal of time on these:
-Intervals to the first octave, and the inversions of each. Unison, minor and major seconds, minor and major thirds, perfect 4th, tritone, perfect 5th, minor and major 6th, minor and major 7th.
-The circle of 5ths (and the inversion of the circle of 4ths) in major and minor. We would spend weeks just drilling this. C major, no sharps or flats, play a C major scale call out every note by name, G major, one sharp, F#, play a G major scale etc, etc, etc,
We would go all the way around the circle, and not simply stopping at the 6th key. For Example:
E-sharp major, 11 sharps, F-double sharp, C-double sharp, G-double sharp, D-double sharp, A-sharp, E-sharp, B-sharp. Play the scale, which is E#, F##, G##, A#, B#, C##, D##, E#.
Again, most people quit at 7 sharps or flats, but our theory teacher was a hard-ass. It's way easier reading in Fmajor instead of E# major.
Once key relationships are ingrained, we moved on to diatonic chords. So in C, you have C major triad C-E-G, D minor triad D-F-A, etc. Do that in all 12 keys, and understand it.
Then you can move on to scales and modes within each key, the chords for each and how they are applied and work. At this point you start to get into 7th chords, 9th chords and all that pretty jazz stuff.
Realistically, while its a few concepts, practicing it and getting it ingrained can take a few months of solid practice time.
None of the above makes you a better player, rather it helps you understand the music you are already making, and then provides portals into new areas to explore.
