Conservatory? I'm impressed (without any ironic undertone tho!).
I never wanted this because I can't seem to learn everything about (in)famous German-speaking composers like Mozart. For me Mozart is what Max Martin (Sweden; Backstreet Boys etc.) is for the pop world - absolutely run-of-the-mill stuff, and nothing to write home about.
Yet...I'm a bit baffled you were at a conservatory and haven't heard anything of the circle of fifths. Or did you forget it?
Well that'd be something else.
But AFAIK these basics are commonly taught there.
(Sorry, that was to be sent via PM - but Ultron does not allow PMs, so ...)