Theory. Intervals1

Walk before running.  I really want to write about the Coltrane cycle and the Hancock chord, but need to make sure I have a handle on the vocabulary first.

It starts with intervals.

The octave is the most fundamental organizing element in music. (It's possible to imagine alternatives I guess, but I suspect that they'd still need to reference the octave, at least by explicit exclusion.)

Preference, practice, and physics all have converged on a division of the octave into 12 mostly equal steps, called semi-tones, and measured by 'cents', though the physical measurement is referred not often in discussion of music theory. Regardless, the cent is logarithmic unit of measure of musical intervals.  1200 cents are equal to one octave, and thus one semi-tome = 100 cents.  Tidy, huh?  By design of course,  but also observe the familiar psycho-physics here.  Weber's law also expresses the relationship between a physical stimulus and its perception in logarithmic terms.  (BTW, the jnd for a tone an interval is about 5 or 6 cents.)

Each of these steps has acquired a name.  Or rather, the number of steps between two semi-tones has acquired a name, and also a somewhat confusing set of abbreviations.

Here they are: