Progression Circle m6/m3 Con’t

OK, I realized my ignorance here. It dawned on me this morning that there was a reason why there were 7 half steps between some notes and 17 half steps between others. What I thought was unique was nothing more than a circle of sevenths. When you actually play this progression you recognize the pattern. The m6 meant nothing – it was just an additional note I was throwing in there before continuing with the circle of 7ths. The other way of looking at it is that any two intervals adding up to 9 returns you to the octave. A m6th and a maj3rd get you back to the octave. That 17 I was seeing was a half step from 18 (2 X 9), which would be one half step short of the second octave – the 7th. Playing these little mathematical games is how I learn theory, so I don’t consider it a waste of time in doing it. But the progression was nothing special, either.