Just some additional remarks to my charts and fingerings:
I started my very first learning of CBA in a local accordion classroom in Taiwan from two teachers there. Both of them are good players and PA/CBA switchable, and they both have professional piano background. It was a very basic course which lasted only 3 months, and I moved to Australia afterward so couldn't learn too much from them. But one valuable thing I learned is this right-hand fingering of C Major scale as I showed on my chart. I just clipped and pasted it here:
I found it very comfortable and suitable for me right after I learned it. I don't know if my teachers figured it out by themselves. Maybe they did it out of their piano/PA background. The best part of this fingering is you always keep your wrist in a natural flat angle (no pointing upward/downward) by using your thumb as a pivot and touch reference to move your whole hand. If you take a selfie video you will find you had a hard time finding your thumb. That's because you always move your thumb under your palm to reach the pivot note first (e.g. E and A in C Major). Quite similar to what we do in the fingering on piano.
Keeping right wrist angle unchanged when doing the scale is a wonderful experience. It can also prevent you from hurting the wrist in the long term.
After learning C Major scale in the classroom, I used same logic to create all other right-hand fingerings in different scales by myself (Major and minor). And you know what? After I got the classic accordion textbook "Complete Method Theoretical-practical Progressive for Accordion" written by L. O. Anzaghi (https://goo.gl/gLzilX
), I found my fingerings are almost 100% identical to those in his book!!
If you got this book please check somewhere between p.80 ~ p.90 and compare them to my right-hand chart. You'll see how similar they are.
Although this book is over 60 yrs old but I was still very happy to find how similar my theory is to that of a great accordion master and teacher.
But that's just for the right-hand. This book didn't cover the left-hand free bass, and my fingerings for free bass is not like any other teaching material I could find. Some of them tell you to use the 1 (thumb) or 5 (pinky) but that just didn't work for me very well, so I basically use only 2,3,4 for scale fingerings.