The 22/7 you refer to has three puzzling questions in it for me I hope you can clarify.
First, you use the western, modern, scales. I'm no expert really but I know the western scales are just one way of dividing notes. Why selcting these scales?
Secondly, you use a major scale, while, within western music, there are plenty other scales. So why selecting the major scale?
Thirdly when playing a major scale in the key of C, the 22 total can only be formed when you include the top C which is actually the first note of the fourth octave.
As in: C-d-e-f-g-a-b-C-d-e-f-g-a-b-C-d-e-f-g-a-b-C totalling 22 notes
The 7 you mention is not including this first note of the following octave.
As in: C-d-e-f-g-a-b- totalling 7 notes
So shouldn’t it be 21/7 or 22/8
Hope you see what I mean.