Comment by ksr

1. Regarding naming of intervals, this has confused me for months, until I understood (or convinced myself) that there are in fact 2 different things that are called "intervals": intervals between tuning pitches (which is your first example) and intervals between scale notes (your second example). Thinking of them as different things (and calling them differently) has helped me a lot with modeling musical objects in scalextric. For example, tuning intervals in different tunings (12-TET vs. Pythagorean) can end up having the same logical interval name because they are approximating the same logical relationship between notes even though the physical frequencies are different.

2. sub-scales = what you call interval sequence.

If you don't mind, we can continue this conversation by email. Mine is in my profile on HN.