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.
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