It is an inexact science: one day we should know how a note plays in our brain (like in a piano), and the next day there is no single clue left that may tell us something important.
The most common theory is that musical scales have one rule for each scale, and that this rule, with some exceptions, is universal: as a general idea, everything scales should follow a common pattern when played. It is generally said that this common rule makes the whole thing easier to learn and remember, though of course it does not make it perfect (though it allows it to be used as a common starting point for learning a wide variety of musical techniques of many kinds).
It is therefore very confusing to me, what “rules” it is for each interval to play. I don’t do any music theory (it was the only field I wanted to study seriously) but I was wondering if there are any general principles that seem to be universally shared among all scales. The theory of scales is only really “general” in the sense that it assumes something universal about scale properties: for instance, that a scale should end on the same note whenever it is played. So what is this universal “rule”?
We can look at how many steps we need in an interval for one scale to end on the same note as another. The key is (1) that we consider every scale the same way when it is played, and (2) that every scale in concert ends on the same note: for all scales any one note is in a different key: we call this common property common to scales, and which is generally considered the “true” rule among scales. I call this rule “the universal rule” or “the pattern” for scales. (I have already mentioned it above in the “what do the notes belong to?” section.)
Of course, if we wanted to learn all scales, and each scale is the same in each key, we must look for a universal pattern or common property. There are no universal rules, and indeed there can even be a “false” universal rule: there are certain intervals that are common for certain types of tunes… but there are also certain intervals that are not so common, as might be expected. To find out how many steps it really takes to end one scale on the same note as another type of scale, we must look back over the list of notes in our entire playing program, and see if any notes are not in the list (since none