Because so many different variations of some intervals are given by differing sources, I decided ages ago to eschew the more mathematical approach to extended just intonation (JI) that most mathematicians take (including Kyle Gann, Harry Partch, etc.) which sets JI intervals based on limiting the size of the numbers used in the ratio, and, instead, extended the above modal approach to all scales that can be spelled with a formula of 1 2 3 4 5 6 7 and accidentals bb, b, #, and natural. This limits there to being 23 intervals, then I minimized the number of step sizes (W, w, h, H, d, and A) necessary to connect them all, in order to find the JI intervals for the more dissonant intervals, like diminished thirds, and such, and then sanity checked those intervals by ear to make sure I didn't get something wrong. IMO, this approach works, but, the part that stumped me is determining the appropriate neutral intervals this way, which, I also feel, are important to understand. So, overall, my goal is to determine tonalities that are least dissonant: Unison can only be 1:1 ratio, or zero cents difference. This, in theory, should always be a perfect interval, "p1." "p" for "perfect," and "1" for "first scale interval," which is basically the root note and itself. The second, from modal theory, should have major and minor variants. Once you expand modal theory through equal temperament into more exotic scales, like the harmonic minor (1 2 b3 4 5 b6 7, the "Yngwie Malmsteen's favourite" scale), you will also have an augmented second interval. I've arbitrarily decided that there ought to be a diminished version of this interval as well, since I'm going to have a step that takes us from a perfect interval to a diminished interval. So, the second should come in flavours of major "M", minor "m", diminished "d", and augmented "A". So, in theory, the second should be either "d2," "m2," "M2," or "A2." The third follows exactly the same logic as the second. There is no major or minor fourth, as such, there should only be diminished "d4," perfect "p4," or augmented "A4." The fifth is like the fourth, the sixth is like the third, and the seventh is like the second. So, all the intervals, according to this system are: p1, d2, m2, M2, d3, A2, m3, M3, d4, A3, p4, A4, d5, p5, d6, A5, m6, M6, d7, A6, m7, M7, A7. There are, of course, other intervals. The neutral versions of intervals that can be major or minor are very important in Persian, Turkish, and Arabic music. The tritone is a sort of important one that maximizes the distance between two notes when the root note is ambiguous. This is a sort of clever way of maximizing dissonance. There's also a harmonic seventh that is interesting, as well as intervals that come out of the harmonic series, mathematically, or out of the natural harmonics of your strings (if they are thin and uniform enough). I think most of those are special cases. In fact, even though I believe the neutral intervals are very important, they really aren't a western (i.e. European music theory) idea, so you might be able to excuse their absence in a tuning temperament if you are focused on western music fundamentals. Obviously, it will get more an more difficult to formulate a universal model of world music theory without figuring out some things about specific musical cultures. I don't mean to downplay non-western music theory, I just don't know very much about those cultures (maybe just enough to know for sure that there are some things that will fit this same train of thought and some things that derail it, like the fact that Indian Classical music has multiple versions of what western music sees as the same interval, particularly the sixths). The JI system is meant to be an open system, with kind of "whatever" for intervals, but it makes it very difficult to delve into it or do any research. Maybe we can have subsets of the JI system? On the guitar, I'm more interested in using this for comparison of different fretting systems.