The concept of stacked intervals isn't all that uncommon. I, and many other musicians, actually prefer to think this way. Standard chords (triads, 7ths and their extensions) are all based on stacked thirds, so each note is either a major or minor (or aug or dim) third above the previous note. The same concept has been applied to fourths (occasionally in jazz), but this is very uncommon and quite limited. Stacking fifths is really just thirds, but skipping every other, and major/minor seconds essentially just make up scales (and tone clusters). Anything above a fifth, or some combination of thirds, fourths, fifths etc. can usually be shuffled around and classified via a different stack (i.e. stacking sixths, C-A-F, is just a spread out stack of thirds, F-A-C, creating a major triad; and stacking a fourth, a third and a fifth, C-F-A-E is also just a stack of thirds, F-A-C-E, a major 7th).
So, 95% of the time, thirds are all we really need. Because we only have 2 options for each interval (m3 and M3) we can determine every possible combination of stacked thirds using a binary system where m3 = 0 and M3 = 1. We will only go up to a 13th, so 7 notes, but since our "digits" are the intervals between them, we only need 6. This gives us 64 (2^6) possible permutations.
m3-m3-m3-m3-m3-m3 = dim7
m3-m3-m3-m3-m3-M3 = dim7, bb13
m3-m3-m3-m3-M3-m3 = dim7, b11, bb13
m3-m3-m3-m3-M3-M3 = dim7, b11, b13
m3-m3-m3-M3-m3-m3 = dim7, b9, b11, bb13
m3-m3-m3-M3-m3-M3 = dim7, b9, b11, b13
m3-m3-m3-M3-M3-m3 = dim7, b9, 11, b13
m3-m3-m3-M3-M3-M3 = dim7, b9, 11, 13
m3-m3-M3-m3-m3-m3 = 1/2dim7, b9
m3-m3-M3-m3-m3-M3 = 1/2dim7, b9, b13
m3-m3-M3-m3-M3-m3 = 1/2dim7, b9, 11, b13
m3-m3-M3-m3-M3-M3 = 1/2dim7, b9, 11, 13
m3-m3-M3-M3-m3-m3 = 1/2dim7, 9, 11, b13
m3-m3-M3-M3-m3-M3 = 1/2dim7, 9, 11, 13
m3-m3-M3-M3-M3-m3 = 1/2dim7, 9, #11, 13
m3-m3-M3-M3-M3-M3 = 1/2dim7, 9, #11, #13
m3-M3-m3-m3-m3-m3 = min7, b9
m3-M3-m3-m3-m3-M3 = min7, b9, b13
m3-M3-m3-m3-M3-m3 = min7, b9, 11, b13
m3-M3-m3-m3-M3-M3 = min7, b9, 11, 13
m3-M3-m3-M3-m3-m3 = min7, 9, 11, b13
m3-M3-m3-M3-m3-M3 = min7, 9, 11, 13
m3-M3-m3-M3-M3-m3 = min7, 9, #11, 13
m3-M3-m3-M3-M3-M3 = min7, 9, #11, #13
m3-M3-M3-m3-m3-m3 = minMaj7, 9, 11, b13
m3-M3-M3-m3-m3-M3 = minMaj7, 9, 11, 13
m3-M3-M3-m3-M3-m3 = minMaj7, 9, #11, 13
m3-M3-M3-m3-M3-M3 = minMaj7, 9, #11, #13
m3-M3-M3-M3-m3-m3 = minMaj7, #9, #11, 13
m3-M3-M3-M3-m3-M3 = minMaj7, #9, #11, #13
m3-M3-M3-M3-M3-m3 = minMaj7, #9, #13
m3-M3-M3-M3-M3-M3 = minMaj7, #9
M3-m3-m3-m3-m3-m3 = Dom7, b9
M3-m3-m3-m3-m3-M3 = Dom7, b9, b13
M3-m3-m3-m3-M3-m3 = Dom7, b9, 11, b13
M3-m3-m3-m3-M3-M3 = Dom7, b9, 11, 13
M3-m3-m3-M3-m3-m3 = Dom7, 9, 11, b13
M3-m3-m3-M3-m3-M3 = Dom7, 9, 11, 13
M3-m3-m3-M3-M3-m3 = Dom7, 9, #11, 13
M3-m3-m3-M3-M3-M3 = Dom7, 9 #11, #13
M3-m3-M3-m3-m3-m3 = Maj7, 9, 11, b13
M3-m3-M3-m3-m3-M3 = Maj7, 9, 11, 13
M3-m3-M3-m3-M3-m3 = Maj7, 9, #11, 13
M3-m3-M3-m3-M3-M3 = Maj7, 9, #11, #13
M3-m3-M3-M3-m3-m3 = Maj7, #9, #11, 13
M3-m3-M3-M3-m3-M3 = Maj7, #9, #11, #13
M3-m3-M3-M3-M3-m3 = Maj7, #9, #13
M3-m3-M3-M3-M3-M3 = Maj7, #9, 13
M3-M3-m3-m3-m3-m3 = AugMaj7, 9, 11, b13
M3-M3-m3-m3-m3-M3 = AugMaj7, 9, 11, 13
M3-M3-m3-m3-M3-m3 = AugMaj7, 9, #11, 13
M3-M3-m3-m3-M3-M3 = AugMaj7, 9, #11, #13
M3-M3-m3-M3-m3-m3 = AugMaj7, #9, #11, 13
M3-M3-m3-M3-m3-M3 = AugMaj7, #9, #11, #13
M3-M3-m3-M3-M3-m3 = (Dom7, #9, b13)
M3-M3-m3-M3-M3-M3 = (Maj7, #9, b13)
M3-M3-M3-m3-m3-m3 = Aug, #9, #11, 13 (no7)
M3-M3-M3-m3-m3-M3 = Aug, #9, #11, 13 (no7)
M3-M3-M3-m3-M3-m3 = (Dom7, #9, b13)
M3-M3-M3-m3-M3-M3 = (Maj7, #9, b13)
M3-M3-M3-M3-m3-m3 = (Dom7, b13)
M3-M3-M3-M3-m3-M3 = (Maj7, b13)
M3-M3-M3-M3-M3-m3 = (AugMaj7)
M3-M3-M3-M3-M3-M3 = Aug