I took a side trip to find more triads in the 31-limit tonality diamond. With the diamond to the 11-limit, using either the otonality or utonality only, there are really only four valid triads, where valid is defined as having a pure major fifth, and four thirds: 7:6, 6:5, 5:4, 9:7. I systematically explored the 31-limit diamond and found many more. Here is a summary table of the thirds I found inside pure 3:2 fifths, in the otonality and utonality only.
|Third name||third ratio|
|smaller undevicesimal major||24:19|
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