Nate BeDell on 29-limit thirds on XA

Nate BeDell
I was talking about 29-limit harmony, and the limit of prime limits the other day on chat, so today I figured out all (assuming I didn't miss anything) of the simple 29-limit intervals that are within the realm of thirds, (in between 7/6 and 9/7) and this is what I found;

29/23 - 401.302847 cents
29/24 - 327.622193 cents
34/29 - 275.378215 cents
35/29 - 325.562426 cents
36/29 - 374.332808 cents

The first thing I noticed, is that this is the first prime in which there are more than three intervals that could be said to be thirds, (once again, unless I missed something) thus making it extremely hard to classify ANYTHING as being characteristically "29-limit".

The next thing I noticed is that even within the 29-limit, there are redundant intervals (29/24 and 35/29) in which there are no real audible distinctions, not to mention ambiguity with other primes (29/23 is very close to the 19-limit major third, for example, both being a good a approximation to the third in 12-equal, which is interesting in it's own right) along with other close (nearly inaudible) approximations to smaller prime intervals.

36/29 however is somewhat interesting, being ~10 cents away from other intervals in my study, seems to be the only *distinct* (relatively speaking) 29-limit interval, but even here, it seems like it is more intuitive to just think of it as a flat 5/4, or as being a just intoned representation of the flat 5/4 in 19-tet.

17, 19, and 23 limit intervals, although sharing some of the problems of the 29-limit, seem to still be more or less useful in their own right. 17 contains super-minor and sub-major, which although closer to neutral intervals, are distinct from. 19 can be thought as a just embodiment of 12-tet harmony, and 23 limit intervals can be thought of as inbetween 5 and 7 limit intervals.

I feel special now! :P