Godtone

:I will also mention that [[87edo|87 EDO]] is very related to 80 EDO, but emphasizes accuracy in the 5- and 13-prime-limit as opposed to the 19-prime-limit of 80 EDO (and I'd argue 80 EDO deals generally well with the 29- (or at least 23-)prime-limit for its size), as both are tunings of the [[Tolermic family]] and its extensions up to the 17-prime-limit, and it may be interesting to you too as it has a [[29edo|29 EDO]] circle of fifths, but all primes up to and including 13 are one step flat of the nearest 29 EDO note, creating a very simple and elegant model of connectivity. 87 is (IMO) very recommendable if you want approximations of the 13-limit but still want all of the intervals to be musically meaningful to distinguish in the senses of [[User:Godtone#Colourful_EDOs|colour]] and melody.

:(Note: like 80, unfortunately, 87's worst prime is 7, but the error and relative error is less and in the opposite direction.)<br/>

:: I'm afraid your understanding of the concept of telicity is an oversimplification.  While the concept of telicity does in fact include the idea of a "circle of n'ths" where "n" is some interval of interest, incomplete circles are still counted, hence the term "chains", and while the concept of telicity not only involves connectivity between multiple chains- specifically of primes- and the the patent val for an EDO agreeing with the connection, the fact remains that the [[direct mapping]] for every interval in both circles up to the point of connection must also agree with the connection.  Stated more mathematically, where "N" is the number of steps in a given EDO, "r" is the ratio of an interval in one of the two circles, and "M" is the monzo of "r", the equation {N, round(log2(3)*N), round(log2(5)*N), round(log2(7)*N), round(log2(11)*N), ...}.{M} = round(log2(r)*N) ''must'' hold true along ''both'' prime chains up until the point of connection.   

:: Just looking at 3-to-2 telicity, which, by definition, involves circles of fifths, the first seven EDOs that pass the test for this telicity are 2, 5, 12, 24, 53, 106, and 159.  80edo, despite being almost half of 159edo, fails the test, which is why I'm not interested in it, the same is true of both 29edo and 87edo. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:27, 22 January 2021 (UTC)