concerns re: noble mediant

[cmloegcmluin]

Hi there! Forgive me, because I'm not familiar with this tool in general. I came across it while reviewing Dave Keenan's recent further work on noble mediants. And he noticed that there are a couple flaws in the implementation of this feature:

1. Only phi-weighted mediants of the form (a+bɸ)/(x+yɸ) where ay-bx=±1 are noble. (Others might be considered "ignoble"). It's useful if your tool can still calculate them, certainly, but it shouldn't imply that they are noble — only that they are phi-weighted mediants.
2. The second issue is similar. The answer your tool gives depends on the order in which you give the arguments. So, if you gave it e.g. (4+3ɸ)/(5+4ɸ), at least that's still a noble number, but the original definition of noble mediant says that it's only the one where the phi-weight is given to the more complex interval, i.e. (3+4ɸ)/(4+5ɸ). See the quote below.

For two such interval ratios i:j and m:n where i:j is the simpler ratio:

                                   (i + Phi * m) 
    NobleMediant(i/j, m/n)     =   -------------  
                                   (j + Phi * n) 

3. The term complexity is used in this paper to mean both (a) the
   complexity of the ratio as given (e.g.) by the product of its two
   sides when in lowest terms, and (b) the way an interval sounds to us.
   We must point out that these do not always correspond, as Paul
   Erlich's example of 3001:2001 makes clear.

So perhaps you can make that clear as well.