Do maths here now

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This is a maths problem that I found interesting and there it is probably a solved/well known problem because it is so genral and basic.

I want to know if a chord contains the same interval several times or only has unique intervals. Every combination of 2 notes has to be considered and none of the resulting distances should be equal to eachother.

But you probably don't care about the application so here it is mathematically:
Let A be a set of natural numbers {a1, a2, ..., an}.
T(A) is the multiset of all possible differences between numbers in A with the conditions that for each pair of ai and aj:
ai > aj and i != j
This just means that we only consider each pair once and not the negative differences too and we don't consider pairs of 2 times the same element.
Essentially if you plotted A on a number line and draw and connect all points with all other ones, T(A) is the set of distances of all these bidirectional lines.

Now T(A) might have duplicate elements (which is why I said multiset) or it might night!
for A={1, 3, 7} T(A) = {2, 6, 4}, no duplicates but for A={1, 3, 7, 9} T(A) = {2, 6, 8, 4, 6, 2}, has duplicates!

So yea this is pretty much the "problem" (I dont know the proper terminology). Do what you want with it, I want to know if there is any pattern to which sets A result in a T(A) with duplicates and which don't and if there is a pattern to it.


An obvious theorem:

The cardinatlity of the multiset T(A) is n*(n-1)/2 because out of the n2 tuples we can form from A n have the same element twice (now we're at n*(n-1)) and for each tuple there is a corresponding reversed tuple but we only consider one of them (n*(n-1)/2).