groups_euclid

application to sort out groups of harmonics

groups_euclid calls gp_euc and euclid to separate a set of harmonics into families or groups of related harmonics, each with its own fundamental tone. The euclid() function accepts two real numbers with uncertainty intervals, and returns their greatest common divisor (gcd), also a real number. The gp_euc() function accepts several real numbers with associated containing intervals, and returns their gcd. These two functions generalize the familiar euclidean algorithms for integers. For explanation and details please see the included Word document. Also note that visual_euclid(a,b) is an extra, visual version of euclid(), to demonstrate the rubber-band theorem.