(
// ~distance is a function that expects two triads as arguments and calculates
// the euclidian distance between them. In other words, it considers both
// triads as points in a three-dimensional space.
~distance = {
	arg tr1, tr2;
	// Given two triads tr1=[a, b, c] and tr2=[x, y, z], the euclidian distance is
	// defined as
	//    dist(tr1, tr2) = sqrt((a-x)² + (b-y)² + (c-z)²)
	// In sclang, we can use
	(tr2-tr1).sum({|i| i**2}).sqrt();
};

// ~findBestInversion expects two triads as argument and returns an inversion
// of the second triad that has the minimal distance to the first in terms of 
// steps in the voices.
~findBestInversion = {
        arg tr1, tr2; // triads given.

        // Let's generate an array of all inversions of the second triad.  We
        // will later find and return the one with the minimal distance.
        var inversions = [
                tr2,                          // root position
                (tr2 + [0 , -12, -12]).sort,  // first  inversion, down an octave
                (tr2 + [0 ,   0, -12]).sort,  // second inversion, down an octave
                tr2 - 12,                     // root position, down an octave
        ];

        // For each chord in the array `inversions` we calculate its ~distance
        // to the first triad and collect the results into an array.
        var distances = inversions.collect({|chord| ~distance.value(tr1, chord)});

        // Find the index that contains the minimal distance.
        var minIdx = distances.minIndex;

        // Return the inversion at that index as our choice for the progression.
        inversions[minIdx];
};

// Test it on C-major → e-minor.  Should return the first inversion, i.e. [-1, 4, 7].
~findBestInversion.value([0,4,7], [4,7,11])
)