Numerical Representation of Variants of Orally Transmitted Tunes

It is a well-known fact that orally transmitted (folk) tunes exist in many variants, which differ from each other musically, textually, and even in the language used.  Sometimes the affinity of a variant with an ideal model-tune is obvious, sometimes it is hard to recognize, harder to establish.  In comparative musicology and folklore the proof of the affinity of a variant or contrafact with a model-tune is a frequent problem: it can rarely be solved with mathematical accuracy.  For the oral tradition of a tune is ever-changing, depending upon the place, time, and the singer; and even when it is notated, the musical signs and symbols fix only discrete tones while neglecting the frequent portamenti di voce or other ligatures, not to mention the many personal habits in the voice production of the singer or transmitter.  The problem of identifying and relating the variants of a model-tune is particularly important, when we compare two or more melodies with different texts, which appear or are claimed to be variants of one and the same model-tune.