Proportion Sequences of Babylonian Medieties

In this chapter (Proportion Series of Babylonian Medieties) we consider the process of perpetual averaging – formations and in this way obtain whole families of babylonian medieties chains as nested iterations. This can be done both in the interior of the interval [a, b] and in its exterior. It leads us to the following three types of iterated mean-value-proportion chains: Hence, chains of proportions of arbitrarily great length are created. For these, too, a harmonia perfecta maxima infinita can be developed, which describes the symmetries running to infinity and thus provides an inner order for the processes of boundless – and partly microtonal – interval generations.