The general subject which underlies the following paper is the geometry of the practical composer, and I regret that I find it impracticable to deal effectively with even a part of that subject by any methods except such as involve much definition, symbolization, category, classification, cataloguing, and so forth. A broad and even aesthetic treatment of the same subject is no doubt possible, and surveys of that class are of great assistance to the art; it seems however sufficient to say that such is not the object of the present paper, which deals rather with the labour of the workshop proper. All the principal writers on the practical aspect of musical form have, whatever their special method, built up their subject in more or less of geometrical fashion. The composer himself must equally have such processes in his mind. More confusedly no doubt than has the analyst, for the sub-division of labour entails this; and perhaps only just enough for his own immediate purposes, for that is human nature. But still the processes must be there. The subject then in short demands a mechanical treatment, and I can only hope that I may be able to offer this with the least offence.