Transcription metadata
     The NeumesXML data stack
Without intending to be formal for its own sake, a somewhat rigorous presentation of concepts is needed so that we can clearly explain the principles on which the NEUMES classification scheme is based.

Definition 1.  An individuation scheme [after Devlin 1] is a set of patterns (be they patterns of concepts or of perceptions) by which a one's mind judges things to be semantic objects, i.e., individual entities of meaning. Given a collection of things, one can use various individuation schemes according to one's intentions at the moment. Some individuation schemes are so common that this definition is superfluous, as, for example, the scheme of individuation for letters of a text. The definition is useful, however, when we discuss less-well-understood objects like neumes. It should be noted that individuation entails more than differentiation, as the first assigns meaning to things, whereas the latter merely judges whether things are the same or different.

Definition 2.  This definition of data representation [Barton 2] relies heavily on the notion of an individuation scheme. A data representation is a mapping (or, correpondence function) from a set of individuated objects, to a set of discrete binary codes. In the degenerate case, ion of a set of objects to abstract from The presence of the manuscript facsimile obviates the need for a strictly diplomatic transcription, and readers may well disagree over fine distinctions in word division, and the like, but will have the electronic facsimiles, including close-up ultraviolet and backlit images, as arbiters. A transcipt does not aim any more at replicating the original, but it becomes essential to extracting information from the document and to representing it in a processable form [Buzzetti;].

Definition 3.  A contingent set is finitary set (i.e., a collection that has countably many members) whose membership cannot be completely enumerated. One can assert, for example, that at any particular time t0, the set of all ants in the world has a finite number of members, and yet as a practical matter it is impossible to count them. The set of neumed documents (at least, under the current state of scholarship) is a contingent set, because their membership is certainly finite, but no one knows how many there are.

[1] Devlin, Keith, Logic and Information, (Cambridge, England: Cambridge University, 1991).
[2] Barton, Louis W. G. "Context-Free Grammar for the Data Representation," online at

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