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The Implication-Realization (I-R) model of melodic expectation was developed by Eugene Narmour as an alternative to Schenkerian analysis centered less on music analysis and more on cognitive aspects of expectation. The model is one of the most significant modern theories of melodic expectation, going into great detail about how certain melodic ...
In vocal music, contrafactum (or contrafact, pl. contrafacta) is "the substitution of one text for another without substantial change to the music". [1] The earliest known examples of this procedure (sometimes referred to as ''adaptation'') date back to the 9th century used in connection with Gregorian chant.
Schenkerian analysis is a method of analyzing tonal music based on the theories of Heinrich Schenker (1868–1935). The goal is to demonstrate the organic coherence of the work by showing how the "foreground" (all notes in the score) relates to an abstracted deep structure, the Ursatz.
Logical consequence is necessary and formal, by way of examples that explain with formal proof and models of interpretation. [1] A sentence is said to be a logical consequence of a set of sentences, for a given language , if and only if , using only logic (i.e., without regard to any personal interpretations of the sentences) the sentence must ...
Let S v be the set of equivalence classes of extensions of v to L and let G be the Galois group of L over K. Then G acts on S v by σ[w] = [w ∘ σ] (i.e. w is a representative of the equivalence class [w] ∈ S v and [w] is sent to the equivalence class of the composition of w with the automorphism σ : L → L; this is independent of the ...
Implication alone is not functionally complete as a logical operator because one cannot form all other two-valued truth functions from it.. For example, the two-place truth function that always returns false is not definable from → and arbitrary propositional variables: any formula constructed from → and propositional variables must receive the value true when all of its variables are ...
The set of exceptional points on is called the ramification locus (i.e. this is the complement of the largest possible open set ′). In general monodromy occurs according to the fundamental group of W ′ {\displaystyle W'} acting on the sheets of the covering (this topological picture can be made precise also in the case of a general base field).
A set C of attributes is a concept intent if and only if C respects all valid implications. The system of all valid implications therefore suffices for constructing the closure system of all concept intents and thereby the concept hierarchy. The system of all valid implications of a formal context is closed under the natural inference.