منابع مشابه
Learning syntactically significant temporal patterns of chords: A masking field embedded in an ART 3 architecture
-In the traditional harmonic s),nta.x of classical music, temporal patterns of chords vao, in length, they often nest one within another, and they may lack overt markers indicating pattern boundaries. Tire selJ:organized learning of such patterns can be accomplished by a maskingfwld embedded in an ART 3 architecture. A simulation of learning the chord patterns in the music of Handel uses a dyna...
متن کاملRequiring chords in cycles
R. E. Jamison proved that every cycle of length greater than three in a graph has a chord—in other words, the graph is chordal—if and only if every k-cycle is the sum of k − 2 triangles. This result generalizes to having or not having crossing chords and to having strong chords, with similar characterizations of a variety of graph classes that includes chordal bipartite, distance-hereditary, an...
متن کاملIntersecting Chords Theorem
This entry provides a geometric proof of the intersecting chords theorem. The theorem states that when two chords intersect each other inside a circle, the products of their segments are equal. After a short review of existing proofs in the literature [1, 3–5], I decided to use a proof approach that employs reasoning about lengths of line segments, the orthogonality of two lines and Pythagoras ...
متن کاملPregroup Grammars for Chords
Pregroups had been conceived as an algebraic tool to recognize grammatically well-formed sentences in natural languages [3]. Here we wish to use pregroups to recognize well-formed chords of pitches, for a given definition of those chords. We show how a judicious choice of basic and simple types allows a context-free grammatical description. Then we use the robustness property to extend the set ...
متن کاملThe chords' problem
The chords’ problem is a variant of an old problem of computational geometry: given a set of points of , one can easily build the multiset of the distances between the points of the set but the converse construction is known for a longtime as difficult. The problem that we are going to investigate is also a converse construction with the difference that it no more the one of the distances multi...
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ژورنال
عنوان ژورنال: The Musical Times
سال: 1922
ISSN: 0027-4666
DOI: 10.2307/912213