On ordered weighted averaging aggregation operators in multicriteria decisionmaking
IEEE Transactions on Systems, Man and Cybernetics
Equal temperament and pythagorean tuning: a geometrical interpretation in the plane
Fuzzy Sets and Systems
Fuzzy Sets and Systems: Theory and Applications
Fuzzy Sets and Systems: Theory and Applications
An Interactive Case-Based Reasoning Approach for Generating Expressive Music
Applied Intelligence
On (un)suitable fuzzy relations to model approximate equality
Fuzzy Sets and Systems - Theme: Basic notions
Applying logistic regression to relevance feedback in image retrieval systems
Pattern Recognition
Music: A Mathematical Offering
Music: A Mathematical Offering
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A theoretical tuning system is a set of pitches that can be used to play music. It is a fact that the human ear perceives notes with very close frequencies as if they were the same note. Therefore, in our approach a musical note and its pitch sensation are modeled as L-R fuzzy numbers with a modal interval and a bounded support. We pay particular attention to the 12-tone equal temperament (12-TET) for being the most widely used tuning system and we define the fuzzy 12-TET composed of 12 fuzzy notes. A similarity relation between a fuzzy note and a theoretical note can be defined, and subsequently a similarity class associated to each one of the fuzzy notes in the fuzzy 12-TET arises. Finally, we study the similarity between the theoretical notes in a given score and those notes played by a musician making use of an OWA operator. Some numerical examples illustrate our approach.