6533b828fe1ef96bd1287833

RESEARCH PRODUCT

Fuzzy tuning systems: the mathematics of musicians

Vicente Liern

subject

Artificial IntelligenceLogicPythagorean theoremCalculusMathematical propertiesEqual temperamentArithmeticFuzzy logicMathematicsJust intonation

description

We present some mathematical properties which determine tuning methods. We introduce the concept of fuzzy tuning systems and we analyze four of the systems coexisting within the current orchestras: Pythagorean, Just Intonation, Holder's and Equal Temperament systems. We show that the theoretical and practical tuning methods are the same. We introduce the idea of compatibility between tuning systems and we give some sufficient conditions to determine an appropriate number of notes into which the octave must be divided.

yearjournalcountryeditionlanguage
2005-02-01Fuzzy Sets and Systems
https://doi.org/10.1016/j.fss.2004.04.002