An Innovative Numerical System Model for Identify Effects and Psychological States of Musical Rhythm and Tempo through Four Temperaments

Rhythm, as one of the most important elements of music, has significant effects on human existence, which its characteristics can be systematically investigated and analyzed through mathematical relationships and numerical rules. The purpose of this research is to identify psychological states and effects of the time signatures of rhythm and tempo in music on humans which is determined by implementing an ancient thought about humans' four temperaments along with innovative numerical rules. The results of calculations show that the temperament of the time signatures 6/4, 6/8, 5/8, 11/8, 15/8, 24/16, 33/8 are warm and dry, 2/4, 8/8, 18/16 are warm and moist, 3/4, 7/8, 12/4, 12/8, 21/8 are cold and moist, and 4/4, 4/8, 9/4, 9/8, 16/8 are cold and dry. In addition, the tempo temperament identification model shows the difference between the psychological state of a rhythm at different performance metronomes. Moreover, the present calculation methods for simple, combined, and irregular time signatures confirm each other's accuracy. This mutual confirmation in the calculation methods validates the reliability of the identified rhythmic temperaments.