ABSTRACT
Music is linked to isometric transformations, a shape-preserving transformation, or movement, in the plane or in space, such as reflection, rotation, and translation and their combinations, to harmonic symmetries and matrices. In music it is possible to do horizontal scaling, which implies a change in tempo, and vertical scaling, a change in the interval distance between the notes. Since ancient times, mathematicians exhibit a natural affinity to music. Archytas, an Italian born ancient Greek philosopher mathematician, astronomer, statesman, and strategist, was a scientist of the Pythagorean school. He gave the numerical ratios for the intervals of the tetrachord on the enharmonic, the chromatic and the diatonic scales. Claudius Ptolemy, a Greco-Roman astronomer, mathematician, astronomer, geographer, and astrologer, analyzed some of the Pythagorean ideas and the music of the spheres. In case there are no strings attached, the two waves will move indefinitely, in opposite directions.
