Math Modeling Essay Example | Topics and Well Written Essays - 750 words

Math Modeling - Essay Example Thus both the subjects are pure creations of the human intellect and exist only in our creative plane of abstraction. In its outset, it seems surprising that there must be a mathematical basis for music, but centuries of mathematical thought form the theoretical foundation upon the modern musicology has been built. All fields of modern mathematics have found applications in musicology – from the simple tuning of instruments and the description of notes to numerical algorithms for tonal temperament. The very description of notes begins with mathematics. All the notes that we are familiar of - A, B, C major, C minor- and so on are ratios of each other. Music is nothing but the harmony of sound waves reaching our ears. Each wave is characterized by its amplitude (which determines its sound or pitch), frequency, shape of its wave envelope, beat and so on. The ‘A’ note for example has a standard frequency of 440 Hz. All corresponding notes until the next octave of 880 Hz are in a fixed ratio to each other (this ratio is the subject of our further discussion). It has been found from our experience that these notes are melodious and when played in the correct combinations create the sensation of music. This description might create a rather mechanistic view of melody but the selection of the right notes is not easy and can come only with deep knowledge, practice and a more than an average talent. String instruments use this manipulation of notes (or equivalently frequencies) to the fullest. A flute produces unadulterated notes. A string on the other hand also produces what are known as ‘harmonics’ of the original notes. A 440 Hz note has its ‘first Harmonic’ at twice the frequency and half its amplitude, the second harmonic at thrice its frequency and a third of its amplitude and so on. This iteration can continue as long as the frequencies are too high to be discerned or the amplitude is too low to be heard. Thus the