# Comparing Math In Relation To Harmonics And Tonal Color Of Instruments

Improved Essays

Musical Notes Can Count
Jerri Pineda
Abstract— The development of mathematics involves early connections with music and the basic physics of sound. Mathematics is present in the natural occurrence of the ratios and intervals found in music and modern tuning systems. As people age, their hearing becomes dull and require change in the music ratio and interval to hear the same tune as when young. In like manner, the interval increases until a perfect pitch is heard. In this paper we will examine both the mathematics and music background for these ideas. We will examine the Fourier series representations of sound waves. Furthermore, we will see how they relate to harmonics and tonal color of instruments. The goal in this paper is aimed at exploring
to a Greek philosopher named Pythagoras. Pythagoras is best known for discovering the Pythagorean Theorem. In fact, most people will know him best for the Pythagorean Theorem in relation to geometry or trigonometry. However, this is not his only claim to fame. Pythagoras studied music as well, and understood the arithmetical relationships between pitches. It is said that he discovered the relationship between number and sound. He believed that numbers were the ruling principal of the universe. Pythagoras turned to the vibrating string. He explored the ideas of the length of strings and pitches. He also found simple ratios relating to harmonizing tones. This is due to the human ear that is not able to numerically analyze sound. Pythagoras turned to the vibrating string and explored the ideas of the length of strings and pitches. A musical tuning system is based on these discoveries. These ratios and harmonizing tones come from the harmonic series. This discovery will be discussed later with greater detail later. The basic idea for now is that harmonics are tones that have frequencies that are integer multiples of the original tone. Harmonics are also tones with a fundamental tone. The fundamental and its harmonics naturally sound good together. Each tone has a harmonic series, which can be used to fill in a scale of notes. Western music is based on harmonic series. When a note is played on an instrument, due to the physics of the sound waves, we don’t hear only that tone that is played. We also hear the played tone as the fundamental, as well as a combination of its harmonics sounding, at the same time. After Pythagoras discovered harmonics, many more explored the idea more thoroughly. At least two unassociated men took significant steps in defining harmonics. The first of these is Marin Mersenne (1588-1648), a French theologian, philosopher, mathematician, and music

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