Pythagoras found the fundamental musical laws, which relate to musical proportions, such as an octave, a fifth, and a fourth (Gamwell, 149). These ratios of tones have been found to give a satisfying feeling to the listener which is created when mathematics are applied. This discovery was the first scientifically well grounded theory of musical harmony. The Golden Mean ratio, which is rounded to 1.618: 1, and its inverse .618: 1, has also been known to show up throughout musical history. Explanations of the Golden Mean can be seen with a brief description of the Fibonacci sequence. The Fibonacci sequence comes up everywhere in nature from the branches and leaves on trees, to the reproductive cycle of certain animals. Numerically shown as 1, 1, 2, 3, 5, 8, 13, 21 with each number being the sum of the two previous numbers going on into infinity. On many trees, branches come forth as you go up the tree in this sequence. You start with 1 trunk, then one 1 branch, then 2 branches, then 3, and so on. We find that the ratio of one number in the sequence to the previous number in the sequence approaches the Golden ratio. The Golden Mean is a special relationship between a part and a whole that acts as a formula for harmony and beauty. Awareness of the Golden Mean's importance has been instrumental in the acceleration of culture throughout history, and is only partially conveyed through musical artwork. Pythagoras is known for his knowledge of arithmetical, geometrical, harmonic proportions, and also for the law of the golden section, otherwise known as the Golden Mean (Stakhov). The Golden Mean proportion began to come up when Pythagoras related his musical theories to the planets of the solar system. He believed that each planet had its own individual tone, which was related to its velocity around the sun (Gamwell, 149). He, and other philosophers and scientists of the time, such as Johannes Kepler looked into this idea of the planets, and how they relate to the golden section.
