Fundamentals Of Music Analysis

Fundamentals of Musical Acoustics. New York: Dover
Publications Ferrara, Lawrence (1991). Philosophy and the
Analysis of Music. New York: Greenwood Press.
Johnston, Ian (1989). Measured Tones. New York: IOP
Publishing. Rowell, Lewis (1983). Thinking About Music.
Amhurst: The University of Massachusetts Press. "Music is the harmonization of opposites, the unification of disparate things, and the conciliation of warring elements...Music is the basis of agreement among things in nature and of the best government in the universe. As a rule it assumes the guise of harmony in the universe, of lawful government in a state, and of a sensible way of life in the home. It brings together and unites." - The Pythagoreans Every school
student
Ironically or coincidentally, these tones were all members of the
Pythagorean scale. In addition, Pythagoras initiated comparable experimentation with pipes of different lengths.
Through this method of study he unearthed two astonishing inferences. When pipes of different lengths were hammered, they emitted different pitches, and when air was passed through these pipes respectively, alike results were attained. This sparked a revolution in the construction of melodic percussive instruments, as well as the wind instruments. Similarly, Pythagoras studied strings of different thickness stretched over altered lengths, and found another instance of numeric, musical correspondence. He discovered the initial length generated the strings primary tone, while dissecting the string in half yielded an octave, thirds produced a fifth, quarters produced a fourth, and fifths produced a third. "The circumstances around
Pythagoras' discovery in relation to strings and their resonance is astounding, and these catalyzed the production of stringed instruments." (Benade, 1976). In
He then reproduces that melody in a different pitch using mathematical transposition. After this, a second melodic theme is created. Returning to the initial theme, Mozart spirals the melody through a number of pitch changes, and returns the listener to the original pitch that began their journey. "Mozart's comprehension of mathematics and melody is inequitable to other composers.
This is clearly evident in one of his most famous works, his symphony number forty in G-minor" (Ferrara, 1991).
Without the structure of musical relationship these aforementioned musicians could not have achieved their musical aspirations. Pythagorean theories created the basis for their musical endeavours. Mathematical music would not have been produced without these theories. Without audibility, consequently, music has no value, unless the relationship between written and performed music is so clearly defined, that it achieves a new sense of mental audibility to the Pythagorean skilled listener.. As clearly stated above, Pythagoras' correlation between music and numbers influenced musical members in every aspect of musical creation. His conceptualization and experimentation molded modern musical practices, instruments, and