Pythagorean Philosophy and its influence on Musical

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 will recognize his name as the originator of that
theorem which offers many cheerful facts about the square
on the hypotenuse. Many European philosophers will call
him the father of philosophy. Many scientists will call him
the father of science. To musicians, nonetheless,
Pythagoras is the father of music. According to Johnston, it
was a much told story that one day the young Pythagoras
was passing a blacksmith’s shop and his ear was caught by
the regular intervals of sounds from the anvil. When he
discovered that the hammers were of different weights, it
occured to him that the intervals might be related to those
weights. Pythagoras was correct. Pythagorean philosophy
maintained that all things are numbers. Based on the belief
that numbers were the building blocks of everything,
Pythagoras began linking numbers and music.
Revolutionizing music, Pythagoras’ findings generated
theorems and standards for musical scales, relationships,
instruments, and creative formation. Musical scales became
defined, and taught. Instrument makers began a precision
approach to device construction. Composers developed
new attitudes of composition that encompassed a
foundation of numeric value in addition to melody. All three
approaches were based on Pythagorean philosophy. Thus,
Pythagoras’ relationship between numbers and music had a
profound influence on future musical education,
instrumentation, and composition. The intrinsic discovery
made by Pythagoras was the potential order to the chaos
of music. Pythagoras began subdividing different intervals
and pitches into distinct notes. Mathematically he divided
intervals into wholes, thirds, and halves. "Four distinct
musical ratios were discovered: the tone, its fourth, its fifth,
and its octave." (Johnston, 1989). From these ratios the
Pythagorean scale was introduced. This scale
revolutionized music. Pythagorean relationships of ratios
held true for any initial pitch. This discovery, in turn,
reformed musical education. "With the standardization of
music, musical creativity could be recorded, taught, and
reproduced." (Rowell, 1983). Modern day finger
exercises, such as the Hanons, are neither based on melody
or creativity. They are simply based on the Pythagorean
scale, and are executed from various initial pitches.
Creating a foundation for musical representation, works
became recordable. From the Pythagorean scale and
simple mathematical calculations, different scales or modes
were developed. "The Dorian, Lydian, Locrian, and
Ecclesiastical modes were all developed from the
foundation of Pythagoras." (Johnston, 1989). "The basic
foundations of musical education are based on the various
modes of scalar relationships." (Ferrara, 1991).
Pythagoras’ discoveries created a starting point for
structured music. From this, diverse educational schemes
were created upon basic themes. Pythagoras and his
mathematics created the foundation for musical education
as it is now known. According to Rowell, Pythagoras
began his experiments demonstrating the tones of bells of
different sizes. "Bells of variant size produce different
harmonic ratios." (Ferrara, 1991). Analyzing the different
ratios, Pythagoras began defining different musical pitches
based on bell diameter, and density. "Based on
Pythagorean harmonic relationships, and Pythagorean
geometry, bell-makers began constructing bells with the
principal pitch prime tone, and hum tones consisting of a
fourth, a fifth, and the octave." (Johnston, 1989). 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 a
way, music is lucky that Pythagoras’ attitude to
experimentation was as it was. His insight was indeed
correct, and the realms of instrumentation would never be
the same again. Furthermore, many composers adapted a
mathematical model for music. According to Rowell,
Schillinger, a