Pythagorean Philosophy And Its Influence On Musical

Essay, Research Paper

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

passe

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