ORIGINS OF MUSICLecture 5 Part III

Physics of Music

September 28, 2004

About 10,000 ya

5000 year old

Ancient Chinese Bells, more than 1,000 years old, on display at Wuhan

The musical scale used today was first discovered by the Greek mathematician Pythagoras in the 6th century BC. While playing the lyre, he noticed that he could create the different harmonics by placing his finger at fractional points on the string. Where he placed his finger corresponded to the nodes of each harmonic.

Pythagoras

Facts about Pythagoras

• He may never have existed!– None of his writings have survived– All we know about him is handed down by

writings of other people– A cult seems to have been built around his

philosophy which “may” even exist today.• Someone may enjoy researching this assertion!

He founded a philosophical and religious school in Croton, which made outstanding contributions to the field of mathematics. Pythagoras and Pythagoras and his cult members believed that his cult members believed that everything was related to everything was related to mathematics and agreed that, mathematics and agreed that, ultimately, "all is number". ultimately, "all is number". Pythagoras is also famous for his study of acoustics and his theorem relating the lengths of the sides of a right triangle, which confirmed the existence of irrational numbers.

Pythagoras

The Structure of Ancient Education

This famous drawing of Pythagoras engaged in testing the relationships of music and numbers dates from a 1492 book of Gaffurius: Theorica Musices, Milan, 1492.

From the Anvil flowed an idea (?)

Pythagoras

The Monochord

Pythagoras Observed …..

• The heavier the bell, the “lower” the tone.

• The water inside a glass was directly related to the tone.

• He probably NEVER made any of these observations.

• But he did look at STRINGS and he did But he did look at STRINGS and he did some very interesting science”.some very interesting science”.

Closer to us.

A SCIENTIFIC INSTRUMENT

Modern Design

L0

L1

L2

FIRST OBSERVATION

• The shorter the plucked length of the string, the “higher” the tone.

• With TWO strings, some lengths sounded well together and some did not.

• Pythagoras studied this carefully and developed the “mathematics” of the musical scale.

CLARIFICATION

• The musical scale was NOT invented by Pythagoras or by anyone else that we know of.

• But he STUDIED IT.• The scale was developed naturally based

upon which tones sounded well together.• The scale probably goes back to the

Neanderthal times (bone flute).

Pythagoras Looked for “Consonance”

• What length of string will be consonant with the open string?

• What is consonance??

Consonance• Two tones are consonant when they sound

pleasing together.• They are dissonant if they do not.• BUT whether or not a harmony is pleasing is

a matter of personal taste, as there are consonant and dissonant harmonies, both of which are pleasing to the ears of some and not others.

• Pythagoras did not subscribe to the last statement.

• Pythagoras tried to define the right string lengths for harmony.

MOST INPORTANT

• Most harmonious sound (according to Pythagoras was (L1/L0) = (1/2)

• This is called the OCTAVE

L0

L1

Properties of the Octave

• The two tones almost sound like the same tone!– Whatever that means.

• When men and women sing together in “unison”, they will sing an octave apart and think they are singing the same tone!

• The octave defines an INTERVAL between two closely related tones.

Octave

• Having defined the interval of the octave, we can proceed to put more tones between them to establish a scale of notes that may be easily played together.

• Some combinations will not be a consonant as others but they are still considered harmonious.

Notation – A practical necessity

FIRST TONE

OCTAVE

Notes between

5pentatonic

7diatonic

What about higher?

What about lower?

HIGH

LOW

Something Better

FDBGE

FDBGE

ECAF

●●

higher