Transcript ORIGINS OF MUSIC Lecture 5 Part III

ORIGINS OF MUSIC
Lecture 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
Pythagoras
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.
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!
Pythagoras
He founded a philosophical
and religious school in Croton,
which made outstanding
contributions to the field of
mathematics. Pythagoras and
his cult members believed that
everything was related to
mathematics and agreed that,
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.
The Structure of Ancient Education
From the Anvil flowed an idea (?)
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.
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
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
L0
L1
• Most harmonious sound (according to
Pythagoras was (L1/L0) = (1/2)
• This is called the OCTAVE
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
HIGH
What about higher?
Notes between
OCTAVE
5
7
pentatonic diatonic
FIRST TONE
LOW What about lower?
Something Better
F
D
B
G
E
F
D
B
G
E
E
C
A
F
●●
higher