Monday, March 14, 2016

MORE ON MONOCHORDS, PYTHAGORAS, and MUSIC

PYTHAGORAS and MUSIC PART 1
PYTHAGORAS and MUSIC PART 2
PYTHAGORAS IN MOTION
PYTHAGOREAN MONOCHORDS
HARMONIC OVERTONES
http://www.jazclass.aust.com/lessons/jt/jt09.htm

Thought for the Day:
The Basics of Sound;
The Overtone Scale
Leonard Bernstein Explains:
Harmonic Series I

THE OVERTONE SERIES
EXPLAINED BY DAVID BURT
https://www.youtube.com/watch?v=w2CA0w85Hfw

http://www.slideshare.net/cogleysclass/math-and-music
PYTHAGORAS MUSIC BASED ON
MATHEMATICAL CALCULATION
video
Pythagoras discovered that a monochord
(single tone) vibrates not only at its
fundamental frequency, but also in partial
segments – halves, thirds, fourths, etc., to
a theoretically infinite degree. The harmonic
series are the notes (or partials) that are
created when a fundamental note is struck.
It is the presence of these overtones that
creates tonal color, and that helps us to
differentiate the sounds of a harpsichord
and a piano, a trumpet and a trombone, or
one voice and another. Humans do not
perceive overtones much past the fifteenth
partial, because as overtones become
higher, they become increasingly difficult
to hear.

The music of the spheres:  the elegant and poetic idea that the revolution of
 the planets generates a celestial harmony of profound and transcendent be
auty

READ ABOUT PLATO and PYTHAGORAS:

by NPR STAFF
It sounds like something out of a Dan Brown
novel, but a scholar in Manchester, England,
claims to have found hidden code in the ancient
writings of Plato. If true, the secret messages
would have made the ancient philosopher and
mathematician a heretic in his day.
Inner%2BWorld
Jay Kennedy tells NPR's Guy Raz that his
discovery was partially luck. Looking at Plato's
works in their original scroll form, he noticed
that  every 12 lines there was a passage that
discussed  music. "The regularity of that
pattern was supposed to be noticed by
Plato's readers," Kennedy says.
Inner%2BWorld
Music in ancient Greece was based on a 12-note
scale, unlike the eight-note scale of modern
Western music. Kennedy posits that Plato
deliberately inserted discussions of music every
12 lines to send a secret, musical message.
Inner%2BWorld
What Plato couldn't tell people was that he was a
closet Pythagorean. Pythagoras and his followers
believed that mathematics and music were the
key to the universe.
Inner%2BWorld
"The Pythagoreans realized that when we hear
beauty and music, when we hear notes
harmonizing, that's because the notes have
simple ratios, like 1:2 or 3:4," Kennedy explains.
"So the beauty of music is direct perception of
the mathematical order underlying the world.
They worshipped that mathematics."
Inner%2BWorld
But the Pythagoreans were a persecuted sect,
Kennedy adds, sometimes violently persecuted.
"They were a threat to traditional religion, like
many new sects." Plato's own teacher, Socrates,
was famously executed for religious heresy. 
Inner%2BWorld
"Simply put, they were threatening to overthrow
the gods on Olympus and put numbers and
mathematics in its place. Prior to Socrates being
executed, a number of other philosophers were
banished or fled because of threats to themselves.
It was dangerous in those days to be a philosopher."
Inner%2BWorld
As far as Kennedy can tell, Plato's message was
one of solidarity simply by acknowledging the
relationship between music and mathematics,
but he suspects there's more to it. "Perhaps
some scholar will find that — in The Republic,
at least — that there is something like a melody
or a score embedded in the text," he says. 
Inner%2BWorld
If that's true, then we've read only half of Plato's
writings. "There are all these hidden layers of
meaning which will enrich our understanding of
Plato," Kennedy says. And maybe what else
Plato has to say could help us today. 
Inner%2BWorld
"Plato's philosophy shows us one way to combine
science and religion," Kennedy says. "The culture
wars we're having today — about evolution for
example — see science and religion as two
polarized opposites. Plato's hidden philosophy
shows us that he combined an emphasis on
mathematics with an emphasis upon beauty,
music, art and divinity. The founder of western
culture, in fact wanted us to combine science
and religion."