Download The Role of Harmonics in the Scientific Revolution

Reading guide
Christensen, ch. 8
“The Role of Harmonics in the Scientific Revolution” by Penelope Gouk
Know who and where Gouk is.
Preparation:
Review the basic tenets of Pythagorean/Platonic philosophy:
The order of the world is explained by n__________________.
Numbers exist in a t____________________ world of I_____________.
The key to the explanation comes from numbers in r________________.
The ratios favored are m____________________ and s____________________________.
p. 223
¶1 When did the scientific revolution occur?
What two books mentioned here played key roles in the revolution?
¶3 The previous paragraph divided ancient harmonics into Pythagorean and Aristoxenian
branches. Yet here Gouk says that a broader, speculative concept could be contrasted to
“this realm of practical harmonics.” She uses the term Pythagorean again to indicate this
speculative view. How would you define practical Pythagorean harmonics? How would
you define speculative Pythagorean harmonics? (For the second answer, see the top of p.
224.)
p. 224
¶1 Gouk talks here about three relationships of number and the world:
(1) Numbers in ratio explain the worlds, the soul, and audible music, and the similarity of
the numerical explanations reveals a special relationship between the three realms.
(2) Numbers can be manipulated to bring about hidden powers of nature. Arranging
numbers in a square, for instance, can bring healing.
(3) Numbers in many relationships will provide the keys to the structure of the universe,
including planetary motions, acoustical phenomena, and other wonders.
How are these views similar? How are they different?
“bodies at a distance”: Newton's conception of gravity was not accepted by many people at
first and was not accepted by Einstein (hence one of the needs for the theory of relativity)
because it involved an effect on one body caused by a body not touching it. This seemed
like magic. (Think of a voodoo doll.)
“sympathy”: Gouk draws another interesting parallel using this word. When you feel
something deeply, you talk with a friend, and if that friend is sympathetic, she will start to
feel the way you do, make the same expressions, and agree with the things you say.
Gouk – p. 2
When the dampers on a piano are open and one low string is played, other strings that
harmonize with it begin to vibrate. You can hear this for yourself by pressing C, E, and G
silently, and then striking a low C loudly. After you let up the key for the low C, you can
hear the chord softly sounding. These are called “sympathetic virations.” It is as if the
expression of the low C seeks like-minded souls, and when those other souls hear what C
has to sing, they want to sing along. Isn't it interesting that science honors this similarity
with the term “sypathetic vibrations” but does not honor the effect of the voodoo doll?
Here also the conditions of one body supposedly cause similar conditions to appear in a
similar body. How is the case different?
p. 225
¶1 How long was Boethius still used as a text in universities? Was this at bizarre little
universities that weren't really having any effect on the world?
¶2 For the last few centuries of its regular use, the Fundamentals of Boethius was of use to
whom? It was of no practical use to whom?
¶3 Be sure you know the Latin of these Boethian phrases at least by sight.
¶4 By the seventeenth century, what happens to Boethius' hierarchy of the three musics?
p. 226
¶0 I love this kind of thing! Once upon a time, I was taught that in the 17th century, Europe, by
giving up its dependence on ancient beliefs, allowed itself to develop modern science and
a more sure path toward truth and power. But Gouk points out that Europe let go of only
certain ancient beliefs, allowing itself to develop both science and occult arts.
¶1 What Florentine was the leader in reviving certain ancient occult beliefs?
What kinds of beliefs were involved?
What famous ancient Greek philosopher is associated with this movement?
What was the new view of that philosophers's system called, and who wrote the classic text?
When did this new interest in ancient Greek philosophy occur compared to the fall of
Byzantium?
p. 227
¶1 History class taught you about another musical movement going on in Florence in the 1580s.
What was it and how did it compare to the subject of this paragraph?
¶2 What four authors from the Age of Science wrote on planetary music (“universal harmony”)?
Gouk – p. 3
Did you notice Kepler on that list? If you don't know how important he is in the history of
science, look him up in the encyclopedia. Again, weren't you taught that the Age of
Science was made possible by giving up ancient beliefs? And here's Kepler writing on
the music of the spheres!
p. 228
¶1 What (or–big hint!–Who) provided the basis for belief in the order of the universe?
Why was Fludd's musical scheme rejected by the more scientific minds?
p. 229
¶0 “the harmonies of the heavens had fallen silent”: an unusual and welcome poetic utterance!
¶1 “Pythagorean”: There's that word again! Which part of the Pythagorean/Platonic cluster of
ideas do you think Newton retained? That 2 existed as a transcendant ideal? That
superparticular ratios explained the universe?
p. 231
¶0 Fludd's pictures are beautiful, but they are indeed flawed. Do you notice that each octave
takes up half the string? What misunderstanding does this reveal?
¶1 What is the main difference between this neo-Platonic relation of music-and-the-universe and
the (standard) ancient view?
p. 233
¶1 This is not really written so we can totally understand it, so don't worry about trying. Just
have fun with it.
¶2 “syntonic diatonic”: An interesting glimpse into a part of history not mentioned previously in
this book! In ancient times, Ptolemy and other Greeks had actually described hundreds of
different tuning systems, perhaps only as mathematical exercises. The just intonation that
was “discovered” centuries later had already been described by Ptolemy. Ptolemy's name
for this just tuning is used several times in the chapter, so make note of it.
p. 234
¶0 Again, it's not really essential, but I can give you a little help here. You may know these
shapes from the dice used in fantasy and adventure games. Kepler, sure that there was a
pattern, wanted to explain why the planets lay at certain distances from the sun. He hit
upon the idea of nesting these shapes inside another like Russian dolls, noting how large
each shape would have to be in order to fit the next smaller shape inside. The
relationship of these sizes, according to Kepler, was the relationship of the distances from
the sun to each of the planets.
Gouk – p. 4
p. 235
¶1 After several attempts, Kepler finally found a way to relate the distances of the planets and the
notes of the scale, as tuned in just intonation. I don't understand just how the relationship
worked, and this account doesn't explain it. You just need to remember that Kepler
believed he succeeded in relating the just tuning of a scale to the relative distances of the
planets. He discovered the contemporary account of just intonation in what theorist?
What explanation from this theorist did he not accept?
¶2 “the inverse square law”: Gouk tells us this has nothing to do with music theory, but I think
every educated person should know it, so I'm taking the opportunity. This law states that
gravitational force between two bodies weakens in relation to the square of their distance.
So if one planet is 3 times farther from the Sun than another, the gravity between it and
the sun will be 9 times weaker.
p. 236
¶1 Here is a beautiful illustration of the difference in the new thinking. According to Mersenne's
theory of consonance (what is it called?), a 3:2 fifth is consonant because the striking of
its vibrations upon the ear is more coordinated than that of the 7:4 tritone. How is this
like the old Pythagorean theory, and how is it unlike it?
This new view is called “mechanics.” How does Gouk define mechanics (or “mechanical
philosophy”)?
¶3 Again, a little help on something not essential to music theory. “Corpuscular” means
“involving particles.” Newton and Hooke and Huygens debated the nature of light, and it
is still mysterious. Is there such a thing as a bit of matter called a photon, or is light (like
sound) a wave moving through other material particles? These two ideas are called “the
corpuscular theory” and “the wave theory” respectively.
p. 237
¶0 If the wave theory is true, then, since light moves through space, space cannot be a vacuum.
Hence the theory of ether or spiritus.
¶1 Here's the first part of Newton's musical theory you ought to know, and Gouk doesn't explain
it well. Newton's theory was based on looking at the spectrum he made with his prisms,
finding the borders between colors (a problem: how can you determine the exact border
between green and yellow in a spectrum?), and measuring the distances between those
borders. These relationships, he claimed, are the same as those of the justly tuned Dorian
scale. What do you think would be the implications if this were true?
p. 238
¶0 Whether you understand the explanation or not, you should know this second point of
Newton's contributions to musical theory: he explained how sound waves travel through
Gouk – p. 5
air.
¶1 “isochronous” = taking equal amounts of time. By watching pendulums, Galileo discovered
that, for instance, no matter how high your child goes on the swing, the amount of time it
takes him to swing back and forth once is always the same. In the same way, a violin
string will vibrate always the same speed no matter how hard you pluck it or bow it.
¶2 Again, while it isn't essential to music theory, I insist that everyone know what “heliocentric”
and “geocentric” mean! If you don't know, the Copernicus presentation in class should
help.
p. 239
¶0 Newton is a fascinating character in western history. I hope you enjoyed the account. The
essential point for us of the last paragraph–the third and last of the main Newton points–is
that Newton also found just intonation to correspond to proportions in the planetary
orbits.
¶2 How does Descartes liken the body to musical instruments?
p. 241
¶1 Did it ever occur to you that the phrases “high strung” or “keyed up” come from music
theory? Can you think of other similar phrases?
¶2 Through the 17th century, the three musics were still recognized, although they were connected
by two new views: neo-Platonism and mechanics. (Be sure you can define these two
views and give some names and key terms associated with each.) Now we find that, by
1750, the connection between music, the soul, and the planets is no longer accepted.
What is the first reason for this separation?
p. 242
¶0 Gouk says that during the 17th century, music served as the explanation for other phenomena,
whereas in the 18th century, the age of Enlightenment philosophy, the mathematical laws
themselves served as the explanation. I'm not sure I was convinced of this from her
account. What do you think?
¶1 What is the second reason for the separation?
¶2 and p. 243, ¶0: By 1750, music had become detached from philosophy, reason, and
explanation, and had become associated with what?
p. 243
¶1 What is the third reason for the separation?