Johannes Kepler (1571-1630) pondered the heavens while living
on the ground in Germany. He was primarily a mathematician, working
as a professor of that discipline, but was also very interested in theology
and astronomy. Unfortunately, his work concerning the heavens was
confined to working with other's observational data; when he was four years
old, a childhood bout with smallpox left him with poor eyesight for the
rest of his life. He did have the good fortune to be hired by the
great naked-eye astronomer Tycho Brahe (1546-1601), who was known for his
precise measurements of planetary movements. His accuracy was possible
due to his use of the finest equipment of the age in the observatory built
for him by King Frederick II of Denmark. (Tycho Brahe is also remembered
for a few other reasons as well - he wore a metal nose after his own was
cut off during a duel with swords; apparently he could be rather disagreeable
- probably even more so after the loss of his nose. His demise was
memorable in an equally bizarre fashion: he died after drinking too much
- not from alcohol poisoning, but from a burst bladder) (Kuhn, 58-60).
Tycho had hired Kepler for his mathematical skills, and wanted
him to attempt to verify Tycho's Earth-centered theory of the solar system.
Kepler probably had different reasons for taking the job: he had his own
ideas and theories that he wanted to test, but he couldn't see well enough
to make his own observations. Tycho's measurements were the most
accurateones made anywhere; taking a position as Tycho's assistant probably
seemed like a good way to get his hands on the data.
After Tycho's death, Kepler continued to work with his data,
searching for orbital shapes that could be used to predict the future position
of the planets in a heliocentric model of the solar system that would match
Tycho's observational data. After four years, he had worked out a
system of circles and epicycles, (orbits around the earth that would account
for retrograde motion of the planets), that would successfully predict
the orbit of Mars to within 0.13 degrees. This was not good enough
for Kepler; he knew that Tycho's measurements were accurate to within about
0.1 degree, and so continued to look for an answer to the problem using
perfect circles, as first suggested by Aristotle. After another nine
years of work, he finally hit upon the answer that would eliminate that
last 0.13 degree error - and the answer didn't use perfect circles at all,
but ellipses! (Kuhn, 60-61).
This discovery was published in Kepler's book The New Astronomy.
His work can be summarized into what are known today as the three laws
of planetary motion, or just Kepler's Laws:
1. All planets follow an elliptical orbit around the Sun, with the Sun at one focus of the ellipse.
2. A planet travels in its orbit at a speed that varies in such a way that an imaginary line from the planet to the Sun will sweep out equal areas in equal periods of time.
3. The squares of the times that the planets require to make complete revolutions around the Sun are in proportion to the cubes of their distances from the Sun (Kuhn, 62) (Menzel, 16).
Being a firm devotee of Pythagoras, Kepler also spent a lot of
time studying the five symmetrical solids: the tetrahedron, cube, octahedron,
dodecahedron, and icosahedron. He believed that they somehow held
a place in the planetary scheme of things, and did finally come up with
a consistent blueprint using these five solids to fix the distances of
the six then-known planets, but he would have had no way to account for
the planets discovered since his time (Kuhn, 64) (Menzel, 15).
As is so often the case for scientific researchers (and composers!),
Kepler received little recognition for his work during his lifetime.
He thought astrology was preposterous, but he was forced into casting horoscopes
to feed his family. His mother was convicted of being a witch, and
his wife and a child died of smallpox. At least, when he died, both
his nose and his bladder were intact (Kuhn, 64).
Kepler was the first piece in the series composed under the supervision
of Dr. Stuart Glazer at Florida Atlantic University. This work is
on a larger scale than any of the preceding pieces, and is consequently
more complex.
There are nine different parts for pitched instruments in Kepler,
each instrument being chosen to represent a planet of the Solar System.
In addition, comets, meteors, and asteroids are represented by non-pitched
instruments.
Mercury ---- Flute
Venus ------ Violin
Earth --------Electric
Piano
Mars --------Trombone
Jupiter ------ Cello
Saturn ------ Clarinet
Uranus ------Bells
Neptune ---- Bass
Guitar
Pluto -------- Oboe
Comets ------Tympani
Meteors & -- Percussion
Asteroids
Each planet/instrument relationship was determined by various
things: history suggested that a brass instrument might be appropriate
for the god of war, Mars; the agility of the flute seemed a perfect match
for the Solar System's speed demon: Mercury. A romantic instrument
such as violin was the only choice for Venus, the goddess of love, whereas
the size and ponderousness of the king of the gods, Jupiter, called for
cello and double bass, (which share the same part). At some time
in the past the author has heard a piece of music (Stravinsky? Holst?),
that used the clarinet to represent Saturn, the father of Jupiter, and
the association was so strong no other instrument seemed appropriate.The
distant coldness of Uranus, ancient father of Saturn and god of the heavens,
suggested bells; the loneliness of Pluto, the brother of Jupiter and ruler
of Hades, demanded an oboe. The Earth, the most familiar planet,
is represented by a keyboard, (electric piano), the instrument that is
most familiar to the composer. Quite frankly, Neptune, another brother
of Jupiter, received the bass guitar as a representative instrument because
that seemed one of the few remaining (traditional) sounds that would display
enough of a difference in timbre; (the composer couldn't really think of
an instrument that sounded as if it were underwater). The various
tympani and percussion sounds that are featured in Kepler seemed perfect
for those bodies that have wreaked such havoc upon all of the (visible)
planetary surfaces for so long: comets, meteors, and asteroids (Hamilton,
13-74).
The MIDI specification allows pan settings to be transmitted
from a sequencer to other devices. Each instrument in Kepler is panned
to a different area in the sound field. Beginning from the left side,
the order of panning is: clarinet (Saturn), cello (Jupiter), and flute
(Mercury). Electric piano (Earth), bells (Neptune) and tympani (asteroids)
are all in the center position. Continuing past the center to the
right are: violin (Venus), trombone (Mars), and finally oboe (Pluto).
The times signature was settled upon quickly: 9/4. The
nine represents the nine known planets; the four represents the four rocky
planets of the inner solar system.
The matrix for Kepler took a bit longer to determine. After
much thought and "doodling" with various numbers, it was decided to base
the row upon the lengths of the semimajor axes of the planets in our Solar
System. The semimajor axis of a planet's orbit is half of the greatest
dimension of that orbit:
As is illustrated in Table VI, the first two or three digits of the planet's semimajor axis were rounded off in various fashions to produce a two-digit approximation for use in the row. The figures for Uranus and Neptune would have been a repeat of previously used digits, and so were directly replaced by unused digits: Uranus' 2.9 became 0, and Neptune's 4.5 became 11, for a final row of:
5 8 10 2 3 7 9 1 4 0 11 6
Earth's semimajor axis was not included in the row.
In addition, each planet's orbital velocity was used to determine
the rows that were to be used in the representative instrument's part.
(In science, and indeed most other endeavors, it is usually desirable to
have a standard unit of measurement to use in all numeric references.
This was not done for Kepler, however; the use of different measurement
units was necessary to generate usable numbers for the matrix and rows.)
Kepler begins with a planetary conjunction - all instruments
entering simultaneously for the duration of a single half-note. All
except the Earth fade away quickly, leaving the representative instrument
of the first planet that humans were aware of playing solo for two measures,
beginning a sequence of rows that outlines the orbital velocity of Earth:
P0, P1, P8, P5, P1, and finally P0 again. This pattern of rows is
repeated five times during the piece, and is always involved in the piano
part except for a three-bar phrase beginning at measure 25 which uses only
P1, and a use of P0 at the end of the work.
The electric piano's entrance is followed by the entrance of
Venus' violin. It seemed reasonable to assume that, (being the brightest
object in the sky except for the Sun and Moon), Venus would probably have
been the first planet observed by primitive peoples. (This correspondence
of order of instrumental entries to order of planetary discoveries was
dropped in favor of musical considerations. The next "planet" that
appears is Jupiter, but might just as well have been Mars.) The violin
follows the rows specified by the orbital velocity, as do all of the pitched
instruments, in this instance R0, R2, R1, R7, and R6. The reader
will notice that only retrograde rows were used for Venus; perfectly reasonable
due to the fact that Venus turns on its axis in retrograde motion, a direction
opposite from that of most of the other planets. (Uranus and Pluto
also display this oddity, therefore their instruments, bells and oboe,
also use only retrograde rows.)
The cello, (Jupiter), makes its entrance at measure 5.
The orbital velocity of Jupiter is 8.12 mi./sec., so the order of rows
is P0, P8, P1, and P2. There is a single occurrence of P8 beginning
at measure 28 that stands alone; at all other times, the above pattern
is adhered to. Moving at a much slower pace that the Earth, Jupiter
only manages to proceed through its pattern twice, unlike Earth's five
times.
At measure 17, the electric piano begins a repeat of the material
at the beginning of the composition, with slight modifications in the rhythm.
The violin and cello drop out, and flute, clarinet, and trombone make their
first appearance. The violin returns in measure 23, but is now playing
pizzicato. Pluto's oboe enters at measure 26, the bells of Uranus
at measure 28, and the bass guitar which represents Neptune at measure
29. From this point on, the instruments drop out and return in different
places in the composition, displaying no real correspondence with any astronomical
data available to the composer, but their "dance" of entries and exits
may be taken to loosely represent the ever-changing combination of visible
planets in the night sky.
The various percussion instruments, (cymbals, tympani, trap set,
etc.), make their appearances when they are needed musically, since astronomically
speaking, the appearance of (new) asteroids, comets, and meteors is still
almost impossible to predict until these bodies are very close to the Earth,
or are discovered by accident. These instruments are not following
any row or underlying pattern, and are all non-pitched, except for the
tympani, of course. The tympani is treated as if it were an non-pitched
instrument; the notes it uses are either borrowed from an accompanying
planet's rows, (some meteorites discovered on Earth are thought to be pieces
of other planets "knocked off" by huge meteor collisions on those planets
far in the past), or have no meaning at all, other than musically.
Although the pitches used are not significant, there is an occurrence at
measures 28-33 characterized by percussion and a change of rhythm that
represents a meteoric bombardment, such as is thought to have happened
to all planets many times in the past.
Another Grand Alignment of the planets takes place at measure
34, and another at measure 41. Together, these two occurrences of
tutti and the musical material in between form a climax for the piece.
The work ends much as it begins, with yet another Grand Alignment
of the Planets, all sounding a single, final note together.
Unlike most of the other pieces which comprise Twelve Scientists,
the tempo of Kepler also carries significance; not in the actual tempo
itself, but in the way the tempo varies. The piece begins at a moderately
fast tempo, 130, and slowly accelerates, reaching its fastest speed (145)
at measure 27, whereupon it begins to slowly decelerate back to the initial
tempo. The change is subtle at first, but the closer the piece comes
to measure 27, the fastest point, the faster the rate of acceleration increases.
It takes 24 measures to speed up from 130 beats per minute to 140, but
only requires an additional three measures to reach 145. Beginning
at measure 24, there is a tempo increase every bar until measure 27 is
reached, then a tempo reduction at every bar takes place until measure
30. This pattern of change is a direct reflection upon Kepler's third
law, (see Table IV, page 40). At the time of composition, the composer
was attending a course in astronomy at FAU, and the instructor, Dr. Stephen
W. Bruenn, was kind enough to furnish the author with the equations necessary
to precisely calculate the changes in speed. However, (as Dr. Bruenn
had pointed out would probably be the case), the resulting speed changes,
if applied to this composition, would have been so small as to have been
completely unnoticed. Therefore, no actual planetary acceleration
curve was followed in the tempo changes. Instead, a rate of change
was adopted that still suggested planetary orbital speeds, but was altered
enough to become detectable by the alert listener.
Kepler was without a doubt the most complicated piece of the
series written up to that time. Previously, the individual compositions
had featured fewer separate parts to contend with; Kepler has nine.
Trying to keep all of the voices balanced and properly utilized as well
as complying to the predetermined sequence of rows for each instrument,
and ending up with a work that was musically meaningful was very complicated.
The composer is indebted to the suggestions and constructive criticism
offered by Dr. Glazer during the composition of Kepler.
Mendel
In the 1860s, an Augustinian monk named Gregor Johann Mendel (1822-1884)
was living a quiet, contemplative life in Brunn, Austria. His interests,
(besides religion), were botany and statistics. By way of satisfying
these two urges, he had embarked upon a program of raising pea plants and
keeping a statistical record of the results of his gardening efforts.
After some time spent at this work, he began to notice some very interesting
things about pea plants. First, he realized that if he crossbred
two plants, one of which produced only yellow peas and the other only green
peas, he didn't get a plant that produced yellow-green peas, or a plant
that produced some yellow peas and some green peas; what these offspring
produced were yellow peas exclusively. This, according to prevailing
wisdom, should not have happened; it was expected that the peas of all
plants would be yellow-green. Moreover, when these exclusively-yellow
pea plants were allowed to reproduce, some of their offspring produced
only yellow peas, (which was expected), but others produced only green
peas (definitely not expected!)
By careful statistical record keeping and analysis, Mendel was
able to form what are now known as the Mendelian laws of inheritance, which
are recognized as being of central importance to all fields of biology,
from breeding dogs or roses to modern genetic engineering. Mendel's laws
have helped humans to understand some of the most perplexing problems ever
contemplated by scientists, among them are: How does evolution work?
What is the mechanism of genetic inheritance? Why do some diseases
behave the way they do?
Mendel had no idea about the importance of his work. He
was, after all merely an amateur biologist, had no sponsors, and was basically
a nobody in the eyes of the scientific world. He did send his findings
to a professor of botany at the University of Munich named Karl Wilhelm
von Nageli. This emanate man was familiar with the idea of evolution,
(put forth recently by Charles Darwin), and now was in possession of Mendel's
work; work which could resolve many problems with evolutionary theory.
In one of history's great blunders, von Nageli assumed that the work of
an amateur was unworthy of consideration by one so highly placed as himself.
Besides, Mendel's papers were covered with numbers, tables, and ratios;
von Nageli, (like most other biologists of the time), cared little for
mathematics and saw no need for its use in his field. He returned
Mendel's work with a rude note pronouncing it unreasonable. Mendel
eventually had the work published (1866) in a small, obscure scientific
journal that was promptly forgotten. He was undoubtedly hurt deeply
by von Nageli's rejection; he terminated his experiments and never returned
to them. (He had also become very fat, and it was becoming difficult
for him to bend over in the garden.) Mendel died in 1884 as a respected
abbot, but without any scientific recognition (Asimov, i, 155-158).
Not until 1900, when three separate researchers independently
worked out the same laws of inheritance, was Mendel's work re-discovered.
These three men, (Hugo de Vries, Karl Correns, and Erich Tschermak), completely
ignorant of each others' existence, performed the necessary experiments
and were ready to publish their work and claim credit, when the idea occurred
to them that perhaps they should search the available literature to see
if anyone had ever done this sort of thing before. (Incidently, the
accepted method in science is to research the literature first, then
do the work. It usually saves a lot of time.) To their great
credit, however, each man, upon finding Mendel's published work, immediately
relinquished all claims and gave Mendel full credit. It is interesting
to see such good examples of human boorishness, prejudice, and self-importance
in the same story with three equally good examples of unselfishness and
honor. Unfortunately, in repayment for their honorable actions, all
three men were promptly forgotten (Asimov, i, 158-159).
Mendel is actually a work representing pea plants and their reproduction.
It is simple in instrumentation, form, and rhythm. Mendel appears
to have been a man with simple needs; content to tend his pea plants and
write in his ledgers for many years without help or encouragement.
Mendel, therefore, attempts to reflect an unencumbered pleasure at following
one's own path, combined with a bit of disregard for the opinions of others.
A certain delicacy is also strived for, recalling the fragile physical
nature of a pea plant as well as the fragility of Mendel's emotional nature
after his work was rejected.
It was decided that Mendel would have to be in 2/2 time, and
chiefly in a two-voice form, even before the tone row was created.
Since the piece describes reproduction, and there are two sexes, (as well
as DNA being a double helix), two was held to be very appropriate as a
numeric reference for the piece.
The original tone row was arrived at using a previously untried,
(by the author), method of determination. A two-voice improvisation
by the author at the synthesizer was recorded into the sequencer on a single
track. Four other two-voice improvisations were also recorded on
separate tracks, and, after carefully considering each improvisation, the
author picked the one that seemed to convey the desired emotions best,
and used it as the raw material for further development. The chosen
improvisation was certainly based in tonality, although during the original
recording, no attempt was made to either avoid or follow tonal practices.
The next step was to move each pitch of the upper voice of the
improvisation to the nearest previously unused pitch, either up or down.
The first note of the improvisation happened to be an E, so that became
the first element of the tone row as well. The next three notes -
A, G, and F, - were also acceptable and required no alteration. The
next note of the original melody was an E, and therefore had to be changed.
The closest available note was a D-sharp, and so that became the fifth
element of the row. Next was a D, which remained unchanged, then
another E, which was shifted to F#. Next was C, followed by B, neither
requiring any action; then an A, which was replaced with an A#. Next,
G was replaced by G#, and lastly, F was replaced by C#. Each new
(serial) pitch was then listed in order, and a number, reflecting the number
of half-steps between that note and the beginning note (E), was assigned
to each pitch, yielding the row:
0 5 3 1 11 10 2 8
7 6 4 9
E A G F D# D F# C
B A# G# C#
Using this basis, the matrix was constructed. The remaining upper
voice pitches of the improvisation were modified to comply with the new
tone row, P0 (pan flute I), and the bass voice was modified to comply with
row R0 (pan flute II). The original rhythms of the improvisation
were modified only slightly. In the second quarter of the piece,
a new improvisation is used in the same way to produce a slightly different
rhythm pattern, and the pitches shifted to comply with rows I0 (oboe) and
RI0 (bassoon).
Mendel begins with pan flutes I & II playing a whimsical
duet. Each voice represents one of the double strands of DNA in the
pea plant's cells, each of which it had inherited from one of its parents;
together they describe the new plant. As the plant grows to maturity,
it remains unchanged at this, (the genetic), level, although the pan flutes
are joined by pizzicato strings at measure 9, representing the flowering
of the plant.
(Throughout the piece, the pizzicato strings are playing only
notes that have been "borrowed" from either the pan flutes or, later in
the piece, the oboe and bassoon. They never have a row of their own;
they merely copy.)
At measure 9, while the pizzicato strings enter, the pan flutes
begin an exact repeat of the previous eight measures, ending at measure
sixteen.
At measure 17, with a wind chime announcing the event, the pan
flutes and pizzicato strings drop out, and the piece is taken over by oboe
and bassoon playing another - different - but equally whimsical duet.
This is, of course, the second pea plant in the story, one that is somewhat
different from the first, but still definitely a pea plant. It goes
through the same eight-bar development, is joined by pizzicato strings
in measure 25, (with a brief appearance of wind bells), while the
oboe and bassoon begin an exact repeat, (just as the pan flutes had done
earlier), and generally follows the same path as the first plant.
At the end of measure 32, however, there is a sudden gong, quickly
followed by the sound of a choir, resulting in an unexpected, dramatic
departure from the ordinary. This short section, (measures 33-37),
is a musical representation of sex in pea plants, and characteristically,
(at least in humans), is a bit confused.
However, beginning at measure 38, (the end of the "reproductive"
section), a new duet emerges with pan flute I and the bassoon playing the
parts. The parts played by each instrument are identical to the parts
they had played earlier in the piece, but together now for the first time,
they define a new pea plant; a hybrid constructed from two strands of melodic
DNA, one from each parent.
At measure 54, a second hybrid is introduced by the second pan
flute and the oboe, again constructed exclusively with material contributed
from each parent. These two hybrids follow the same basic path of
life their parents followed, (not really surprising for a pea plant), until,
at measure 71, they are abruptly "harvested" by Mendel; whether to count
in his studies or to enrich his diet is not elaborated upon.
Cuvier
Baron Georges Leopold Chretien Frederic Dagobert Cuvier (1769-1832),
was the Frenchman who is known as the father of vertebrate paleontology.
He was not the first to study fossils, but his work with them led to the
establishment of paleontology as a science separate from other sciences.
His most important work in connection with the establishment of general
principals of the history of life was published in 1825, bearing a title
that, amazingly, was even longer than his own: "Discourse on the
Revolutions of the Globe and on the Changes That They Have Produced in
the Animal Kingdom" (Simpson, 7-9).
It was known to Cuvier that some fossils were similar to animals
alive today, but others seemed to bear no resemblance at all to present
forms. He formulated three hypotheses, any one of which could explain
these facts:
As would be revealed over time, all three of these hypotheses
turned out to be correct. There have been several animals that were
discovered in the fossil record first, and only later were living examples
found. Latimeria, an example of the suborder Coelacanthina was thought
to have been extinct since the Devonian Period, some 400 million years,
when a specimen was captured in the Indian Ocean in the 1950s. Darwin's
theory of evolution shows that the second hypothesis is correct, and it
has become evident over the years that the third hypothesis is correct
as well. (The world has seen the last passenger pigeon, the last
dodo, the last seaside dusky sparrow, and the last of many others species)
(Simpson, 7-10).
Cuvier and others did finally come up with some guiding principals
of the history of life:
In 1812, Cuvier published a massive work called Ossemens Fossiles,
(Fossil Bones). In it, he included drawings of the first known skeleton
of Megatherium, a giant ground sloth of the Miocene Epoch, (which lasted
from 24 million to 5 million years ago) (Simpson, 9) (Stearn, 18,
285). The author has visited the George C. Page Museum in Los Angeles,
and was greatly impressed by the huge skeleton of Megatherium which greets
visitors at the door. Because of the importance of Megatherium in
Cuvier's work, and this personal experience with the giant sloth himself,
it was decided to base the tone row on this animal's name. (There
are certainly plenty of numbers associated with the science of paleontology,
but none of the important ones are precise enough to yield a 12-digit number
suitable for use in a row.)
The name Megatherium was written down, and each letter given
a number using the following method: the "a" in the name, being the first
letter of the alphabet, was assigned a 1. The next closest letter
(alphabetically) in the word is "e". The first "e" was given a 2;
the second "e" a 3. Again, following the order of the alphabet, the
next letter is "g", and it was assigned a 4. This method was continued
until every letter had a number from 1 to 11 assigned to it:
M E G A T H E R I
U M
0 7 2 4 1 10 5 3 9
6 11 8
The first number, 0, was simply tacked onto the beginning of the number sequence. Once again, the keyboard was numbered, this time beginning with C as 0:
C# D# F#
G# A#
C D E F
G A B
0 1 2 3 4 5 6 7 8
9 10 11
Finally, each number previously assigned to the name Megatherium, was matched with its corresponding pitch, yielding the final tone row:
0 7 2 4 1 10 5 3
9 6 11 8
C G D E C# A# F D# A F# B
G#
As might be expected, the beginning note of the piece is the first
letter of the scientist's name: C.
The time signatures for Cuvier were chosen to represent one estimate
of the age of the Earth: 4.5 billion years. Consequently, the piece
begins in 4/4, (four measures and a lead-in bar), and then switches to
5/4. The times signatures continue to alternate throughout the piece:
four measures of 4/4 followed by five measures of 5/4. (The last
section of 4/4 at the end is three measures long; the "missing" bar is
present at the beginning of the piece.)
Other numbers from the science of paleontology are present in
Cuvier, for example, the violins and cellos, (which are doubling the same
part two octaves apart), follow the rows P0, P2, P4, and P5, which, (ignoring
the leading 0), marks the beginning of the Triassic Period 245 million
years ago. The choir part, in measures 22-34 uses rows P2, P0, and
P8 - the beginning of the Jurassic Period 208 million years ago
(Stearn, 18).
Cuvier was written with a desire to create powerful-sounding
music to reflect the large dinosaurs, reptiles, and mammals that
once inhabited the Earth. Much more attention was paid to producing
pleasing music than to strict rules; therefore examples can be found where
strict serial technique was not employed. For example, the alto sax
part is comprised of notes borrowed primarily from the brass part, and
does not strictly follow a row of its own. However, the overwhelming
majority of the work is strictly serial in nature.
Newton
Isaac Newton (1642-1727) was born on Christmas Day, a real Christmas
present for the world of science. He was an Englishman who made amazing
advances in almost every branch of science he was inclined to put his hand
to. He is credited with inventing calculus, (in an amazingly short
period of time). He invented the reflecting telescope, which used
concave mirrors; he was the first to detect the compound nature of white
light by studying a solar spectrum produced by a prism. Not content
with that, he worked out a theory of universal gravitation, and three laws
of physical motion. Newton's theories held up admirably for about
two hundred years, until Einstein produced his theories of relativity,
(which explained conditions in high-velocity travel that Newton's theories
couldn't account for), in the first part of the Twentieth Century.
Even today, for almost every purpose, Newton's Laws can still be used with
complete accuracy
(Asimov, i, 203).
Most people don't know that Newton was also something of a religious
fanatic. The author remembers reading, (years ago in an unknown source),
that Newton spent almost as much time on religious study as he did on science.
Newton is based on the scientist's work dealing with the nature
of falling bodies. One could conceivably write a series of compositions
based on Newton's work alone; the author contented himself with writing
one.
In a vacuum, an object free-falling to Earth will gain speed
at a rate determined by the mass of the Earth, the mass of the falling
object, and the distance between the two. The actual relationship
can be expressed in the following equation:
(Kuhn, 88)
This means that the free-falling weight mentioned earlier will, in the first second, fall 16.0833 feet, and continue on to obtain the following velocities:
Rounding or truncating these numbers as needed, the following number sequence was arrived at:
32.1 64 97 128.5
The first two digits of the last number were replaced with 0, and the
two remaining unused digits, (10 & 11), were appended to the end, yielding
the final number sequence:
3 2 1 6 4 9 7 0 8 5 11 10
The keyboard was numbered beginning with G as 0:
G# A# C#
D# F#
G
A B C D
E F
0
1 2 3 4 5 6 7 8
9 10 11
Matching the pitches to the number sequence yields the final tone row:
3 2 1 6
4 9 7 0 8 5
11 10
A# A G# C# B
E D G D# C F# F
By arranging the pitches in this order, the note G appears in a diagonal
across the matrix, stretching from upper left to lower right (see Appendix
1), standing, of course, for Gravity.
Newton begins a little differently than the other pieces constituting
Twelve Scientists, starting with English Horn using row R0. The reason
for this is simple: the horn part was written after the main beginning
of the song, (which begins in a more conventional manner with row P0).
When the English Horn was added, in order to have it end on the proper
pitch, it was necessary to use row R0. (French horn was briefly considered
for this part, but aside from being a more agile instrument, it was decided
that English horn was more appropriate for an English scientist.)
All instruments enter using a "zero" row, (P0, Trumpet; R0, strings),
at measure 2, except for the piano, which begins a sequence of rows which
outlines the velocity of a falling body after a one-second fall: P3, P2,
P1, and P6. This sequence ends at measure 10, where the piano drops
out for four bars, and the focal point becomes the trumpet, which for these
four measures plays using rows P1 and P6. At measure 14, the English
horn becomes dominate in the next four-measure segment, utilizing rows
I0, I2, I6, and I0. The last note of I0, an A, is not played by the
English horn, but is played by clarinet and bassoon in measure 18.
The section from measures 18 through 21 function as a transition leading
to a piano "cadenza", which is only loosely serial in nature. The
progression of the bass voice in the piano follows row RI10, but the right
hand part makes no attempt at serialism. This is the only piece in
Twelve Scientists that serialism is abandoned to such a degree, (except
for Heisenberg, which was not conceived as a serial piece). The original
intention was to improvise on the piano, and then adjust the pitches to
conform to one row or another, but the composer liked the effect of a sudden,
almost-tonal intrusion, and decided to leave it as is. (This decision
was greeted by Dr. Glazer with his best poker face, but the composer did
detect some low mumbling from him; something to the effect of "Too New
Wave for me." He was very gracious, however, and stated that if that
was what was intended, then it was acceptable to him. In his own
defense, the composer wishes to point out that he does NOT listen to New
Age music, and to be perfectly honest, is not even sure what the definition
for New Age music would be. Perhaps the composer has re-invented
the wheel; albeit a square one.) At measure 28, violins join the
piano, and play through row I0, until the end of this section. A
second "cadenza" appears later in the piece; it, too, is only serial in
the bass voice.
The woodwinds in Newton deserve a comment; they are written in
a sectional manner, something not done in any of the other pieces.
There are large sections of repeated parts in Newton, but they
are usually accompanied by new material in a different instrument, or slightly
modified in some way so as not to be a verbatim repeat of earlier material.
Newton ends with the flute, clarinet, English horn, bassoon,
and pizzicato double bass, (in their order of entry), all fading out while
playing a composite line from earlier in the piece. The technique
used is a combination of stretto and augmentation. As each instrument
enters, the individual notes used are a bit longer than the ones used in
the preceding instrument; finally terminating with the double bass playing
the last few lonely notes almost inaudibly.
Galileo
Galileo Galilei (1564-1642), was born on February 15, in Pisa,
Italy. He was a contemporary of English poet John Milton, Shakespeare,
and Johannes Kepler, with whom he corresponded. His father, Vincenzio
Galilei, was an accomplished musician, and had also written books on music
theory. (The fact that "some things never change" can be illustrated
by the fact that later in life, Galileo found himself responsible for the
unpaid bills of his brother, Michelangelo, who was, oddly enough, ...a
musician.)
Galileo lost his sight in 1638, probably from years of peering
at the Sun through his telescope while doing his study on sunspots.
He was sentenced by the church to house arrest during the last year of
his life; a result of his statements concerning the movement of the Earth
around the Sun, which were considered heretical at the time. (The
Catholic Church's official condemnation of Galileo and his work remained
in effect until Pope John Paul II finally rescinded it just a short time
ago.) He died on January 8, 1642. A century after his burial,
his remains were disinterred and moved into his parish church, where a
monument was erected to him and his work (Kuhn, 70-71).
Galileo didn't invent the telescope, but he was the first one
to look at the sky through one. He discovered the first four moons
of Jupiter, (the Galilean moons), studied and described features on Earth's
moon, and, as previously mentioned, studied sunspots.
He was also active in the study of falling weights, pendulums,
and other subjects, and is generally credited with forming the scientific
method of experimentation.
Galileo lived the last forty-two years of his life in the Baroque
Period. When this was realized by the author, the immediate thought
was to write Galileo for pipe organ; an piece exclusively for that instrument
had not yet been written for Twelve Scientists, and besides, the author
has had a long-standing love for Baroque organ works. It was at the
suggestion of Dr. Glazer that the author decided that the work would also
be a fugue.
The tone row for Galileo is based on astronomical data having
to do with the four moons of Jupiter that Galileo discovered in 1610.
The orbital period of each moon was listed and examined: (Soderblom,
73)
(The figure for Callisto was not rounded for reasons which shall become clear). These rounded-off orbital periods were written one after another, yielding:
1.8 3.5 16.69 7.2
Any repeated digits were then dropped:
1.8 3.5 6.9 7.2
The number of the Galilean moons, (four), was then inserted at the beginning of the number sequence, and after it a zero was placed to separate it from the orbital periods:
4 0 1.8 3.5 6.9 7.2
The two unused numbers, 10 and 11, were then appended to the end of the sequence, and the decimal points were eliminated to yield the final number row:
4 0 1 8 3 5 6 9 7 2 10 11
As in previous Twelve Scientists compositions, the keyboard was then numbered, beginning with D# as 0:
D# F# G#
A# C#
E F G
A B C D
0 1 2 3 4 5 6 7
8 9 10 11
By beginning the keyboard numbering with D# as 0, it was possible to
begin the composition with the subject's initial: G
The piece is written in 4/4 to correspond with the number of
Galilean moons. (Incidently, the latest information available to
the author reveals that the most recent count of Jupiter's moons has reached
sixteen!) The rhythmic placement of the notes was determined by the
composer improvising at the keyboard until an appropriate rhythm was discovered.
Before proceeding further with this description, an explanation
should be tendered about terminology. When speaking of fugues, there
are many technical descriptive terms that unfortunately have been
adopted, (with different meanings), by the present-day musical community,
e.g., sequence, voice, etc. In the following description of Galileo,
these terms will revert to their Baroque meanings.
The exposition of Galileo begins with row P0 presenting the subject
of the fugue in the upper voice, (the piece is primarily in three voices).
The countersubject appears in measure 5, with the answer accompanying it
in the middle voice. The countersubject uses rows P1, P6, P1, and
P0 in that order to reflect the year in which Galileo made his remarkable
discovery of Jupiter's moons. (This date - 1610 - can be found in
various other locations in the work as well.) At measure 9, there
begins a sequence, using P9, P7, and P5. The sequence leads to the
third introduction of the subject, this time in the bass (pedal) voice,
which terminates with a cadence at measure 15. This cadence, of course,
is not a tonal harmonic cadence, but as was pointed out to the author by
Dr. Glazer, not all cadences need to be a V-I harmonic progression - a
cadence is primarily a point of resolution, or a point of rest. Needless
to say, this made things much simpler, and no attempt was made by the composer
to contrive tonal-type cadences in the piece.
After the cadence, (following standard fugal form), comes the
development. Short sections of material from the exposition were
used at varying pitch levels; e.g., the rhythmic motif formed by the first
three notes of the composition, (dotted quarter, eighth, and a dotted quarter),
is utilized in the upper voice in measures 16 and 18 in diminutive form,
(dotted eighth, sixteenth, dotted eighth). At the same time, in measures
16-18, a rhythmic figure from the countersubject is offered; in the middle
voice in bars 16 and 18, and in the upper voice in bar 17.
Measure 19 marks the beginning of a stretto section with the
middle voice beginning a repeat of the subject, a perfect fourth higher
than the original statement, followed in the upper voice in measure 20
with another repeat of the subject. At measure 23 the bass voice
begins the subject once again, down an octave and a perfect 4th from the
original. After completion in measure 26, the same voice begins an
immediate repeat in measure 27, down a minor third from the original subject,
but this time augmentation is used, extending the line through measure
33. The answer and countersubject are again heard together beginning
at measure 35, at yet another pitch level.
Measures 39 and 40 comprise a transitional section, using material
in the upper voice that is borrowed from the countersubject. However,
this time the rows used are R0 and R1. By using retrograde (in the
serial connotation of the word), rows, this section can also be described
as retrograde in the fugal sense, as well. The two lower voices are
using material that is essentially free, and playing together in parallel
motion. Additionally, the rows used in this two-measure segment once
again commemorate the year of discovery, 1610. These two measures
form the end of the development.
The recapitulation starts at measure 42, with the subject in
the upper voice and the countersubject in the middle. The subject
enters for the last time in the bass at measure 46, and the fugue ends
at measure 50 with a powerful D(no 5th) chord. (It would have been
nice if the composition could have closed on some type of G chord, since
the piece began on a G note, but a variety of considerations made this
impossible.)
The author owes a debt of thanks to the clarity of Bruce Benward's
text, Music In Theory And Practice, the guidance of Dr. Glazer, and
to J. S. Bach, for his marvelous models of fugal perfection.
Von Braun
Wernher von Braun (1912-1977) was a German rocket scientist who,
during World War II, built V-2 rockets for Hitler. Near the end of
the war, he surrendered to the Americans readily, and arranged for most
of his staff and co-workers to go with him. He has maintained that
he was completely caught up in the work at hand and had no thought as to
how the actual labor was being performed; (imported slave labor from conquered
countries), and that he had no influence over such matters, anyway.
All of this is probably true; at least he was never charged with any war
crimes (Dornberger, 282-293).
After coming to the United States, he and his colleagues were
put to work developing the U.S.'s infant rocket program. Several
A-4 rockets (V-2 was a military/political label; during research and development,
the rocket was designated A-2, and later A-4) were brought to the U.S.
and test fired under the direction of von Braun and his team.
Von Braun proceeded to play an instrumental part in the development
of the Saturn 5 moon rocket, and thus helped realize one of Man's oldest
dreams: traveling to the Moon. His former affiliations with Nazi
Germany were not exactly hidden, but according to the memory of the author,
they were rarely, if ever, referred to. The author considered von
Braun a great hero, and was somewhat disillusioned and confused when, some
years later, details of his past became known. (While attending grade
school and high school, the author was an extremely avid follower of all
things having to do with to space travel - and still is.)
Von Braun was to be the last work in Twelve Scientists.
The author wanted to end the series with a "bang", as well as utilize some
of the sound effect capabilities of the various synthesizers used in the
series. Robert Goddard was considered as a subject; he was a far
less controversial figure than von Braun. However, the very contradictions
presented by von Braun tipped the scales, and so a former Nazi became the
subject of the last composition.
The author found himself troubled by nagging questions about
von Braun's moral fiber. Was he really completely innocent of wrongdoing
during World War II? His invention, the V-2, killed hundreds
of civilians, (its primitive guidance systems precluded use against smaller
military targets). Does the fact that he helped mankind reach the
Moon excuse any moral slips that may have taken place in his past?
These questions have gone unanswered in the author's mind, but they have
undoubtedly exerted some influence over the creative process that led to
the creation of Von Braun.
The tone row for Von Braun is based on Earth's escape velocity:
11 kilometers per second. Of course, the number 11 doesn't really
fill the bill as far as requirements for a tone row, so further calculations
were called for. First the figure was converted to a scale that would
give a number with more digits; 24,596.273 miles per hour. (This
number is probably not precise; it was obtained by calculation from the
11 km/sec value, which was undoubtedly a rounded value to begin with.
But it resulted in a useful number with only one repeated digit.)
The second 2 in the number was directly replaced with a 0, and the four
remaining unused numbers were placed ahead of and after the velocity number:
10 11 2 4 5 9 6 0 7 3 1 8
The now-familiar process of numbering the keyboard was the next step; this time starting with C# as 0:
C# D# F#
G# A#
D E F
G A B
C
0 1 2 3 4 5 6
7 8 9 10 11
Again, the numbers were matched with pitches, yielding the final tone row:
10 11 2 4 5
9 6 0 7
3 1 8
B C D# F F# A# G C#
G# E D A
Determining the row for Von Braun was different in at least one
respect: it was chosen with great care to make possible the inclusion
of a phrase from another work; Richard Wagner's Tristan and Isolde.
In casting about looking for ideas for Von Braun, the author happened upon
a section of a book, Anthology for Musical Analysis, that contained a section
on the Prelude and Liebestod from this work. On the very first page
was a set of musical examples taken from Tristan; a set of six melodic
leitmotifs, including three that had been traditionally assigned names
descriptive of the psychological states of mind they were supposed to describe.
Two of these motives seemed tailor-made for the purposes of the composer:
the motive of Desire or Longing, and the motive of Death. The emotions
of desire and longing were no strangers to von Braun; to his colleagues,
at least, he made no secret of the fact that he desperately wanted to find
a way for mankind to go to the Moon. (He was less talkative about
this to his superiors in Germany; they would have considered him insane).
The motive for death, considering the first use of his work, needs no explanation.
In addition, these motives were appropriate because of their composer;
Hitler considered the music of Wagner to be the perfect example of Germanic
music, and held Wagner in high regard. This, unfortunately, has led
to the virtual boycotting of Wagner's music in some circles, (certainly
understandable when one finds out that Jewish musicians were forced to
perform Wagner's music next to the lines of people walking into the gas
chambers, in order to cover up the sounds of anguish and death).
Von Braun begins with the sound of a rocket being launched.
Immediately a direct, unaltered quotation of the motive of Desire is heard
on piano. (This is the only time in Twelve Scientists that another
composer's work was used. The author wanted to make sure that it
was recognizable as Wagner, and so made no modification whatsoever.)
As the last notes of the piano are fading away, the sound of marching troops
accompanied by a military snare drum approach from the left side of the
sound field, gradually getting closer. As the troops pass in front
of the listener, the sound of a large crowd of cheering people is heard.
After a few seconds, the sound of the marching troops begin to recede into
the distance on the right side of the sound field, while the rocket continues
to get fainter as it "gains altitude". The beginning of the actual
music contains the last two pieces of this sound collage; a drill whistle
is sounded, and shortly thereafter, the sound of falling bombs is implied
by a synthesizer sliding down in pitch from very high to very low.
All of these sounds are produced through synthesis; the rocket launch and
the "bombs" are synthesizer "patches" written by the composer, the
sound of marching troops is constructed from two bass drum and two tom-tom
sounds, all detuned below their normal pitch, and offset slightly from
one another to give a more realistic "human" sound. The crowd sounds
were a factory-supplied program on the Korg 01R/W synthesizer; it's actually
a digital recording of a large crowd at a pop concert.
The music begins with a tom-tom pattern, (while the whistle is
blowing), which introduces the first tone row. The first three notes
of this row, P0, are the three notes that make up the Death motive.
This single-voice motive is doubled in four octaves by violins, cellos,
double basses, and electric bass guitar, resulting in a rather powerful
sound. (Wagner's motive begins on beat four of a 6/8 measure; Von
Braun is written in 4/4; in it, the motive begins on beat one.) By
beat two of measure 20, Wagner is abandoned, and original material begins.
At measure 25, however, Wagner's Death motive reappears briefly in the
first three notes of the brass part as it begins row P0.
This first section of the piece is loosely representative of
von Braun's period in Germany. The music is heavy and portentous,
punctuated at times by the sounds of strange weapons falling from the sky.
The rows used are mostly P0 and P1, P2 appearing once in the bass guitar
part beginning at beat four of measure 21. From measures 27 to 29,
the bass guitar is simply playing the lowest note that appears in the score
above it; it is not following a row. At measure 30 a rhythmic change
takes place, using rows R1, P1, and, at bar 35, P11. (The reader
will recall that Earth's escape velocity is 11 km/sec). R1 is used
by all of the strings, and bass guitar. At measure 35, these instruments
begin a repeat of the previous four bars, while the solo trumpet moves
on to new material, using rows P1, R1, P11, and R11. Measure 41 sees
the first use of row RI9, which supplies the pitches for a very driving
sixteenth-note pattern extending through measure 44.
The section from measure 45 through 49 is constructed in a
completely different manner. Several hours of work were required
to properly execute the intended design. The first three measures
of the brass part is a restatement of the motive of Desire and Longing,
but this time it is placed in an entirely serial setting. This was
accomplished by carefully choosing the rows used and the notes within the
rows. Row R0 was used to supply the first note, A, for the trumpets;
element #8 of row RI9 supplied the second note, F. The third note
was supplied by element #3 of row R0, element #2 having appeared in the
harmony below the first note. The rest of the section was constructed
in the same fashion, using rows R0, RI9, and R11. The composer also
was concerned with making these five measures compatible with what had
come before; a transition was desired, but not one so abrupt as to sound
ridiculous. The resulting harmonic background of the motive is certainly
different from the setting devised by Wagner, but it was never intended
to be like his work.
The motive of Desire and Longing supplies a transition in another
way, as well, by representing the end of World War II and the period in
America afterwards, when the motive of Desire replaces the motive of Death.
The sound heard immediately after is of a helicopter picking up a Mercury
capsule from the ocean after re-entry. (Incidently, the computer
sequencer was used to control the digital reverb used by the composer.
By sending the proper MIDI commands, the reverb was turned off during the
simulations of the troops, rocket launches and helicopter. After
these parts concluded, the computer gradually increased the amount of reverberation
to a preset level).
Measure 51 begins the era of American space exploration.
The entire tone of the piece changes to a more American sound, featuring
a walking bass part, a jazzy feel in the part for drums, and an alto saxophone
playing an intricate solo over this foundation. The alto sax solo
proceeds through rows P2, P4, P5, P9, P6, P2, P7, and P3, outlining the
velocity of escape, 24,596.273 mi/hr. In the background, however,
is a choir following row P0, and so, (since it is "built into" this row),
the motive of Death has not been completely obliterated, (something of
a philosophical comment by the author on the dual use of rockets for peace
and war). The rhythm becomes increasingly more complex as the section
starts a repeat at measure 59. Immediately after this repeat, there
is a reprise of measures 39 through 49, which includes the serial arrangement
of the motive of Desire. This section is symbolic of the preparations
made for the launch of Apollo 11 (eleven again!), which is heard blasting
off for the Moon, at this, the end of the composition. Finally, there
is one more rendition of the motive of Desire and Longing, this time using
a very heavy, but etherial sound, (ironically named "Death Star" by Korg,
the manufacturer), symbolically saying that the end has not yet been reached,
and that the Desire and Longing for the exploration of space continues
to live on.
Appendix 1
Matrices
1. Heisenberg - no matrix
2. Euclid
based on pi - 3.141592653
0 3
1 4 5 9 2 6
7 8 10 11
0 | A C A# C#
D F# B D# E F
G G#
9 | F# A G A#
B D# G# C C# D E
F
11 | G# B A C
C# F A# D D# E F#
G
8 | F G# F# A
A# D G B C C#
D# E
7 | E G F G#
A C# F# A# B C D
D#
3 | C D# C# E
F A D F# G G#
A# B
10 | G A# G# B C
E A C# D D# F
F#
6 | D# F# E G
G# C F A A# B
C# D
5 | D F D# F#
G B E G# A A#
C C#
4 | C# E D F
F# A# D# G G# A B
C
2 | B D C D#
E G# C# F F# G A
A#
1 | A# C# B D
D# G C E F F#
G# A
3. Pythagoras
based on the Pythagorean theorem - 3 4 5
0 4
9 1 6 2 7 3
5 11 10 8
0 | D F# B D#
G# E A F G C#
C A#
8 | A# D G B
E C F C# D# A
G# F#
3 | F A D F#
B G C G# A# E
D# C#
11 | C# F A# D G
D# G# E F# C B A
6 | G# C F A
D A# D# B C# G F#
E
10 | C E A C#
F# D G D# F B
A# G#
5 | G B E G#
C# A D A# C F# F
D#
9 | B D# G# C
F C# F# D E A# A
G
7 | A C# F# A# D#
B E C D G# G
F
1 | D# G C E
A F A# F# G# D C#
B
2 | E G# C# F
A# F# B G A D# D
C
4 | F# A# D# G C
G# C# A B F E
D
4. Einstein
based on the speed of light - 186,282 mi/sec
1 8
6 2 10 3 0 9
5 11 7 4
11 | G# D# C# A F
A# G E C F# D
B
4 | C# G# F# D A#
D# C A F B G
E
6 | D# A# G# E C
F D B G C# A
F#
10 | G D C G#
E A F# D# B F
C# A#
2 | B F# E C
G# C# A# G D# A F
D
9 | F# C# B G
D# G# F D A# E C
A
0 | A E D A#
F# B G# F C# G D#
C
3 | C G F C#
A D B G# E A#
F# D#
7 | E B A F
C# F# D# C G# D A#
G
1 | A# F D# B
G C A F# D G#
E C#
5 | D A G D#
B E C# A# F# C G#
F
8 | F C A# F#
D G E C# A D#
B G#
5. Darwin
based on random chance
7 0
3 11 8 9 4 6
5 10 2 1
4 | Eb Ab B G
E F C D Db Gb
Bb A
11 | Bb Eb Gb D B
C G A Ab Db F
E
8 | G C Eb B
Ab A E Gb F Bb D
Db
0 | B E G Eb
C Db Ab Bb A D Gb
F
3 | D G Bb Gb
Eb E B Db C F
A Ab
2 | Db Gb A F
D Eb Bb C B E
Ab G
7 | Gb B D Bb
G Ab Eb F E A
Db C
5 | E A C Ab
F Gb Db Eb D G B
Bb
6 | F Bb Db A
Gb G D E Eb Ab C
B
1 | C F Ab E
Db D A B Bb Eb G
Gb
9 | Ab Db E C
A Bb F G Gb B
Eb D
10 | A D F Db
Bb B Gb Ab G C E
Eb
6. Doppler
based on the speed of sound - 3,916,800 ft/hr
3 9
1 6 8 0 4 10
2 7 5 11
9 | B F A D
E G# C F# A# D# C#
G
3 | F B D# G#
A# D F# C E A
G C#
11 | C# G B E
F# A# D G# C F D#
A
6 | G# D F# B
C# F A D# G C
A# E
4 | F# C E A
B D# G C# F A# G#
D
0 | D G# C F
G B D# A C# F# E
A#
8 | A# E G# C# D#
G B F A D C
F#
2 | E A# D G
A C# F B D# G# F#
C
10 | C F# A# D# F
A C# G B E D
G#
5 | G C# F A#
C E G# D F# B
A D#
7 | A D# G C
D F# A# E G# C# B
F
1 | D# A C# F# G#
C E A# D G F
B
7. Kepler
based on the semimajor axis of the planets
5 8
10 2 3 7 9 1
4 0 11 6
7 | A C D F#
G B C# F G# E
D# A#
4 | F# A B D#
E G# A# D F C# C
G
2 | E G A C#
D F# G# C D# B A#
F
10 | C D# F A
A# D E G# B G
F# C#
9 | B D E G#
A C# D# G A# F# F
C
5 | G A# C E
F A B D# F# D
C# G#
3 | F G# A# D
D# G A C# E C
B F#
11 | C# E F# A# B
D# F A C G# G
D
8 | A# C# D# G G#
C D F# A F E
B
0 | D F G B
C E F# A# C# A G#
D#
1 | D# F# G# C C#
F G B D A# A
E
6 | G# B C# F
F# A# C E G D# D
A
8. Mendel
based on improvisation and the number 2
0 5
3 1 11 10 2 8
7 6 4 9
0 | E A G F
D# D F# C B A# G#
C#
7 | B E D C
A# A C# G F# F D#
G#
9 | C# F# E D
C B D# A G# G
F A#
11 | D# G# F# E D
C# F B A# A G
C
1 | F A# G# F# E
D# G C# C B A
D
2 | F# B A G
F E G# D C# C
A# D#
10 | D G F D#
C# C E A# A G# F#
B
4 | G# C# B A
G F# A# E D# D C
F
5 | A D C A#
G# G B F E D#
C# F#
6 | A# D# C# B A
G# C F# F E D
G
8 | C F D# C#
B A# D G# G F# E
A
3 | G C A# G#
F# F A D# D C# B
E
9. Cuvier
based on the word Megatherium
0 7
2 4 1 10 5 3
9 6 11 8
0 | C G D E
C# A# F D# A F# B
G#
5 | F C G A
F# D# A# G# D B E
C#
10 | A# F C D
B G# D# C# G E A
F#
8 | G# D# A# C A
F# C# B F D G
E
11 | B F# C# D# C
A E D G# F A#
G
2 | D A E F#
D# C G F B G#
C# A#
7 | G D A B
G# F C A# E C# F#
D#
9 | A E B C#
A# G D C F# D# G#
F
3 | D# A# F G
E C# G# F# C A D
B
6 | F# C# G# A# G
E B A D# C F
D
1 | C# G# D# F D
B F# E A# G C
A
4 | E B F# G#
F D A G C# A#
D# C
10. Newton
based on Gravitational Attractive Force
3 2
1 6 4 9 7 0
8 5 11 10
9 | G F# F A#
G# C# B E C A
D# D
10 | G# G F# B A
D C F C# A# E
D#
11 | A G# G C
A# D# C# F# D B F
E
6 | E D# D G
F A# G# C# A F# C
B
8 | F# F E A
G C A# D# B G# D
C#
3 | C# C B E
D G F A# F# D# A
G#
5 | D# D C# F# E
A G C G# F B
A#
0 | A# A G# C# B
E D G D# C F#
F
4 | D C# C F
D# G# F# B G E A#
A
7 | F E D# G#
F# B A D A# G
C# C
1 | B A# A D
C F D# G# E C# G
F#
2 | C B A# D#
C# F# E A F D
G#
G
11. Galileo
based on orbital periods of Jupiter's Galilean moons
4 0
1 8 3 5 6 9
7 2 10 11
8 | D# B C G
D E F G# F# C# A
A#
0 | G D# E B
F# G# A C A# F C#
D
11 | F# D D# A# F
G G# B A E C
C#
4 | B G G# D#
A# C C# E D A
F F#
9 | E C C# G#
D# F F# A G D
A# B
7 | D A# B F#
C# D# E G F C
G# A
6 | C# A A# F
C D D# F# E B
G G#
3 | A# F# G D
A B C D# C# G# E
F
5 | C G# A E
B C# D F D# A# F#
G
10 | F C# D A
E F# G A# G# D# B
C
2 | A F F# C#
G# A# B D C G
D# E
1 | G# E F C
G A A# C# B F# D
D#
12. Von Braun
based on Earth's escape velocity - 24,596.273 mi/hr
10 11 2
4 5 9 6 0 7
3 1 8
2 | C# D F G
G# C A D# A# F# E
B
1 | C C# E F#
G B G# D A F
D# A#
10 | A A# C# D# E
G# F B F# D C
G
8 | G G# B C#
D F# D# A E C
A# F
7 | F# G A# C
C# F D G# D# B A
E
3 | D D# F# G# A
C# A# E B G F
C
6 | F F# A B
C E C# G D A#
G# D#
0 | B C D# F
F# A# G C# G# E D
A
5 | E F G# A#
B D# C F# C# A G
D
9 | G# A C D
D# G E A# F C# B
F#
11 | A# B D E
F A F# C G D#
C# G#
4 | D# E G A
A# D B F C G#
F# C#
Appendix 3
Equipment used in the production of
Twelve Scientists
KEYBOARDS & SYNTHESIZERS
Roland Juno 106 polyphonic synthesizer
Korg DW-8000 polyphonic synthesizer
Korg BX-3 double keyboard organ w/MIDI retrofit
Korg 01R/W polyphonic synthesizer module w/M-series and T-series
sound cards
Yamaha TX81Z polyphonic synthesizer module
Yamaha FB-01 polyphonic synthesizer module
(2) 360 Systems MidiBass sample playback modules
DRUM MACHINE
Sequential Drumtraks 400 digital drum machine
AUDIO MIXERS
Tascam MM-1 20x2 mixing board w/MIDI
Tascam M-216 16x4x2 mixing board
DIGITAL EFFECTS
Korg DRV 2000 MIDI programmable digital reverb
Effectron II digital delay
COMPUTERS & ACCESSORIES
PC Systems 486SX 33mhz (IBM clone) computer, 8mb RAM
Commodore C-128 computer
Commodore C-64 computer
Commodore 1571 disk drive
Commodore 1541 disk drive
Commodore 1902 color video monitor
Commodore 1702 color video monitor
Samsung SM3Ne Hi-Res VGA color video monitor
AVT monochrome video monitor (amber)
Sanyo monochrome video monitor (green)
Hercules monochrome graphics card
Paradise Super VGA color graphics card
Okimate 10 color printer
Epson RX-80 9-pin dot matrix printer
MIDI SWITCHERS
Casio TB-1 MIDI Thru box
Roland MPU-104 MIDI switching box
Roland MPU-105 MIDI switching box
MIDI INTERFACES
Voyetra V-22m dual-port MIDI interface (IBM)
Passport MIDI interface w/ tape sync (Commodore)
COMPUTER SOFTWARE
Sequencer Plus Gold sequencing software by Voyetra (IBM)
The Note Processor notation software by Thoughtprocessors (IBM)
Encore notation software by Passport (IBM)
Korg 8000 Voice Editor and librarian software (C64)
TX81Z Editor & Librarian software by Opspring (C64)
FB-01 Design editor and librarian software by Sonus (C64)
WordPerfect 5.1 word processor software (IBM)
WordPerfect 6.0a word processor software (IBM)
WordWriter 128 word processor software by Timeworks (C128)
EQUALIZATION
Alesis M-EQ-230 stereo 30-band graphic equalizer
DOD R-231 stereo 31-band graphic equalizer
Teac EQA-10 stereo 10-band graphic equalizer
POWER AMPLIFIERS
Phase-Linear 400
Peavey CS-400
Peavey CS-800
Pioneer VSX-5000 audio/video integrated amplifier
SPEAKERS
2 Electro-Voice Eliminator I speaker systems (15")
2 JBL 4312 control monitors (12")
2 Technics SB-L95 speaker systems (15")
2 Teac 5111 speaker systems (4")
2 Arkrat Model 8+ speaker systems (8")
Fostex T-20 Regular Phase stereo headphones
TAPE RECORDERS
Teac R-425 stereo cassette deck
Mitsubishi HS430UR HiFi stereo VHS VCR
Denon DAT digital mastering deck
MISCELLANEOUS
2 Hybrid keyboard stands
3 DeArmond volume pedals
hundreds of cables
Berol Mirado 174 #1 pencils
Pink Pearl erasers
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