three types of music the music we play
on instruments the unheard music that
exists inside our bodies and a music
created by the cosmos centuries later in
his discovery that the orbits of the
planets were elliptical Johannes Kepler
ascribed a musical scale to each planet
and he believed the planet sang a cosmic
chorus as they traveled around the Sun
the attempts by both Pythagoras and
Kepler to find music in nature is
ultimately bound by the scientific
observation and can be disproven but
what would happen if a composer whose
artistic freedom was not bound by the
rigor of the scientific method where do
attempt to do the opposite to take
something that is not music and make it
musical now this idea is not new Baroque
composers wrote music to evoke human
effects romantic composers wrote
programmatic music that told epic tales
but what I am thinking of are the kinds
of techniques pioneered by the composer
and architect Yanis Tanaka’s who use
mathematical formulas to generate music
and a large body of my own compositions
I take a similar approach creating
systems or sets of rules based on
concepts borrowed from mathematics
physics and technology and I want to
start with my first venture into this
way of composing music with a piece that
I wrote in 2003 called what hath God
wrought now this weather ominous title
is taken from the first Telegraph
message that Samuel Morse sent from the
US Capitol to Baltimore on May 24th 1844
and we have no idea why Morse chose to
send such an ominous message but
arguably the invention of the Telegraph
marks the start of the Information Age
or at least foreshadows it for the first
time information could be transmitted
from one place to someplace far away
simultaneously and the code that Morse
invented is binary a precursor to the
binary systems used by computers over a
century later from a composer standpoint
Morse code lends itself easily to a
translation to music we simply make a
dot a short note value and a dash a
longer note value and we get rhythms I
mean Morse code is basically the
and when we convert it the word what
would sound like this do-do-do-do-do
do-do-do-do-do a similar approach could
be applied to the pitch or what notes
are played a dot could be two notes that
are close together a small interval a
dash could be two notes that are further
apart a larger interval and when these
two elements are combined the words
become melodies for example the word god
played here by the english horn bassoon
an electric bass sounds like this and
the word what played by the electric
guitar sounds like this
now what I’m gonna do is play you a
short excerpt of the piece so you can
hear these things in action you’re gonna
hear that God melody played and it’s
gonna be followed by all of the
instruments playing the entire message
what hath God wrought and they’ll be
playing in Canon meaning they’ll play
the same music but they’ll start at
different times this will be followed by
all of the instruments playing the word
what in Canon again but this time
playing the melody at different speeds
this recording is by my group pulse
[Music]
[Applause]
[Music]
[Applause]
[Music]
[Applause]
[Music]
[Applause]
[Music]
now this way of composing music built on
systems really excited me for one I
created music I could have never have
conceived of in any other way but it
also allowed me to communicate with an
audience I mean regardless of whether or
not an audience member knows Morse code
it’s still possible for them to hear
that a message is being transmitted but
my approach was not entirely rigorous
and as a composer I had great freedom
and ever since writing this piece I
wanted to write a piece that was
entirely based on a system a composition
where I could explain every note every
rhythm every formal choice I wanted to
write the perfect algorithmic
composition and that came several years
later with Libra bossy for percussion
ensemble in this piece I was interested
in two concepts both from mathematics
fractals and the Fibonacci sequence now
I want to start with fractals a fractal
can be defined as a fragmented geometric
shape that can be split into smaller
parts each of which are reduced copy of
the hole and fractals are generated
using reiterative processes where the
same set of rules are applied to the
object again and again and the creation
of the sierpinski triangle is a great
demonstration to create this triangle we
start with an equilateral triangle then
we invert it and reduce its size
creating now three new equilateral
triangles and we can do the same thing
to each of those triangles to leave us
with nine triangles and we could
reproduce repeat this process again and
again on each new triangle and
eventually we’re going to be left with
smaller units that are just miniature
replicas of the larger unit and I
thought what would it be like to have a
piece of music that was just like this
triangle and had the same relationships
the large triangle would be the overall
composition smaller triangles would be
smaller sections and the smallest
triangles would be the individual notes
the second aspect that I was interested
in is the Fibonacci sequence and this
sequence was first presented by Leonardo
of Pisa better known as Fibonacci in his
twelve thousand two book Libra basi or
book of calculation and it appears on
one small page of this rather large tome
where Fibonacci is describing the
reproduction of rabbits and Fibonacci
set up the following rules it takes one
month for a bunny to grow to mature a
bit and each month a mature rabbit will
produce one offspring so if we follow
Fibonacci the first month
have a bunny in the second month that
bunny grows into a mature rabbit in the
third month that rabbit praises a new
offspring and now we have two rabbits in
the fourth month the first rabbit
creates another offspring and the bunny
matures and we can continue it in month
five they’re gonna be five rabbits in
month six there will be eight in month
seven there will be 13 and we can
continue this process to infinity by the
time we reached we 14 our rabbit
population has grown to 610 there’s
another way that we can make the
Fibonacci sequence and that’s using a
mathematical formula where we start with
0 and 1 and each new number is a sum of
the previous two so starting with 0 and
1 the next number is going to be 1 which
is 1 plus 0 the next one will be 2 which
is 1 plus 1 then 3 which is 1 plus 2 5
which is 2 plus 3 8 3 plus 5 and
continues well that makes the Fibonacci
sequence so fascinating is that as our
numbers increase the same ratio appears
between adjacent numbers let’s look at
the last three notice that the ratio
between 233 and 377 is 0.618 and the
ratio between 377 and 610 is also 0.618
now this ratio has begins given several
names the golden ratio the golden
section the golden mean and it’s math
it’s fascinating mathematicians since
Euclid it appears regularly in nature
and the layout of the seeds of a
sunflower and also in the ratio between
the chambers of a nautilus shell and the
attraction of the golden ratio is the
belief that we as humans find it
aesthetically pleasing architects have
used it in their design most notably the
caboose EA in the mid 20th century
artists have used it in their paintings
but composers have used it extensively
Beyla Bartok cloud Debussy Michael
Gandolfi William Duckworth just name a
few and when an architect uses it they
might use it to determine the size of
windows in a building or the size of the
balconies as shown here an artist may
use it to place an object perfectly
within a canvas but composers use it for
time or how long a section of music will
be in relation to the whole young
composers are taught using Bayla
Bartok’s
music for Strings percussion and to last
as a model that if they place the climax
of their composition right at the golden
ratio right at 61.8% of the way through
the piece it’s guaranteed to be
successful but I thought why stop there
why not have it between all the sections
of the piece between all the music
musical phrases and between every note
and I started visually with what we call
Fibonacci tiling and to do this we start
with the tile that is one by one it’s
rather small here but it will get bigger
then another one by one square then we
do a two by two square a three by three
square a five by five eight by eight
thirty by thirteen and we can continue
it now if we inscribe an arc in between
each of these squares we gets what is
known as the Fibonacci spiral which you
can see closely resembles the shape of
the nautilus shell and I thought what
would it be like to write a piece of
music where the experience of hearing it
would be like traveling through the
chambers of the nautilus shell hearing
the same music again and again at
smaller and smaller intervals but still
maintaining that same relationship but
music works linearly in time so we have
to lay the squares out in a row and if
you recall when we what we talked about
with fractals where we created the
sierpinski triangle using the same
process again we can do this with the
squares reducing each square to its sum
so a 34 square would become a 13 and a
21 a 21 square become an 8 and a 13 and
it would continue and then we continue
this process again and again reducing
each square to a smaller unit until
we’re left with the smallest unit which
is a single 1×1 square and the next step
is to remove the scaffolding replace the
squares with note heads add stems and
beams add a musical staff and we have
music now if we assign each one of these
notes to a drum from high to low the
now when I got to this point I was both
excited and disappointed excited that
I’d made this happen but disappointed in
the way it sounded and I knew that I
couldn’t make a performer do this for
ten minutes or more and I definitely
couldn’t make an audience member
listened to more than ten minutes of
this but if the similar approach were
applied to other aspects of music what
pictures are played
what register they are how high or low
those pictures are in orchestration what
instruments are playing there’s always
much more enjoyable and now before I
play you a short segment of this piece I
want to talk briefly about the form or
how it’s constructed it starts by
Counting sixteenth notes which are the
smallest note value and it starts that X
should actually be a sixteenth note but
that’s okay and it starts at 610 and
counts this way down to one then 277 all
the way down to one 233 down to one
until we’re left at one and then the
process repeats again starting at 277
and working all the way down to one and
then it for each new number after that
until we’re left at the very end with
just one note I what I’m going to do is
play a short segment from 233 to where
it resets at 377 this recording is by
the Truman State University percussion
ensemble directed by Michael bump the
group that premiered the work and what
you’re going to see as it plays is a
video that will count down the numbers
it took me over a year to compose
Liebherr bossy and it was a laborious
process it also completely fulfilled any
desire I had to write such formalized
and as a colleague of mine mentioned
once in many ways Libra bossy is more of
an experiment than actual music and like
many experiments I went into it with
certain expectations but left it with
completely unexpected results composing
is a lot like learning to play a new
technique on a musical instrument
the musician spends hours days weeks
months carefully practicing the
technique again and again until it
becomes intuitive and similarly the
methodical composing Libra bossy where
the focus wasn’t on the notes but how
and especially when they were presented
left me with a more under into ative
understanding of how time works in music
and how I as a composer can use time for
dramatic effects so this is drastically
changed all of my work since then both
in my own compositions but most
importantly is my work as an educator
training young musical composers thank you so much