me$a.elech/tele
| download |
-
rnd_msic
(windows XP or mac OSX only)
in the .zip file,
-rnd_msic, a music generating software using liner
congruence
-music for piano generated by additive series with
condition #1, a graphical scaore generator
-three abstractions for max/msp (random-lm, random-as,
random-lc)
| rnd_msic |
this is a simple music generator using liner congruence
described on the bottom. the keyboard sound may
be changed by three faders right below where it
says "sound". also it comes with simple
buffer loop effect. you may change tempo and humanizing
factor by clicking on the top of the numbers and
dragging up or down. the same is true for changing
numbers in the equation. here are mp3 examples:
- example01
-
example02
| music for piano generated by additive series with
condition #1 |
*note: this software does NOT generate sound...
this is a graphical score generator for piano using
additive series with condition. directions are described
in the score. spacebar will change the score.
| notes on abstractions |
if you are a max user, i know in many occasions
you use [random] object. and maybe, if you're like
me, you've even tried to make music with [random]
object by simply connecting it to [makenote]. i
did, and i was very disappointed by the result.
[random] object seems a little too random (duh!)
to use directly to make something "musical".
then i learned that i had to work my way around
to use [random] object to make it "musical".
indeed,
[random] object that comes with max is a very sophisticated
random generator that provides decent random numbers
that are fairly unperiodical and unpredictable.
as a result, if you simply connect [random] object
directly to [makenote], the resulting music will
be unperiodical and unpredictable, which is interesting
by all means except not necessarily very "musical".
i put quotation marks on the word "musical"
because what's musical is very debatable. (damn
you, Cage!) but being a big fan of music like bach,
webern and morton feldman, i think one of the keywords
for "musical" is "motific" (whether
it's presented as series of notes or as sound like
musique concrete. i find many field recordings very
"musical" because they have sonic "motives").
the problem with computer generated random numbers,
or pseudo-random numbers, for they are NOT true
random numbers, is they often could be periodical
and predictable, which then don't serve as good
random numbers for many applications like computer
game programming and security coding. so programmers
bang their heads to the wall to make pseudo-random
numbers unperiodical and unpredictable. as a matter
of fact, like i said, whoever wrote [random] object
did a good job. but a wait a minuet, aren't periodical
and predictable parts of "motific" quality?
when we say "motific", it usually means
somewhat repetitive with variety. and of course,
repetitive means periodical and predictable. so
there we have it. the "problem" among
computer programmers is a welcoming factor for music.
while top computer scientists put their genius minds
together to make pseudo-random numbers as sophisticated,
as random as possible, all we the musicians need
to do to make pseudo-random numbers applicable to
music is dumb it down.
in order to dumb it down, let's not use very complicated
math stuff. here are the ones that are going to
be used:
[ + ] for adding
[ - ] for subtracting
[ * ] for multiplying
[ / ] for dividing
[ % ] for calculating the remainder after division.
for example, [20 % 6 = 2] because [20 = (6 * 3)
+ 2]
another thing that you'll see a lot is the expressions
like,
{X[0], X[1], X[2], X[3], X[4], X[5], ... X[n], X[n+1],
X[n+2], X[n+3], etc.}
this represents series of numbers. for example,
what is (A)?
{1, 2, 4, 8, 16, 32, (A), 128...}
yes, the answer is 64 because the number following
is always twice of the number right before.
so this series can be represented as:
X[n+1] = X[n] * 2
X[n+1] is the number right after X[n] in the series.
fair enough?
| pseudo-random generators |
1. logistic
map
2. additive
series with condition
3. liner
congruence
4. other
pseudo-random generators
5. musical
examples (mp3s)
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| logistic map |
X[n+1] = X[n] * a * (1 - X[n]),
0 < a < 4,
0 < X[0] < 1
first inlet: bang to generate random numbers
second inlet: value of (a) between 3 and 4 in float
(0. ~ 100.).
outlet: float (0.~1.)
logistic map is rarely used to generate random numbers
because even at the most chaotic point where (a=4),
it still has a very strong tendency in distributions,
or I can say, the distribution of logistic map is
"modal", meaning that it's not true random
or "atonal". And the distribution, or
the "mode" is determined by the value
of (a). in general, higher the value of (a), more
complex the output values. but at some point this
may not be the case. Here are some graphs of different
values of (a):
second inlet = 75 (a=3.75)
second inlet = 82.75 (a=3.8275)
second inlet = 84 (a=3.84)
second inlet = 100 (a=4)
value of 100 (i.e. a = 4) looks very random, but
as you can see in this graphical representation,
it has very strong tendency.
second inlet = 100 (a=4)
you can see it yourself by opening a patch called
"overview.txt" in max/msp
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* * * * * *
| additive series with condition |
X[n+2] = X[n] + X[n+1]
if X[n] > 100, then X[n] - 100
0 < X[0] < 100
first inlet: bang to generate random numbers
second inlet: value of X[0] (1. ~ 100.).
outlet: float (0.~1.)
if you start this series with 1, the series will
be infamous fibonatchi series till 100. the distribution
or the "mode" of is determined by X[0],
i.e. what number you start the series from. if you
start from 50, the series will be,
{50, 50, 100, 50, 50, 100, 50, 50, 100…}
and so on.
if you start from 20,
{20, 20, 40, 60, 100, 60, 60, 20, 80, 100, 80, 80,
60, 40, 100, 40, 40, 80, 20, 100, 20, 20…}
so the numbers and the cycle period vary depending
on where you start.
here are the graphs of different values of X[0]:
second inlet = 20 (X[0]=20)
second inlet = 2 (X[0]=2)
interesting feature of the series is the tendency
to "shift". If you take a look at some
of the graphical representation of the series, it
looks as if you drew a similar geometry over and
over on top of each other but moving it a little
bit each time.
second inlet = 2 (X[0]=2)
if you use decimal points, you will get more complex
outputs with more shifts and longer period.
you can see it yourself by opening a patch called
"overview.txt" in max/msp
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* * * * * *
| liner congruence|
X[n+1] = (X[n] * a + b) % 100
0 < X[0]
liner congruence method is one of the oldest methods
of generating pseudo-random numbers. the distribution
or the "mode" is determined by values
of (a) and (b), and the value of X[0]. for easy
control over the output, the last variable is fixed
to 100, but actually you can get more variety by
changing this as well. this method generates various
patterns of tendencies that can be seen both on
graphs and graphical representations.
a=51, b=51, X[0]=28
graph
 |
graphical
representation
|
a=97, b=61, X[0]=38.67
graph
|
graphical
representation
 |
a=82.5, b=61, X[0]=26
graph
|
graphical
representation
 |
as you can see, if you use decimal points, you get
more complex results.
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* * * * * *
| other pseudo-random generators |
there are numbers of pseudo-random generators. some
are like ones on the above and some are made with
completely different concepts such as use of irrational
numbers and other mathematic mothods. here are a
list of some that are similar to the ones on the
above.
-mixed congruence
X[n+1] = int((X[n] * a + b) * pow(10, c)) % pow(10,
d)
c < 0 < d
-middle-square method
X[n+1] = int(X[n]^2 * pow(10, c)) % pow(10, d)
c < 0 < d
-lagged fibonacci
X[n]=X[n-a] + X[n-b]%c
0 < a < b
-blum blum shub
X[n+1] = X[n]^2 % a
these are easy to put in max/msp's [expr] object,
so if you are interested, you should give it a try
and see what kind of random numbers they generate.
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| musical examples |
01.
beats056.mp3
in this piece of D major for organ, logistic map
is used to determine both pitch and rhythm. since
there are two [random-lm] used with different values
of (a), pitch and rhythm don't correspond to each
other.
02.
beats076.mp3
this piano piece has a similar concept with the
above but using [random-as]. again, pitch and rhythm
are determined by additive series with condition.
03.
beats011.mp3
this is a short example of how you can apply logistic
map to rhythm. the hihat sound keeps the "steady"
rhythm generated by logistic map. and everything
else is derived from the rhythm.
04.
beats054-001.mp3
05.
beats054-002.mp3
06.
beats054-003.mp3
07.
beats054-004.mp3
08.
beats054-005.mp3
09.
beats054-006.mp3
10.
beats054-007.mp3
these are examples of a composition using MTL and
logistic map. once again, logistic map is used to
determine both pitch and rhythm. but this time,
for rhythm, logistic map is used to give a "human
touch" to the rhythm in conjunction with a
normal constant rhythm generator to randomize the
constant rhythm.
11.
beats038.mp3
this piece employs logistic map to generate short
motives and repeats the motives. once again pitch
and rhythm are determined by logistic map. this
piece was inspired by erik satie's "chinema".
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