What is the mechanism behind WolframTones?
(See How WolframTones Works.) Each
composition
is produced by running a program found by searching the computational
universe, taking the pattern the program produces, and converting it to a
musical score. WolframTones uses a type of
program known as a one-dimensional cellular automaton, or Wolfram automaton, studied by Stephen
Wolfram since the early 1980s.
Why does WolframTones work?
It's a rather direct consequence of a core phenomenon of Stephen Wolfram's science: that programs with very simple
underlying rules can generate great complexity of behavior. (See Chapter 2
of A New Kind of Science.)
The presence of simple rules leads to local regularities, and a certain overall
consistency in each composition. The complexity leads to "surprises" that our
ears seem to like. One day we'll probably understand more about how it relates
to human auditory perception. (Compare the
discussion in A New Kind of Science,
for example about chords.) It's presumably connected to why visual
images from
A New Kind of Science have become so popular.
Does WolframTones use stored samples of existing music?
No. Everything it generates is original. All its compositions are built up from scratch by running programs that it
finds in the computational universe.
Does WolframTones use randomness?
Once WolframTones has picked a Rule to use, all the notes it will
generate are in principle determined. But that
doesn't mean there's an easy way to predict them; in fact, Wolfram's
phenomenon of computational irreducibility
shows that in general there can't be. So even though there's no explicit
randomness put in, WolframTones rules can
still intrinsically generate effective randomness.
But there are still rules, and that's crucial to
producing compositions that
globally "make sense."
Does WolframTones use musical principles?
Only in very local ways. It uses musical scales, and certain
local rhythm structures, to convert the results of its simple programs into musical
scores. But no overall rules such as counterpoint are directly included. Sometimes,
though, they can emerge. But often in rather "creative" ways.
Does WolframTones use mathematical principles?
In a sense it uses a generalization. Traditional mathematical systems (like arithmetic and geometry) are specific
examples in the general universe of formal computational systems.
WolframTones uses a broader set, so that in a sense almost
every composition is associated with a different possible generalized kind of mathematics. Like traditional
mathematics, though, WolframTones is based on using definite
abstract systems that have their own "internal logic." If history had been different,
perhaps Pythagoras would have used WolframTones rules instead
of mathematics and numbers to describe music.
Why do I see definite classes of patterns across WolframTones
images?
Those are essentially the Wolfram Classes,
discovered by Stephen Wolfram around 1983. There are four Classes: 1:
becomes uniform; 2: becomes cyclic; 3: makes randomness; 4: makes complex
localized structures. WolframTones mostly
picks Class 3 and 4 rules to use. Class 4 rules often yield the richest compositions.
How complicated is WolframTones inside?
The core is simple, but there's a lot of sophistication in the details. There are many complex
search criteria used in finding appropriate rules.
Then there are style-dependent topological algorithms that pick
out features of Rules to optimize roles of different
Instruments, and create rhythms and harmonic
progressions. The methods we're using are (so far as we know) essentially all new; most were invented as part of the
project by Peter Overmann, who has a long history in computer music composition (and happens to be a senior executive
at Wolfram Research).
What is the role of Mathematica in WolframTones?
It's the language and system in which WolframTones was developed,
and it's what's used to run this site. (Specifically,
the site is powered by webMathematica
running on
a collection of servers. Searches are done using gridMathematica.)
Many symbolic language and pattern-matching capabilities of
Mathematica are used for WolframTones. As well, of course,
as its optimized CellularAutomaton function, and music and
graphics Export function.
What are the historical antecedents of WolframTones?
Ideas of "generative music" or "algorithmic composition" go
back a long way. Mozart, for example, was said to have a scheme for
composing minuets based on throwing dice. In the early 20th century, composers
like Schoenberg considered formal matrix-like methods, and especially in connection
with early synthesizers there was interest in deriving music from electronic
and other physical processes. In the late 20th century, many experiments were
done using 1/f noise, fractals, L systems, and even cellular automata. Most often,
explicit randomness was taken as the foundation, and extensive layers of
post processing were done. The publication of A New Kind of Science led to a new approach,
and much purer ways to derive music from the computational
universe--culminating in WolframTones.
What is NKM?
It stands for "New Kind of Music." It's an analog of NKS--which
is derived from the title of Stephen Wolfram's book A New Kind of Science.
Are cellular automata related to cellular phones?
No! It's just a coincidence of terminology. Cellular automata
consist of discrete elements called "cells," while cellular phone networks consist
of regions called "cells" served by single transmitters. Strangely, additive cellular
automata are actually used in CDMA technology for phones. One day cellular automaton
rules may well be used to control cellular phone networks--but we'll leave that confusion for later.
What is the "computational universe"?
It's the universe of possible computer programs. Programs have traditionally
been complex artifacts created to for specific tasks. A key idea in Stephen Wolfram's A New Kind of Science is to think abstractly about all possible programs.
What is then remarkable is that even among simple programs--that can for example be specified by short
numbers--there is already rich and complex behavior. Exploring the abstract universe of these
simple programs opens up many important new frontiers. There isn't
anything that requires the programs to be computer programs: they're really just sets of
abstract rules. But these days we're most familiar with such things in the context of computers.
Do WolframTones ideas apply to things other than music?
Absolutely! There are an amazing range of emerging applications of the
ideas in A New Kind of Science to science,
technology, medicine, the arts, etc. The visual arts and architecture are
two areas closely related to WolframTones.
How can I learn more about ideas behind WolframTones?
Read Stephen Wolfram's book A New
Kind of Science! It's very accessible, and it's available in
most major bookstores and libraries, or on the
web. You can ask questions on the NKS Forum.
The Wolfram Technology Conference will also feature a
special track
about WolframTones. And each year, a select group of students are
accepted to the NKS Summer School.
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