Markov Chains And Microtonality

Hello tuners!

I could assume that one of the good methods of creating "human composed sounding" microtonal music, is with the use of a Markov chain.

Let us say that I had 5 octaves of 12Et (60), and 7 note durations, with 3 note volumes (arbitary numbers, by the way....), this could give me a first order Markov chain, with approximately 1260 lines of code.

A second order Markov chain would have 1260^2 lines of code 1587600, and a third order Markov chain would have 1260^3 lines of code or 200037600 lines of code.

I could further assume that the higher the order of the Markov chain, that music of ever greater complexity of music could be generated, and in principal, IF we got all of the parameters in our code, for a say 20000 order Markov chain, then we'd have music which sounded very human like.

In principal we could programe such a programe, in practice no, for, I mean, how bigger number is:

1260^20000?

(Please see my recent post to the alternative tuning list as to how big the numbers will become in music in the vast future).

What you have to realize about such a number is that, whilst it IS big, but it is NOT infinite.

Has anyone ever done, or heard about music, especially microtonal music composed with Markov chains, and genetic algorithms used to make, and to manipulate Markov chains.

Somewhere in the process you'd have to listen to the music made with these huge beasts of code, to select and to mate them to make further generations of code.

By the way, I do believe that computers will both think and feel in the 2030's, and I look forward to this day with awe and with fear.

What if they take over, and start running the world?

---Sarn.

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I don't understand what you mean here.

Markov chains were used in music analysis for statistical evaluations
of certain elements, parameters of music in consecutive order
(neighboring). I emphasize this process was done on individual
parameters of music, not on music itself. For example: music is done
from notes, but music is something more than notes only. (Obvious
fact often ignored even by some famous performers who don't play
music, only notes.)
So results of such analysis don't say too much about music itself as
a language. It's still in the beginning.
Main problems are: which parameters should be analyzed in certain
music work in certain style (which are relevant for that style), and
how to interpret the results...

You can do such analysis with Markov chains of various length - with
two members in the chain you will have very common results which
don't say much about the music. The more longer chains, you can get
some patterns which have sense. This way you can analyse some work,
compare it with the other works, try to find level of similarity or
identity.

That's all you can do with it.

Concerning the music composition - there are more easy ways how to
compose music, with more interesting results. Even in the computer
assisted composition, algorithmic composition, there was some
development, and some results. From the used methods I don't think
using of pseudorandom generators can give musically good results,
randomness is white noise and this is not so interesting.

Composition on the base of Markov chains is also possible, but it
will be always done from the results of previous analysis. Thus it
will be less or more similar to the analyzed composition, or music
style (depending on the length of Markov chains). In my opinion this
has no sense and you can even get more interesting results with some
kind of controlled, filtered randomness.

What would be really interesting, if only computer analysis of music
is possible to such depth, to make some musicological games from it,
for example to create a virtual composer who will be able not only to
invent music in the certain style, or personal style of historical
composers or era, but to do something like morphing, for example a
composer who will write music exactly in between let's say Chopin and
Debussy, or to get more interesting results, Gesualdo and Ligeti...
Or 40% of Bartók, 35% Vivaldi, 20% Jobim and 5% gamelan... Or to
compose new works of dead composers, as an scientifically based
attempt to guess which music could have be written from 75 years old
Mozart in 1831...

For this would be necessary to perform a multiparameter statistical
analysis of all music and its parameters, together with compositional
rules (how music is done as a language), create a huge database of
results and feed a powerful computer with it. OK, something for the
next century musicologists. Until then we have to do such games with
our limited powers. Which I do always with a pleasure...

Daniel Forró

On 10 Feb 2010, at 5:08 PM, Sarn Ursell wrote:

>
>
> Hello tuners!
>
> I could assume that one of the good methods of creating "human
> composed sounding" microtonal music, is with the use of a Markov
> chain.
>
> Let us say that I had 5 octaves of 12Et (60), and 7 note durations,
> with 3 note volumes (arbitary numbers, by the way....), this could
> give me a first order Markov chain, with approximately 1260 lines
> of code.
>
> A second order Markov chain would have 1260^2 lines of code
> 1587600, and a third order Markov chain would have 1260^3 lines of
> code or 200037600 lines of code.
>
> I could further assume that the higher the order of the Markov
> chain, that music of ever greater complexity of music could be
> generated, and in principal, IF we got all of the parameters in our> code, for a say 20000 order Markov chain, then we'd have music
> which sounded very human like.
>
> In principal we could programe such a programe, in practice no,
> for, I mean, how bigger number is:
>
> 1260^20000?
>
> (Please see my recent post to the alternative tuning list as to how
> big the numbers will become in music in the vast future).
>
> What you have to realize about such a number is that, whilst it IS
> big, but it is NOT infinite.
>
> Has anyone ever done, or heard about music, especially microtonal
> music composed with Markov chains, and genetic algorithms used to
> make, and to manipulate Markov chains.
>
> Somewhere in the process you'd have to listen to the music made
> with these huge beasts of code, to select and to mate them to make
> further generations of code.
>
> By the way, I do believe that computers will both think and feel in
> the 2030's, and I look forward to this day with awe and with fear.
>
> What if they take over, and start running the world?
>
> ---Sarn.

--- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote:
>
> What would be really interesting, if only computer analysis of
> music is possible to such depth, to make some musicological games
> from it, for example to create a virtual composer who will be able
> not only to invent music in the certain style, or personal style of
> historical composers or era, but to do something like morphing, for
> example a composer who will write music exactly in between let's
> say Chopin and Debussy, or to get more interesting results,
> Gesualdo and Ligeti...
> Or 40% of Bartók, 35% Vivaldi, 20% Jobim and 5% gamelan... Or to
> compose new works of dead composers, as an scientifically based
> attempt to guess which music could have be written from 75 years
> old Mozart in 1831...
>

David Cope has done exactly that, and indeed with Markov chains - more specific, hidden Markov models. Results (quite impressive) can be heard on http://artsites.ucsc.edu/faculty/cope/experiments.htm .

But apparently the Markov chains were not used in a "simplistic" way with but rather on more abstract levels of musical parameters.
--
Hans Straub

I know about him, he's on good way... Thanks for the link.

Daniel Forro

On 10 Feb 2010, at 6:29 PM, hstraub64 wrote:

>
> --- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote:
> >
> > What would be really interesting, if only computer analysis of
> > music is possible to such depth, to make some musicological games
> > from it, for example to create a virtual composer who will be able
> > not only to invent music in the certain style, or personal style of
> > historical composers or era, but to do something like morphing, for
> > example a composer who will write music exactly in between let's
> > say Chopin and Debussy, or to get more interesting results,
> > Gesualdo and Ligeti...
> > Or 40% of Bartók, 35% Vivaldi, 20% Jobim and 5% gamelan... Or to
> > compose new works of dead composers, as an scientifically based
> > attempt to guess which music could have be written from 75 years
> > old Mozart in 1831...
> >
>
> David Cope has done exactly that, and indeed with Markov chains -
> more specific, hidden Markov models. Results (quite impressive) can
> be heard on http://artsites.ucsc.edu/faculty/cope/experiments.htm .
>
> But apparently the Markov chains were not used in a "simplistic"
> way with but rather on more abstract levels of musical parameters.
> --
> Hans Straub
>

Why would every combination require a line of code? That is, what would you do in a line of code for each combination that could not be accomplished by nested loops with the inner loop visiting all combinations of note, duration and volume and performing the appropriate calculations? With a thoughtful algorithm you can probably make an arbitrary order Markov chain in feasible time.

-----Original Message-----
From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Sarn Ursell
Sent: Wednesday, February 10, 2010 2:08 AM
To: tuning@yahoogroups.com
Subject: [tuning] Markov Chains And Microtonality

Hello tuners!

I could assume that one of the good methods of creating "human composed sounding" microtonal music, is with the use of a Markov chain.

Let us say that I had 5 octaves of 12Et (60), and 7 note durations, with 3 note volumes (arbitary numbers, by the way....), this could give me a first order Markov chain, with approximately 1260 lines of code.

A second order Markov chain would have 1260^2 lines of code 1587600, and a third order Markov chain would have 1260^3 lines of code or 200037600 lines of code.

I could further assume that the higher the order of the Markov chain, that music of ever greater complexity of music could be generated, and in principal, IF we got all of the parameters in our code, for a say 20000 order Markov chain, then we'd have music which sounded very human like.

In principal we could programe such a programe, in practice no, for, I mean, how bigger number is:

1260^20000?

(Please see my recent post to the alternative tuning list as to how big the numbers will become in music in the vast future).

What you have to realize about such a number is that, whilst it IS big, but it is NOT infinite.

Has anyone ever done, or heard about music, especially microtonal music composed with Markov chains, and genetic algorithms used to make, and to manipulate Markov chains.

Somewhere in the process you'd have to listen to the music made with these huge beasts of code, to select and to mate them to make further generations of code.

By the way, I do believe that computers will both think and feel in the 2030's, and I look forward to this day with awe and with fear.

What if they take over, and start running the world?

---Sarn.

________________________________

Yahoo!7: Catch-up on your favourite Channel 7 TV shows easily, legally, and for free at PLUS7. Check it out <http://au.rd.yahoo.com/tv/catchup/tagline/*http://au.tv.yahoo.com/plus7/?cmp=mailtag> .

Ok,

Here are some markov chain programs

http://clones.soonlabel.com/public/mark_text/

Now... these are used to process text documents and have 2 and 3 chain
variants.
The original author was attempting to use Markov chains to process posts on
USENET as a sort of artificial intelligence means of posting to
conversations by re-assembling previous posts.

I used this program to generate the test for "I See The Void" video

http://www.youtube.com/watch?v=3ROb89b1Cr4

Obviously since marktext uses ascii text it may take a bit of work to use it
for music - though I bet it can be done with csound (it can do anything in
theory!)

One word of caution - these are 16-bit programs (circa 1998) so you will
need an emulator like DOSBOX http://www.dosbox.com/ or a Win 98/95/3.1 box
to run them.

Also... this is old time command line stuff !! though you can feed it a list
of text files to process which helps immensely - the more you feed it the
better it works imho.

Chris

Howard M says:Why would every combination require a line of code?

Sarn says:When you say this, exactly what do you mean by this?

Can you please explain in more depth and be more specific?

Howard M says:That is, what would you do in a line of code for each combination that could not be accomplished by nested loops with the inner loop visiting all combinations of note, duration and volume and performing the appropriate calculations?

Sarn says:Please be more specific...

I have revised my formula and I have realized that I have left a few things out from it.

One variation on this formula would be:

C=((T*O*L*V)+1)^K

Where: C=Approximate lines of code in the Markov Chain algorithm,
T=Equal Temperament Steps Used,
O=Number of Octaves used,
V=Note Volumes used,
K+Order of the Markov Chain used.

T*O*L*V has one added to it for silence, and L are the lengths of notes used, breve, minim, crotchet, dotted notes, quaver, semi-quaver, and of course triplets (1/6 and 1/3) notes.

---Sarn.