Fractal Tunes

[webmonkey]

Hi All,

This is from Harlan Brothers, that I got directly as the group owner.
 He just joined, by the way.
------------------------
Hi, Phil.

Robert Walker just pointed me to this discussion.  Thank goodness.

I am unpleasantly surprised to find that you have taken such offense
to things that I have written.  The irony is that I am EXTREMELY
impressed by your music and have, in fact, pointed others to it when
asked about algorithmic composition.  I wish I had taken time to
write to you earlier.

Contrary to your impressions, I am not in any strict sense
an "academic."  I am first a musician who became a mathematician
later in life.  Through sheer serendipity, I found myself working
with Benoit Mandelbrot.  It was Benoit who set me on the task of
trying to provide a mathematically rigorous approach to "fractal
music."

You wrote:

"This is blinkered, condescending, academic arrogance of the highest
and order and shows a massive amount of disrespect to everybody who
has been working in this field for a decade or more longer than he
has."

In fact, I first met Benoit at "New York Notes: Music and Fractals by
B. B. Mandelbrot and Charles Wuorinen" at the Guggenheim Museum in
April of 1990.  I had written a short paper on the subject a few
years earlier that I wanted to share with him.

Clearly, anyone is free to use any "term" in any manner they please.  
In this case, the man who invented the term "fractal" and one of his
most trusted and knowledgeable associates both felt that, with regard
to music, the term was being used so loosely as to render it
meaningless relative to its intended meaning.

You also wrote:

"Yet he has the hypocritical nerve to dismiss all books and web-sites
on the subject of fractal music other than his own as "the worst kind
of nonsense."

Clearly you assumed these were my words.  They are not.  They came
from the Yale site on fractal geometry:

http://classes.yale.edu/Fractals/

which is mirrored on my site.

Furthermore, when a person claims that an onion is "fractal" because
peeling it reveals more onion, this is "nonsense" that only serves to
confuse people.

I mean no disrespect to fellow artists of any ilk.  My intention is
simply to draw a distinction between music that possesses a
mathematically demonstrable or measurable distribution that
is "fractal" in the sense intended by Benoit and, on the other hand,
music that is more generally of an algorithmic nature.  Hence the
terms "fractal-based" or "fractal inspired."

The truth is that you and I clearly have more in common in terms of
our musical influences and sensibilities that it seems you
appreciate.  It is apparent just from listening to your compositions
that you have devoted great time, energy, and soul into developing
your sound.

Please remember that, until now, I have never written a word about
Phil Thompson's music or his sources of inspiration.

Respectfully yours,
Harlan



--- In cnfractal_music@..., v_e_n_h_a_r_i_s
<no_reply@...> wrote:
>
> Last night I visited Mathematician Harlan Brothers' web-site
relating

> to Fractal Music and was appalled by his commentary on it.
>
> http://www.brotherstechnology.com/math/fractal-music.html
>
> On the opening page…
>
> A quick Web search will reveal widespread misconceptions about what
> constitutes fractal music.
>
> Clicking on "widespread misconceptions" takes you to the following…
>
> Google the term "fractal music" and you will find a vast array of
> misconceptions concerning the subject.  There are three common

errors:
>
> * Perhaps the most popular misunderstanding comes from assuming
that
> if an image is fractal, then any music derived from it in a
> methodical manner must also be fractal.  Take for example, the
> interesting, if sometimes disconcerting, succession of notes that
can
> be generated from images of the Sierpinski Gasket, Koch curve, and
> Mandelbrot set.  This type of "fractal music" is often neither and
is
> probably more aptly described as "fractal inspired, musical
sound."  

> While it is possible that compositions generated in this fashion
> possess some inherent power-law relation, this is by no means
> guaranteed.
>
> * There is also a common error of logic whereby it is assumed that
> because fractal patterns often emerge from iterative processes,
> iteration must always result in some sort of fractal structure.  As
> the logistic map illustrates, this is clearly not the case.
>
> * Finally, a fundamental misunderstanding arises from the notion

that
> self-similarity is synonymous with fractality.  Self-similarity is
a
> necessary but insufficient condition for claiming that a structure
> is, indeed, fractal.  To be clear, onions, spirals, and Russian
dolls
> are not fractal; they do not contain a minimum of two matching or
> similar regions in which the arrangement of elements either mirrors
> or imitates the structure of the object as a whole.
>
> Clearly, iterative algorithms can generate interesting and even
> pleasing musical patterns and textures. However, the burden of
> demonstrating specific fractal characteristics falls to those
making
> the claim.
>
> ...
>
> I find this offensive, and this is why.
>
> Brothers is accusing members of the fractal music community (such
as
> myself) of misunderstanding and misrepresenting fractal music.  But
> really, what he is doing above is demonstrating his own
> misunderstanding of what the fractal music community has been
doing,
> and in particular what they mean by the term "fractal music", and
is
> therefore misunderstanding and misrepresenting us.
>
> Brothers' writings imply that people who have been active in this
> community have somehow "misappropriated" the term "fractal music"
to
> describe their work, which according to his rigidly defined
> mathematic definition is not correct.
>
> I take exception to because there has not been any formal
definition
> of the term "fractal music" until Brother decided to publish his
own
> version of it and claim that this is the only correct
interpretation
> of the term.  He does not seem to consider that many of us have
been
> using the term simply to mean "music derived directly from
fractals",
> in full awareness of whether the resultant data is "fractal" or not
> according to the definition that he is now attempting to apply
> retrospectively.
>
> Now for him to "lay down the law" in this way, in 2004, a whole
> THIRTEEN YEARS after people such as myself, Chris Sansom and Hugh
> McDowell began to make music derived directly from fractals really
> does strike me as attempting to close the stable door long after
the

> horse has bolted, a horse he doesn't seem to be capable of
> recognising that many others were riding a very long time before he
> was.  
>
> And I have to say that having listened to his experiments in music
> that he does consider "fractal" I think his remarks about "fractal
> inspired, musical sound" really are a pot calling a kettle black.  
> Glass houses, stones, and all of that.
>
> So this is just to say again: I call my music "fractal music"

because
> it is music derived directly from the Mandelbrot and Julia fractal
> formulae.  Whether or not that qualifies it as being "fractal
music"
> according to Brothers' narrow, mathematically blinkered
> interpretation of the phrase, well, I suspect in many cases it does
> if he bothers to investigate, but I really couldn't care less.
>
> Over the years members of the fractal music community have shown a
> great deal of respect towards the mathematicians who inspired their
> software and music.  I am saddened that certain members of the
> mathematic community don't seem to have the ability to show a
similar
> amount of respect to those in the artistic community who have done
a
> great deal to popularise the scientific fields they are working in.
>
> And finally, a note to Mr.Brothers just in case he might read this
> some day: it appears to me that Fractal Music is merely the latest
> bandwagon you have decided to jump upon.  Well, catch up – it
> departed this station in 1992.  And I wouldn't bother to try and
> patent it if I were you, you'll find my music and software have
been
> using the principles you describe, and have been in the public
> domain, since 1997.
>
> ...
>
> Phil Thompson
> http://fractalmusician.com
>

[webmonkey]

Perhaps we need to call a truce here and let Harlan speak a bit, and
perhaps all mend some fences....

Phil J.
 

On Sat, 2008-09-27 at 03:38 +0000, v_e_n_h_a_r_i_s wrote:

>
> > You also wrote:
> > "Yet he has the hypocritical nerve to dismiss all books and web-
> sites on the subject of fractal music other than his own as "the
> worst kind of nonsense."
> > Clearly you assumed these were my words. They are not. They came
> from the Yale site on fractal geometry:
> > http://classes.yale.edu/Fractals/ 
> > which is mirrored on my site.
>
> Whether or not they are your words, you chose to present them on your
> web-site, and in so doing made those words your own.
>
> Also, your opening statement on the subject in which you dynamically
> link to every other web site on this subject, by default criticsing
> ALL for "widespread misconceptions" applies the ultimate level of
> sweeping generalisation possible towards everybody else who has ever
> been active in this field, or will EVER BE active in this field in
> the future. And whilst you have not criticised me directly, this
> generalisation by nature includes myself and many others. So if you
> are wondering why I have taken offense, look only to your own
> writings.
>
> > I mean no disrespect to fellow artists of any ilk.
>
> I find it hard to contemplate how your writings could possibly be
> regarded as anything but disrespectful. In all of the years I have
> been active in this field I have never seen AMY other person in it be
> so dismissive towards the work of others. Frankly, your web-site
> disgusts me in the way it turns a blind eye to so many people who
> have done so much for this genre over the years.
>
> >My intention is simply to draw a distinction between music that
> possesses a
> > mathematically demonstrable or measurable distribution that
> > is "fractal" in the sense intended by Benoit and, on the other
> hand, music that is more generally of an algorithmic nature. Hence
> the
> > terms "fractal-based" or "fractal inspired."
>
> Yes, but your erroneous misconception is that other people in this
> field such as myself have not been making music that has such
> a "measurable distribution" of this kind all along. And you go on to
> demonstrate methods that have been old hat to many of us and have
> featured in our work for over a decade. In fact your techniques have
> been in compositions of mine since the mid 1980s, before I even
> considered them to be "fractal".
>
> I think you should consider that not all fractals are as simplistic
> to look at as a Serpinski Triangle. And likewise not all fractal
> music is as simplistic to audibly detect. But that does not mean it
> is not fully "fractal" even by your own classification standard,
> which I personally feel is incredibly inflexible and pedantic.
>
> And you are also assuming that everybody working in this field has
> been using the term "fractal music" to apply to music that is more
> correctly described as "generative". We have not. We are fully
> aware and have differentiated between between music generated in part
> or whole from a fractal, to music that has fractal characteristics,
> and music that is generative but has nothing to do with fractals at
> all, but to us in terms of "fractal music" the differentiation is
> trivial - our use of fractals to create music has been much more in
> the spirit of Benoit Mandelbrot's "sledgehammer" - it might not all
> be fractal but we use fractals as a tool to produce it whenever and
> however we can.
>
> Now had you perfomed any kind of "rigorous" examination of this field
> as tasked by Benoit Mandelbrot you might have discovered this.
>
> As I have already said, you have criticised others
> for "misconceptions" when the real misconception is that many of us
> weren't fully aware of the kind of observations you have made a great
> many years before you.
>
> And as for not criticising my work directly previously, I honestly
> couldn't care less about any observations you might make about it.
> It wouldn't bother me if you classify it as "Disco". My focus has
> always been making this music, not leaning out of an ivory tower to
> pontificate over what it should be called.
>
> Phil Thompson
> http://fractalmusician.com
>
>
>
>
>  

[Lauri Grohn-2]

Hi,

Not being a native English speaker it still seems
to me that "Fractal music" and "Music based on
fractals" are two different matters.

Best,

Lauri Gröhn
http://selfgeneratedmusic.blogspot.com/

[Robert Walker-7]

Hi Lauri,

Yes, I think everyone would agree if you take extreme examples,
some music is obviously fractal however you draw the line,
well certainly my cantors set tune fractally constructed and
infinitely divisible in pitch and time domain, anyone has to call
that one a fractal.

Then for instance music consisting of just repetitions of a single
note wouldn't be fractal at all, no matter how it is generated.

Similarly e.g. the Koch snowflake is definitely a fractal,
and a perfect disk wouldn't count as a fractal even if
generated by methods that often create fractals.

The thing is that as there is such a lot in between the two extremes
- a lot of the most interesting stuff - Visually also - so what do you
say there?

Musically in my Tune Smithy program you can start with a sloth canon
which is about as fractal as fractal music can be apart from the
ones that go to infinite detail such as my cantor set piece.

Then you can e.g. permute or reflect the notes in the seed phrases
as the piece continues - and it would be reasonable to still call
the result a fractal by analogy with the random visual fractals,
there are no strict similarities any more, but definitely
a type of motivic scaling where you get the same patterns at
faster and slower time scales.

Then you can also play about with assignments of notes to instruments.
You've got exactly the same notes as before, but assigned to instruments
in such a way that it breaks up the motivic canon structure so that a
human listener will find it very hard to hear it at all. There is no motivic
scaling, or hardly any, in the melody lines a human listener hears,
but a feeling of overall structure still, which is helped probably by the
now completely hidden motivic canon. Someone very analytical in their
hearing might still be able to pick out the original canon in some way
or you could spot it by looking at it on paper and reconnecting the notes
in the right way to recover the original canon, sort of like connecting
the dots on a page to recover a picture.

Then one can superimpose chord progressions on the result as well
so that the notes are the same, but instead of played within a single scale
for the duration of the piece, they play notes from different chords in a progression.

At this point - is it still a fractal tune or is it something different?
The motivic canon structure is completely broken up. If you didn't know it
was there you would be unlikely to find it when you analyse the piece.
But if you listen to successive versions of the piece, starting from the original
motivic canon, then with the permutations added, then the instrument
assignments changed, then the chord progression version, you can
still hear that you get from one to the other by audible similarities.

Also, the result isn't trivial and obviously "non fractal" like a circle
visually, so it seems that analgous to the visual randomised fractals,
perhaps one should still call it a fractal after all.

What makes it harder than the visual case is that you have only finite divisibility
while in the visual case, though there could be hard to call cases, generally
if you look for intricate infinitely divisible detail, and a sort of "sense of sameness"
in that detail with the overall tune, then you can reasonably still call it a fractal.
Visually it is a bit fuzzy too but musically it is much harder to draw an exact line
becaue of the finite divisibility - and perhaps a tendency for music to be fractal anyway
if it sounds interesting.

So then another approach is to think that music generated by a fractal in some
way or another is likely to have some kind of scaling properties even if you
can't easily spot it sometimes, or know how to unravel the music to spot
the hidden fractals in it. So if you know how it is constructed, unless you
can see easily that it isn't fractal, if constructed using fractal methods e.g.
from visual fractals, and if it sounds interesting, it tseems to me a reasonale
guess that it very probably is  fractal in some way or another.

So I'd vote for calling music fractal music unless it is obviously not
fractal, if generated from fractals, even if the underlying fractal
is quite hidden, so long as the result is "interesting".
That's just my own point of view please be clear, I'm not trying
to lay down the law and convince others to it. I'd say that perhaps
it is also what the term has come to mean colloquially amongst
those working in the area as well, but may be wrong there.

The interesting thing about Harlan Brothers research
is that it is to do with finding out how to tell if music has scaling
properties. It could be used to analyse fractal music
to see if it has various scaling properties. Sort of analagous
to hausdorf dimension which we can't really use in musical
fractals because you don't have the infinite divisibility.

So I think it is an interesting line of investigation to learn more about.
It could be used to find out more about the fractal music we have
been working on, and also about other composed music, not intentionally
fractal but with fractal properties probably nevertheless.

I'd start by saying - this music is fractally generated, lets call it fractal
music to give it the benefit of the doubt as it were as it probably is
- then see if we can unravel it and find its fractal scaling properties
in some way - either directly or in some indirect way as in my
permuted, instrument reassigned, chord progression superimposed,
motivic canons.

If you don't find anything, rather than say it is definitely "not fractal"
- I think it is very hard to say that for music, one would just say
I can't yet pick out any scaling properties in it yet - but it is possible
that future analysis might find something, and if it sounds "interesting"
then the chances are that there is something fractal there
as for ordinary composed music.

By selecting for music that sounds good, we are probably helping to
pick out the most fractally structured of the fractally generated music.
So that's another thing - it could be fractally generated, and have
fractal structure, but the structure is there only because the human composer
has chosen the most fractal of the tunes you could generate using that
particular method, so not necessarily an inevitable result of the method,
but a result of a combination of the method and human involvement in the
composition process.

> Not being a native English speaker it still seems
to me that "Fractal music" and "Music based on
fractals" are two different matters.


[Non-text portions of this message have been removed]

[Harlan Brothers]

OK.  My guess is that our collective time is better spent making
music regardless of how we individually choose to classify it.  I
will try to clarify some erroneous comments about my work.  

> It appears to me that Harlan's definition
> of "fractal music", however, seeks to define
> only exact self-similarity as being truly
> fractal,

I am not sure how anyone who did due diligence reached this
conclusion.  In fairness, the main page devotes substantial space to
mensuration canons, but that is because they are easiest to
understand and give some historical sense to the creative expression
of our inherently fractal nature.  However, the same page states "As
with graphics, music can exhibit a wide variety of scaling
behavior."  The link to background information includes details on
duration and pitch scaling, both of which involve distribution-
related analysis.  My paper on Bach and Cantor that was recently
trashed by at least one member of this group on Ivars Peterson's blog
also discusses the existence of statistical self-similarity with
respect to music.


> ...dismissing all other definitions
> as "relatively meaningless. ""

None of us here invented the word "fractal."  Only one man did.  I
have been fortunate enough to work with Benoit and the extraordinary
Michael Frame for almost six years.  I can't speak for anyone else,
but if the "prerequisites" for fractality that are listed on my site
are good enough for them, they're good enough for me.


> So it's one rule for visuals, but another for music?

No!  And you have hit the nail precisely on the head.  Fractal
geometry is, first, geometry.  The characteristic of being "fractal"
is inextricably tied to structure.  Take the Koch curve.  Here is the
generator:

_/\_

For the purpose of this illustration (and my sanity), we will imagine
two iterations of this generator.  It is composed of 4^3 individual
line segments.  Here I rearrange those 64 segments:

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

I hope no one would claim that this is "fractal."  There, are
however, many ways to use these segments to construct something else
that is either rigidly or statistically self-similar.

The point is, when one deconstructs a graphic and arbitrarily maps
its features in a different way, there is no guarantee that the
result is still fractal.  It may be.  It may not be - unless specific
care is taken in the mapping to insure a fractal distribution.  One
of the many things I've been working on (and I am not alone) is how
to assess the extent to which any music exhibits some kind of fractal
distribution.

That's all for now...  I hope this helps to clarify things.

Best,
Harlan

[Phil Thompson-6]

"I hope this helps to clarify things".

Which precisely illustrates my point, Harlan.  All over your web-site
you assume that such clarification is necessary and if a person is
using the term "fractal music" in any way that is different from your
own they are guilty of "misconception" or "common errors" and
engaging in "the worst kind of nonsense" – and not only on your web-
site but you quoted these words in PDF documents to download, print
and distribute.  Trashing?  These are techniques used by
misinformation propaganda.

You do not seem to realise that since the early 1990s the
term "fractal music" has not just been used as an adjective and a
noun and in fact has been used as the title of a genre which has
included both music derived from fractals, and music with fractal
characteristics.  And many people in that field including myself
fully understood the difference and used the title to apply to all
because we regarded the distinction as trivial.  

Thanks for the lesson about Koch curves.  As if we needed it.  Sheesh.

"I am not sure how anyone who did due diligence reached this
conclusion."

This is rich coming from someone who has allegedly been tasked to
perform a "rigorous treatment" of this subject because had you done
much research into this field you would know this.  I wonder how many
of the sites you criticise on your own you actually bothered to
read.  Rigorous screwing-over, more like, of many people who have
spent a huge amount of time writing software, making music and
promoting these techniques for relatively little reward since the
early 1990s or before, long before you or your friends at Yale ever
showed much of an interest in it.

"OK. My guess is that our collective time is better spent making
music regardless of how we individually choose to classify it."

That has been precisely my point for well over a decade.  Yet by all
accounts you are the one on the personal crusade to define how
everybody should classify it.  Hypocrisy.

And it doesn't remotely surprise me that Lauri would comment in
support of you on this, because he's another person who arrived in
the field very late in the day having developed techniques that had
been in use by others in this field for over a decade.

Regarding Benoit Mandelbrot, I have always paid him nothing but the
utmost respect for his work, and I can only assume that his implied
support of your sweeping generalisations regarding the activity of
others in the field is a result of his misunderstanding of the level
of reverence many of us out here have always felt towards him.

But you aren't the only person in this field to have support of
influential people – people such as Ian Stewart through to Arthur
C.Clarke have been supporters of mine from as much as ten years ago.  
And they fully understood how my music is made and whether it is
derived from a fractal, or has fractal characteristics, or in many
cases both, have not had any qualms about supporting it as such.  But
unlike you I have rarely mentioned such support because I am not in
the habit of name-dropping.

I have now cancelled my next fractal album and removed all fractal
formulae and methods from my next music generation system and will be
focusing my efforts on non-fractal generative music.  Because
frankly, I no longer wish my work to be associated with you, Yale,
etc. in the future, even in error.  I feel your writings on this
subject have done many people in this field a huge personal injustice
and the genre itself a huge disservice.  As a result I am no longer
interested in it, the appeal has been totally ruined for me, you're
welcome to it.

I will no longer be visiting this forum.  Respect to all those that I
have corresponded with over the past ten years, and particular to
Phil Jackson for not only our endless shared adventures in
composition for over a decade, but also for being a true friend
through the worst times, as well as the best.

Phil Thompson
http://fractalmusician.com

[webmonkey]

Phil T,

Take a deep breath and do not do this.  An argument over terms is just a
silly thing....

Phil J.

 

On Mon, 2008-09-29 at 05:40 +0000, Phil Thompson wrote:

> "I hope this helps to clarify things".
>
> Which precisely illustrates my point, Harlan. All over your web-site
> you assume that such clarification is necessary and if a person is
> using the term "fractal music" in any way that is different from your
> own they are guilty of "misconception" or "common errors" and
> engaging in "the worst kind of nonsense" – and not only on your web-
> site but you quoted these words in PDF documents to download, print
> and distribute. Trashing? These are techniques used by
> misinformation propaganda.
>
> You do not seem to realise that since the early 1990s the
> term "fractal music" has not just been used as an adjective and a
> noun and in fact has been used as the title of a genre which has
> included both music derived from fractals, and music with fractal
> characteristics. And many people in that field including myself
> fully understood the difference and used the title to apply to all
> because we regarded the distinction as trivial.
>
> Thanks for the lesson about Koch curves. As if we needed it. Sheesh.
>
> "I am not sure how anyone who did due diligence reached this
> conclusion."
>
> This is rich coming from someone who has allegedly been tasked to
> perform a "rigorous treatment" of this subject because had you done
> much research into this field you would know this. I wonder how many
> of the sites you criticise on your own you actually bothered to
> read. Rigorous screwing-over, more like, of many people who have
> spent a huge amount of time writing software, making music and
> promoting these techniques for relatively little reward since the
> early 1990s or before, long before you or your friends at Yale ever
> showed much of an interest in it.
>
> "OK. My guess is that our collective time is better spent making
> music regardless of how we individually choose to classify it."
>
> That has been precisely my point for well over a decade. Yet by all
> accounts you are the one on the personal crusade to define how
> everybody should classify it. Hypocrisy.
>
> And it doesn't remotely surprise me that Lauri would comment in
> support of you on this, because he's another person who arrived in
> the field very late in the day having developed techniques that had
> been in use by others in this field for over a decade.
>
> Regarding Benoit Mandelbrot, I have always paid him nothing but the
> utmost respect for his work, and I can only assume that his implied
> support of your sweeping generalisations regarding the activity of
> others in the field is a result of his misunderstanding of the level
> of reverence many of us out here have always felt towards him.
>
> But you aren't the only person in this field to have support of
> influential people – people such as Ian Stewart through to Arthur
> C.Clarke have been supporters of mine from as much as ten years ago.
> And they fully understood how my music is made and whether it is
> derived from a fractal, or has fractal characteristics, or in many
> cases both, have not had any qualms about supporting it as such. But
> unlike you I have rarely mentioned such support because I am not in
> the habit of name-dropping.
>
> I have now cancelled my next fractal album and removed all fractal
> formulae and methods from my next music generation system and will be
> focusing my efforts on non-fractal generative music. Because
> frankly, I no longer wish my work to be associated with you, Yale,
> etc. in the future, even in error. I feel your writings on this
> subject have done many people in this field a huge personal injustice
> and the genre itself a huge disservice. As a result I am no longer
> interested in it, the appeal has been totally ruined for me, you're
> welcome to it.
>
> I will no longer be visiting this forum. Respect to all those that I
> have corresponded with over the past ten years, and particular to
> Phil Jackson for not only our endless shared adventures in
> composition for over a decade, but also for being a true friend
> through the worst times, as well as the best.
>
> Phil Thompson
> http://fractalmusician.com
>
>
>
>
>  

[Lawrence Ball]

Dear Phil,

The term fractal music means what anyone wants it to mean, not what an
academic wants to make it.
Nobody has a monopoly on it, nor should they, creative words should
remain open-ended. Lets debate and not cut up the space that belongs to
everyone.

I feel Phil it would be good to not buy into external influences,
particularly belief systems of others,
that invoke doubt concerning sincere and virtuous endeavours.
If there is one salient observation I have from observing the community
of musicians, it is that those who encourage others, who find something
to say about what they like about the creative work of others are more
worthwhile than those who feel a need to criticise, put down or
discourage.
Those are more likely artists who do have something genuinely and
substantially solid to say when they are behind the "driving wheel".

Just felt to encourage you not to believe but to intuit and let the mud
dry before pulling it off.

When did you ever see a statue of a critic?

best wishes
Lawrence Ball

http://www.lawrenceball.org                              PERSONAL WEB SITE
http://www.myspace.com/lawrenceballmusic               LB MYSPACE MUSIC
SITE
http://www.myspace.com/planettreemusic                        CONTEMPORARY MUSIC FESTIVAL


On Sep 29, 2008, at 06:40, Phil Thompson wrote:

> "I hope this helps to clarify things".
>
> Which precisely illustrates my point, Harlan.  All over your web-site
> you assume that such clarification is necessary and if a person is
> using the term "fractal music" in any way that is different from your
> own they are guilty of "misconception" or "common errors" and
> engaging in "the worst kind of nonsense" – and not only on your web-
> site but you quoted these words in PDF documents to download, print
> and distribute.  Trashing?  These are techniques used by
> misinformation propaganda.
>
> You do not seem to realise that since the early 1990s the
> term "fractal music" has not just been used as an adjective and a
> noun and in fact has been used as the title of a genre which has
> included both music derived from fractals, and music with fractal
> characteristics.  And many people in that field including myself
> fully understood the difference and used the title to apply to all
> because we regarded the distinction as trivial.
>
> Thanks for the lesson about Koch curves.  As if we needed it.  Sheesh.
>
> "I am not sure how anyone who did due diligence reached this
> conclusion."
>
> This is rich coming from someone who has allegedly been tasked to
> perform a "rigorous treatment" of this subject because had you done
> much research into this field you would know this.  I wonder how many
> of the sites you criticise on your own you actually bothered to
> read.  Rigorous screwing-over, more like, of many people who have
> spent a huge amount of time writing software, making music and
> promoting these techniques for relatively little reward since the
> early 1990s or before, long before you or your friends at Yale ever
> showed much of an interest in it.
>
> "OK. My guess is that our collective time is better spent making
> music regardless of how we individually choose to classify it."
>
> That has been precisely my point for well over a decade.  Yet by all
> accounts you are the one on the personal crusade to define how
> everybody should classify it.  Hypocrisy.
>
> And it doesn't remotely surprise me that Lauri would comment in
> support of you on this, because he's another person who arrived in
> the field very late in the day having developed techniques that had
> been in use by others in this field for over a decade.
>
> Regarding Benoit Mandelbrot, I have always paid him nothing but the
> utmost respect for his work, and I can only assume that his implied
> support of your sweeping generalisations regarding the activity of
> others in the field is a result of his misunderstanding of the level
> of reverence many of us out here have always felt towards him.
>
> But you aren't the only person in this field to have support of
> influential people – people such as Ian Stewart through to Arthur
> C.Clarke have been supporters of mine from as much as ten years ago.
> And they fully understood how my music is made and whether it is
> derived from a fractal, or has fractal characteristics, or in many
> cases both, have not had any qualms about supporting it as such.  But
> unlike you I have rarely mentioned such support because I am not in
> the habit of name-dropping.
>
> I have now cancelled my next fractal album and removed all fractal
> formulae and methods from my next music generation system and will be
> focusing my efforts on non-fractal generative music.  Because
> frankly, I no longer wish my work to be associated with you, Yale,
> etc. in the future, even in error.  I feel your writings on this
> subject have done many people in this field a huge personal injustice
> and the genre itself a huge disservice.  As a result I am no longer
> interested in it, the appeal has been totally ruined for me, you're
> welcome to it.
>
> I will no longer be visiting this forum.  Respect to all those that I
> have corresponded with over the past ten years, and particular to
> Phil Jackson for not only our endless shared adventures in
> composition for over a decade, but also for being a true friend
> through the worst times, as well as the best.
>
> Phil Thompson
> http://fractalmusician.com
>
>
>
> ------------------------------------
>
> Yahoo! Groups Links
>
>
>
>

http://www.lawrenceball.org                              PERSONAL WEB SITE
http://www.myspace.com/lawrenceballmusic               LB MYSPACE MUSIC
SITE
http://www.myspace.com/planettreemusic                        CONTEMPORARY MUSIC FESTIVAL



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[Robert Walker-7]

Yes don't do this, truth prevails.

Honestly I think a lot of it is that he is new to the field and just wasn't aware of the work done. When I first wrote FTS then I thought that I was the first to have the idea of a fractal tune because I hadn't come across any. Like when you know where to look there's lots of work out there but it is so easy to not come across it. In my case, since the 1990s FTS has been available for download with motivic canons as the main construction method, yet some of you on this list weren't aware of it. I know I'm not aware of a lot of work in the field because I spend most of my time naturally working on my own program, just look in here to see some of the discussions from time to time or listen to some of the example tunes people post here or on their web sites, but I haven't explored the programs much at all. Some time when I have lots of time on my hands :-). So similarly I don' t expect the rest of you to necessarily know much about my program either. That's fine :-).

So let's extend the same courtesy to him. I'm sure he has a lot to offer to the field, with a new perspective. And articles like that even if some of what they say may seem obvious to old hands - yet they are interesting to newbies, and still brings many new people in the field.  And one can find some things of interest as well, everyone has a fresh look on it. I hadn't looked at the Bach bourree in that way myself before, and was interested in what he said.

I think his line of research is interesting and may well lead somewhere, trying to get a handle on how you can measure fractal features in fractal music. Perhaps we can suggest new ideas to investigate?

Robert

[Non-text portions of this message have been removed]

[Robert Walker-7]

Hi Phil

> Absolutely.  In fact "Steeltown", the first ever piece I wrote, in the
mid 1980s, used a mensuration canon.  It's a piece I have always loved
and made several versions of over the years, but never released on a
fractal album, because until a couple of years ago when I was looking
at the sequencer file the penny hadn't dropped that it was fractal - I
had assumed it wasn't because I created it by hand.  I'd been inspired
by the basslines on things like Eurythmics "Sexcrime (1984)" and
Queen's "Radio Ga Ga" and had doodled repeating sequences of bass
notes in parallel using different durations to cause a "polyrhythm".
Once I realised it was fractal I decided I would release it some day
and it's going to be on my next album.  (And it has been on my MySpace
player for months)....

Interesting. That must be just about the same time I got my idea of a fractal
tune. In those days I didn't have a computer of my own, I was studying maths
but in a field (mathematical logic) that required no computation at all at least
in those days - so I used computers just for word processing.

So I remember writing it out and then playing the result, or trying to work it all
out in my mind as I played - and I could get so far, but not really far enough to
get a good idea of what the possibilities were so just left it to one side. Later on
well the first computer I got didn't have musical capabilities. But as soon as I
had a computer with a soundcard then I programmed it within a month or two
probably, can't remember the dates, could look it up easily but some time in the
1990s.

> And I agree with you regarding "scaling" also.  You can't "zoom in" on
a piece of fractal music.  The only way to really do that would be to
have a composition that had some kind of dynamic generator that would
create layer upon layer of additional intermediary note detail
depending upon listening / viewing "dimension".  

Did you see my cantors set mensuration canon? That works exactly like that.
It has notes so short and close together that they merge, and you could zoom
in on those just like a visual fractal, and hear more detail. It is a bit of a curiosity
really, because arbitrary small pitch differences don't fit our usual ideas of how
music works, but you could imagine it would work like a visual fractal for a
species whose ears worked in a similar way to our eyes (bats??).

http://robertinventor.com/software/tunesmithy/tune_smithy_seeds.htm#fractalpitches

For us humans it is probably more interesting as a way of illustrating why
musical fractals *normally* aren't infinitely divisible.

Robert



[Non-text portions of this message have been removed]

[Robert Walker-7]

Just another thought, maybe it will help. I anyway don't think of fractal as a value
judgement, any kind of a way of deciding whether the music is better or not.
I don't think Harlan is either from what I read on his web site. Rather more in
a mathematical spirit, trying to give the word a precise mathematical meaning
as far as he can, in a field where such precise meanings seem to be a bit
elusive..

That may be a reason for using a more neutral term such as "scaling properties"
and reserving fractal music for music derived from fractals in any way
(apart from the trivial things that are clearly not fractal at all). Especially
given the consensus of usage that has sprung up in the field.

The person who coins a word doesn't usually have the last word on how it
is to be used. Since Mandelbrot apparently hasn't got much involved in
fractal music, he may not be the best person at this point to decide how
the word should be used in this field, not yet anyway, and if so of course,
he is in no position to decide who should make that decision either and
I shouldn't think he has tried to do that. I'm sure it would be more of an open
ended question to stimulate research in a field that he is not personally
involved in. No disrespect intended to anyone of course!

Well I've posted rather a lot, better bail out for now, got lots of programming to do
for that matter, sorry if I've said too much, I do tend to get carried away and
type quickly.

Thanks,

Robert

[Non-text portions of this message have been removed]

[webmonkey]

I think, or hope we all can agree to disagree at times on the
particulars of some term or another.  If we all agreed 100% of the time
and thought identically, there would be need of only one of us!

Phil J.
 


On Mon, 2008-09-29 at 08:07 +0100, Lawrence Ball wrote:

> Dear Phil,
>
> The term fractal music means what anyone wants it to mean, not what an
> academic wants to make it.
> Nobody has a monopoly on it, nor should they, creative words should
> remain open-ended. Lets debate and not cut up the space that belongs to
> everyone.
>
> I feel Phil it would be good to not buy into external influences,
> particularly belief systems of others,
> that invoke doubt concerning sincere and virtuous endeavours.
> If there is one salient observation I have from observing the community
> of musicians, it is that those who encourage others, who find something
> to say about what they like about the creative work of others are more
> worthwhile than those who feel a need to criticise, put down or
> discourage.
> Those are more likely artists who do have something genuinely and
> substantially solid to say when they are behind the "driving wheel".
>
> Just felt to encourage you not to believe but to intuit and let the mud
> dry before pulling it off.
>
> When did you ever see a statue of a critic?
>
> best wishes
> Lawrence Ball
>
> http://www.lawrenceball.org                              PERSONAL WEB SITE
> http://www.myspace.com/lawrenceballmusic               LB MYSPACE MUSIC
> SITE
> http://www.myspace.com/planettreemusic                        CONTEMPORARY MUSIC FESTIVAL
>
>
> On Sep 29, 2008, at 06:40, Phil Thompson wrote:
>
> > "I hope this helps to clarify things".
> >
> > Which precisely illustrates my point, Harlan.  All over your web-site
> > you assume that such clarification is necessary and if a person is
> > using the term "fractal music" in any way that is different from your
> > own they are guilty of "misconception" or "common errors" and
> > engaging in "the worst kind of nonsense" – and not only on your web-
> > site but you quoted these words in PDF documents to download, print
> > and distribute.  Trashing?  These are techniques used by
> > misinformation propaganda.
> >
> > You do not seem to realise that since the early 1990s the
> > term "fractal music" has not just been used as an adjective and a
> > noun and in fact has been used as the title of a genre which has
> > included both music derived from fractals, and music with fractal
> > characteristics.  And many people in that field including myself
> > fully understood the difference and used the title to apply to all
> > because we regarded the distinction as trivial.
> >
> > Thanks for the lesson about Koch curves.  As if we needed it.  Sheesh.
> >
> > "I am not sure how anyone who did due diligence reached this
> > conclusion."
> >
> > This is rich coming from someone who has allegedly been tasked to
> > perform a "rigorous treatment" of this subject because had you done
> > much research into this field you would know this.  I wonder how many
> > of the sites you criticise on your own you actually bothered to
> > read.  Rigorous screwing-over, more like, of many people who have
> > spent a huge amount of time writing software, making music and
> > promoting these techniques for relatively little reward since the
> > early 1990s or before, long before you or your friends at Yale ever
> > showed much of an interest in it.
> >
> > "OK. My guess is that our collective time is better spent making
> > music regardless of how we individually choose to classify it."
> >
> > That has been precisely my point for well over a decade.  Yet by all
> > accounts you are the one on the personal crusade to define how
> > everybody should classify it.  Hypocrisy.
> >
> > And it doesn't remotely surprise me that Lauri would comment in
> > support of you on this, because he's another person who arrived in
> > the field very late in the day having developed techniques that had
> > been in use by others in this field for over a decade.
> >
> > Regarding Benoit Mandelbrot, I have always paid him nothing but the
> > utmost respect for his work, and I can only assume that his implied
> > support of your sweeping generalisations regarding the activity of
> > others in the field is a result of his misunderstanding of the level
> > of reverence many of us out here have always felt towards him.
> >
> > But you aren't the only person in this field to have support of
> > influential people – people such as Ian Stewart through to Arthur
> > C.Clarke have been supporters of mine from as much as ten years ago.
> > And they fully understood how my music is made and whether it is
> > derived from a fractal, or has fractal characteristics, or in many
> > cases both, have not had any qualms about supporting it as such.  But
> > unlike you I have rarely mentioned such support because I am not in
> > the habit of name-dropping.
> >
> > I have now cancelled my next fractal album and removed all fractal
> > formulae and methods from my next music generation system and will be
> > focusing my efforts on non-fractal generative music.  Because
> > frankly, I no longer wish my work to be associated with you, Yale,
> > etc. in the future, even in error.  I feel your writings on this
> > subject have done many people in this field a huge personal injustice
> > and the genre itself a huge disservice.  As a result I am no longer
> > interested in it, the appeal has been totally ruined for me, you're
> > welcome to it.
> >
> > I will no longer be visiting this forum.  Respect to all those that I
> > have corresponded with over the past ten years, and particular to
> > Phil Jackson for not only our endless shared adventures in
> > composition for over a decade, but also for being a true friend
> > through the worst times, as well as the best.
> >
> > Phil Thompson
> > http://fractalmusician.com
> >
> >
> >
> > ------------------------------------
> >
> > Yahoo! Groups Links
> >
> >
> >
> >
> http://www.lawrenceball.org                              PERSONAL WEB SITE
> http://www.myspace.com/lawrenceballmusic               LB MYSPACE MUSIC
> SITE
> http://www.myspace.com/planettreemusic                        CONTEMPORARY MUSIC FESTIVAL
>
>
>
> ------------------------------------
>
> Yahoo! Groups Links
>
>
>

[webmonkey]

Nice thoughts, Robert.  I don't think we need to develop a scale of
"fracticality" as if we were measuring a hurricane or earthquake.  It is
what it is.  Just because a piece is a Cat 3 Major Fractal Music Work
does not make it good...but anyone feel free to do so if you wish.

Besides, a good number of folks will combine output from different
generators & perhaps even a live instrument or two to create their
pieces.  

The ultimate criteria is "do you enjoy listening to it"?

Phil J.
   


On Mon, 2008-09-29 at 17:47 -0700, Robert Walker wrote:

> Just another thought, maybe it will help. I anyway don't think of
> fractal as a value
> judgement, any kind of a way of deciding whether the music is better
> or not.
> I don't think Harlan is either from what I read on his web site.
> Rather more in
> a mathematical spirit, trying to give the word a precise mathematical
> meaning
> as far as he can, in a field where such precise meanings seem to be a
> bit
> elusive..
>
> That may be a reason for using a more neutral term such as "scaling
> properties"
> and reserving fractal music for music derived from fractals in any way
> (apart from the trivial things that are clearly not fractal at all).
> Especially
> given the consensus of usage that has sprung up in the field.
>
> The person who coins a word doesn't usually have the last word on how
> it
> is to be used. Since Mandelbrot apparently hasn't got much involved
> in
> fractal music, he may not be the best person at this point to decide
> how
> the word should be used in this field, not yet anyway, and if so of
> course,
> he is in no position to decide who should make that decision either
> and
> I shouldn't think he has tried to do that. I'm sure it would be more
> of an open
> ended question to stimulate research in a field that he is not
> personally
> involved in. No disrespect intended to anyone of course!
>
> Well I've posted rather a lot, better bail out for now, got lots of
> programming to do
> for that matter, sorry if I've said too much, I do tend to get carried
> away and
> type quickly.
>
> Thanks,
>
> Robert
>
> [Non-text portions of this message have been removed]
>
>
>
>
>  

[Harlan Brothers]

Hi, Phil (T).

I nothing about you other than the fact that you are talented and
passionate about your music.  You should probably listen to your
friends, take a deep breath, and continue doing what you naturally do.

Your anger at me is misdirected.  Perhaps you should channel your
respect for Benoit into realizing that there are a host of wonderful
reasons for him to set me on this path.  If you truly believe that
music and images should have the same standard with regard to fractal
classification, then you and I share a fundamental agreement on the
subject.

It also follows that there are many misconceptions out there.

It is unfortunate that you hold such ill-will.  The example of the
Koch curve I mentioned TO THE ENTIRE GROUP was a response your
assertion that *I* am somehow the one who wishes to treat graphics
and music differently.  I took this to be a sincere discussion and
yet, for whatever reason, you felt compelled to mock me.  I hope you
at least understand now that your assertion was simply wrong.

Like others in this group, I am only one person with many interests
and responsibilities.  I plug ahead and have enjoyed the
input of others.  You still seem to miss the point that there is no
competition here and that I am working primarily on mathematical
analysis.

Anyone can use the term "fractal music" however they like.  History
is replete with terms that come to have multiple meanings.  In this
case, Benoit's original term makes no sense without a mathematical
underpinning and, by extension, my work would be meaningless without
having a rigorous frame of reference and clearly defined terms.  If,
for the sake of everyone present and future, we can avoid confusion,
all the better.  Either way, the music goes on.

As I believe you've said, why should you give a "rat's ass" what I
think?  It sounds, however, like you do.  People who understand the
math and wish to share their work and their insights with me already
do that.  You have no obligation here.

Contrary to your angry assertions, "my" definition of "fractal music"
deliberately casts a wide net with regard to music that possesses
*some kind* of power-law relation.  One of the big challenges,
particularly with non-algorithmic music, is figuring out what forms
such relations might take.  I find that challenge compelling.

I also find that even heartfelt issues can be more effectively
discussed in civil tones.

Harlan

[Lauri Grohn-2]

On 29.9.2008, at 8.40, Phil Thompson wrote:

> And it doesn't remotely surprise me that Lauri would comment in
> support of you on this, because he's another person who arrived in
> the field very late in the day having developed techniques that had
> been in use by others in this field for over a decade.

I did my first experiments 1988 and some results of those are  
available on my pages. The techniques is not the point but the music  
generated without too much of human involvement.

Lauri Gröhn
http://selfgeneratedmusic.blogspot.com/



[Non-text portions of this message have been removed]

[jacky schreiber]

Hi all,

I have a question for Lauri, Phil T, Phil J, Rober W, Dr. Brothers or
anyone who wants to answer,
can any of you identify a fractal music by listening to it? OR by analizing
a midi file (if available) OR by looking/analizing at a score (if
available)?

regards


jacky

----------- Mensaje Original --------------

De: Lauri Gröhn [lauri.grohn@...]
Para: cnfractal_music@... [cnfractal_music@...]
Cc:
Asunto: Re: [cnfractal_music] Re: Fractal Tunes and Some Clarification
Fecha: 01/10/2008 00:56:38
Mensaje:


On 29.9.2008, at 8.40, Phil Thompson wrote:

> And it doesn't remotely surprise me that Lauri would comment in
> support of you on this, because he's another person who arrived in
> the field very late in the day having developed techniques that had
> been in use by others in this field for over a decade.

I did my first experiments 1988 and some results of those are
available on my pages. The techniques is not the point but the music
generated without too much of human involvement.

Lauri Gröhn
http://selfgeneratedmusic.blogspot.com/

[Non-text portions of this message have been removed]


 

[Lauri Grohn-2]

On 1.10.2008, at 15.13, jacky schreiber wrote:

> Hi all,
>
> I have a question for Lauri, Phil T, Phil J, Rober W, Dr. Brothers or
> anyone who wants to answer,
> can any of you identify a fractal music by listening to it? OR by  
> analizing
> a midi file (if available) OR by looking/analizing at a score (if
> available)?

I have never heard any real fractal music. Does it even exist? Of  
course my SW can generate music from any fractal picture, but it is  
not fractal music.
Lauri Gröhn
http://www.synestesia.fi/

>
> regards
>
>
> jacky
>
> ----------- Mensaje Original --------------
>
> De: Lauri Gröhn [lauri.grohn@...]
> Para: cnfractal_music@...  
> [cnfractal_music@...]
> Cc:
> Asunto: Re: [cnfractal_music] Re: Fractal Tunes and Some Clarification
> Fecha: 01/10/2008 00:56:38
> Mensaje:
>
>
> On 29.9.2008, at 8.40, Phil Thompson wrote:
>
>> And it doesn't remotely surprise me that Lauri would comment in
>> support of you on this, because he's another person who arrived in
>> the field very late in the day having developed techniques that had
>> been in use by others in this field for over a decade.
>
> I did my first experiments 1988 and some results of those are
> available on my pages. The techniques is not the point but the music
> generated without too much of human involvement.
>
> Lauri Gröhn
> http://selfgeneratedmusic.blogspot.com/
>
> [Non-text portions of this message have been removed]
>
>
>
>
>
> ------------------------------------
>
> Yahoo! Groups Links
>
>
>

[Will Grant]

To what degree would anybody consider Mozart's 41st symphony  
fractal?  It's constructed from very few microscopically small  
musical units.  Could one say that the level of fractal intensity is  
a standard measure of excellence in Western Common Practice music?

[Robert Walker-7]

Hi There,

This one is fractal by almost any definition - well the rhythm certainly. The pitch also - that's assume you treat the pitch axis much as another space axis:
http://robertinventor.com/software/tunesmithy/tune_smithy_seeds.htm#fractalpitches

The similarity would involve slowing down the time to stretch the time axis, and spreading notes out in pitch (e.g. re-map subdivisions of a whole tone to similar subdivisions of an octave or whatever) to zoom in to the pitch axis.

One could say that pitch is highly non linear because of things like preferred intervals like octaves, fifths etc which we don't have in visual fractals. So though mathematically that is certainly a good fractal, musically it doesn't work quite as visual fractals do.

My sloth canons are fractal using a different kind of a similarity. It doesn't have infinite divisibility of pitch or time. So you can only zoom in a few steps. But you can zoom out a long way (though not for ever as eventually you hit the limits of human pitch perception).

The similarity is that if you play the tune faster, e.g. three times faster, and if you then remove every third note in the tune, then it sounds the same as it did before. Repeat that process any number of times and you still get the same tune.

Also if you take any phrase that occurs in the tune, and then play the tune for long enough, then that phrase will recur. So there is that uniformity and the fractal scaling effect.

Because pitch works so differently from vision, I think this is a better analogue of the visual fractal. You can easily test to see if a tune is fractal in this sense - by looking for a fractal construction of this type. It is usually immediately obvious if you listen to any of the standard sloth canons in Tune Smithy, what the seed phrase is, because you will hear a musical phrase that keeps repeating at different transpositions (often with different step sizes depending on the transposition but musically it sounds like a variant on the "same phrase" each time). Once you identify that phrase, just count how many notes it has, and if it has say seven notes, then eliminate all except every seventh note in the tune. If the result still sounds the same as the original tune - and if you can repeat that process for a large number of steps, then that is the first requirement for it to be one of these sloth canons. Then if you also get the almost periodicity, that any phrase in the tune of any length will eventually repeat, that's the other requirement satisfied.

So it is very well defined mathematically. The only question is whether to call this a fractal or not. The sloth canons that originally came with FTS use the same technique as the Koch snowflake, so a very simple iterative construction. The individual seed phrases are well defined and distinct.

There's another type that FTS can make, the fibonacci fractal tunes. These use Fibonacci rhythms, which is a well defined pattern. An example of this pattern is the sequence of wide and narrow rhombs along a row of a Penrose tiling. Because of the inflation / deflation rules, you can show that you can compose a short plus a long beat to make a new slower version of the long beat at the next level, and use the original long beat as a new version of the short beat at the next level. The result is the same identical rhythm, played more slowly. You get it by omitting notes in the original tune, but this time you use a more elaborate procedure. You look for a long beat followed by a short beat, and you just omit the note that divides those two beats to be left with a single long beat. The result is the same rhythm as before. You can use the same process to go out and out as often as you like with the rhythm.

So long as you are working in the realm of rhythm, where it makes sense in theory to slow down the rhythm by any arbitrary amount, then you can even make the rhythm infinitely detailed like a visual fractal, as the inflation rule can be used both ways either to zoom out for an existing pattern or to zoom in to add more subdivisions to make even faster versions of the same rhythm.

You could pick out the fractal structure there in a fractal rhythm e.g. by making the beats that mark out the slowest rhythm loudest of all, and the fastest beats quietest until they get so quiet you can hardly hear them but exceedingly rapid. In fact I could easily make an example of that using FTS if anyone is interested (no example included with FTS at present because I have only just thought of the idea of doing it while writing this).

The fibonacci rhythm is connected with the Penrose tiling which has a fractal type structure because of the aperiodicity and the inflation rules. The usual way the Penrose tiles are shown don't really bring this out as they are extremely uniform seeming when you zoon out and see them from a distance, not fractal like. But you could bring it out in some way if you  could make a 3D landscape out of a Penrose tiling so that it undulates by bringing out the underlying inflation rules that make it up.

I've not seen this suggested before so am thinking about it as I write. But I'm pretty sure it could be done.

Something like this (might be not quite right yet):

Take a penrose large rhomb. Substitute the small and large rhombs as here:
http://tilings.math.uni-bielefeld.de/substitution_rules/penrose_rhomb
Raise the vertex in the middle of the broad rhomb by a large amount say by the length of one of the edges in the tiling. Now substitute again for all the wide and narrow rhombs in the tiling so far. Leave the narrow ones unchanged and raise the centre of the broad rhombs again by the edge length, but this time in the new tiling so the amount it is raised is smaller. Keep repeating the process. Don't bother to try to keep the rhombs flat, just treat the tiling as a texture that you allow to rise and fall to follow the undulations of the landscape you are constructing.

Repeat the process and the result will look pretty much like a fractal. I'd need to do some work to make sure it really is one or maybe you need to modify it in some way. You would even get the infinite detail by going inwards to smaller and smaller tiles as subdivisions of the original tile.

That then would give an infinitely spiky type fractal landscape a bit like a 3D koch snowflake affair. Then in that fractal landsape, the fractal rhythms correspond to the undulations along one of the rows of tiles.

Perhaps I might get out pen and paper and see if I can make this rigorous, for now it is mainly arm waving.

But the 1D fractal rhythms of the fibonacci rhythms - they are very clear. The rhythms anyway because that's just time, - and maybe two dimensional if you include volume as the second dimension. Both are (more or less) linear and straightforward and anything you can do with a visual fractal of this type you can do equally well with a rhythm. So the cantor set type fractal you can do as a rhythm with fluctuating volumes or a fibonacci rhythm ditto. This time the two similiarities are - slowing down the time - and adjusting the volume range and threshold if necessary so that you can hear very quiet notes or small differences in volume.

Pitch is more tricky because the way we hear pitch is so different from volume and time, but I think the sloth canons anyway are a form of audible pitch fractal structure.

Just a few thoughts there. I can make those fractal rhythm examples though with FTS. Maybe I'll give that a go. Got a bit of programming I must do tomorrow but could try it out in a day or two. Also maybe have a go at that 2D penrose fractal idea if I have a bit of time for it :-).

Thanks, hope this helps,

Robert


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[Robert Walker-7]

Sorry, correction to that last e-mail - though probably it is obvious anyway just in case it gets you confused:

The similarity is that if you play the tune faster, e.g. three times faster, and if you then remove every third note in the tune, then it sounds the same as it did before. Repeat that process any number of times and you still get the same tune.

Should be

The similarity is that if you play the tune faster, e.g. three times faster, and if you then remove ALL EXCEPT every third note in the tune, then it sounds the same as it did before. Repeat that process any number of times and you still get the same tune.

Robert

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