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Re: Re: [cnfractal_music] Re: Fractal Tunes and Some Clarification

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  • 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
    Message 1 of 27 , Oct 1, 2008
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      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@yahoogroups.com [cnfractal_music@yahoogroups.com]
      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 Gröhn
      ... 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.
      Message 2 of 27 , Oct 1, 2008
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        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@yahoogroups.com
        > [cnfractal_music@yahoogroups.com]
        > 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
        Message 3 of 27 , Oct 1, 2008
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          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
          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
          Message 4 of 27 , Oct 1, 2008
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            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


            .

            [Non-text portions of this message have been removed]
          • Robert Walker
            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
            Message 5 of 27 , Oct 1, 2008
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              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

              [Non-text portions of this message have been removed]
            • Robert Walker
              BTW just want to make very clear. I don t in any way think that the Tune Smithy fractal tunes are the only musical analogues of a visual fractal. Clearly there
              Message 6 of 27 , Oct 1, 2008
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                BTW just want to make very clear. I don't in any way think that the Tune Smithy fractal tunes are the only musical analogues of a visual fractal. Clearly there are many, e.g. the Bach Bourree for one, seen in one way.

                It is just an example of one that I feel is perhaps particularly clear and easy to analyse, also obviously one that I have worked on for some time, so can easily talk about. I hope that it might perhaps suggest a few ideas to add to the mix when looking for fractal structures elsewhere.

                Robert

                [Non-text portions of this message have been removed]
              • Harlan Brothers
                Hi, Jacky.   First, a quick correction - I am not a Ph.D.  Perhaps the previous derisive talk of me as an academic type gave you the wrong
                Message 7 of 27 , Oct 1, 2008
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                  Hi, Jacky.
                   
                  First, a quick correction - I am not a Ph.D.  Perhaps the previous derisive talk of me as an "academic" type gave you the wrong impression.  I am a perfectly normal person who enjoys both music and mathematics. (Mind you, I hold nothing against people with advanced degrees). 
                   
                  > can any of you identify a fractal music by listening to it?
                   
                  There is at least one type of fractal construction for which the answer is "yes."  Composers began experimenting with "mensuration canons" about six centuries ago (I believe the earliest example dates back to the late 14th century).
                   
                  The idea is to take a theme or motif and repeat it simultaneously at different tempos.  It is a time-honored approach to composition.  I'm sure many of the members of this group have either written software that does this or have at least experimented with the technique.  Here is an example from one the geniuses of that early period:
                   
                  http://www.brotherstechnology.com/fractal-music/josquin.html .
                   
                  The one caveat is that it is necessary to have a minimum of three levels of scaling in order to exhibit the "power law relation" that is at the heart of the concept of what it means for something (or anything) to be fractal.
                   
                  I would add here that many fractal enthusiasts (of all kinds) express concern over the idea that a fractal must posses endless or infinite scaling.  This is NOT a requirement for identifying fractal structure.  Mathematical constructions often have this property, but it's worth remembering that Mandelbrot's seminal work on the subject was called "The Fractal Geometry of Nature."  Natural fractals can only exhibit scaling symmetry over a limited range of scales.  I believe music falls into this category.
                   
                  > ...OR by analizing a midi file (if available)
                   
                  This is a rich subject of research.  The answer is yes, but you must know what kind of scaling symmetry you are looking for.
                   
                  > OR by looking/analizing at a score
                   
                  Mensuration canons lend themselves well to this.  Here is a different type of example from Bach:
                   
                  http://www.maa.org/mathtourist/mathtourist_9_3_08.html .
                   
                   
                  Best,
                  Harlan
                   



                  ----- Original Message ----
                  From: jacky schreiber <jackysch@...>
                  To: cnfractal_music@yahoogroups.com
                  Sent: Wednesday, October 1, 2008 8:13:17 AM
                  Subject: Re: Re: [cnfractal_music] Re: Fractal Tunes and Some Clarification


                  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@ kolumbus. fi]
                  Para: cnfractal_music@ yahoogroups. com [cnfractal_music@ yahoogroups. com]
                  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://selfgenerate dmusic.blogspot. com/

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






                  [Non-text portions of this message have been removed]
                • Robert Walker
                  Hi Phil, I d say that I have two hats as it were. With my mathematical hat on then I m very interested in the fractal structure behind the music, make tunes
                  Message 8 of 27 , Oct 2, 2008
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                    Hi Phil,

                    I'd say that I have two "hats" as it were. With my mathematical hat
                    on then I'm very interested in the fractal structure behind the music,
                    make tunes that make it as obvious as possible, and would certainly
                    welcome a scale of "fracticality".

                    With my fractal composing hat on then I am often doing what I can
                    to make the fractal structure of tunes less obvious, or obscuring it in
                    many ways, and trying to see how far I can take that process while
                    keeping the sense of shape and architecture in the music that you get
                    with the fractals.

                    I'd say that the most obviously fractal music is by no means the best
                    musically - any more than the most exact metronomic rhythm is the best
                    musical rhythm. That is another thing I've worked a lot on in my program,
                    ways of making the rhythm sound less metronomic and more natural.

                    Nor could one really say - if it is say x% fractal then that's the best
                    exact percent to aim for. It depends on the piece. Some very fractal
                    pieces may sound good while others may sound better musically
                    if they are only slightly fractal, to the extent that you can't pick out
                    the fractal at all by ear, just have a feeling of overall architecture
                    and things happening at many time scales.

                    So I don't think "fracticality" is any kind of a value measure, just another
                    interesting tool for construction and analysis of the music.

                    Robert

                    > 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"?

                    [Non-text portions of this message have been removed]
                  • Robert Walker
                    Hi Will, That s an interesting thought. It might be a bit like those L-system trees with flowers and leaves, like the ones you can make with my Virtual Flower
                    Message 9 of 27 , Oct 2, 2008
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                      Hi Will,

                      That's an interesting thought. It might be a bit like those L-system trees with
                      flowers and leaves, like the ones you can make with my Virtual Flower program:
                      http://www.robertinventor.com/software/virtualflower/index.htm

                      The fractalness would come from the way a movement is structured
                      overall, with various levels of construction, and the themes would be
                      like the flowers and leaves bringing out that structure at the final level
                      of the fractal layer - well except the fractal structure if considered rhythmically
                      to some extent may extend to within a theme as well.

                      I think that many tunes have a rhythmic fracticality and a good example
                      would come from dance music. Example, because my relatives play
                      them all the time, I hear a lot of scottish folk music - fiddle tunes
                      etc - and they are often very fractal in structure with each bar
                      usually in two halves which answer each other, then
                      bars group in twos as "call and answer" rhythmically,
                      those then fall in to four bar units with the two halves answering each
                      other, and the four bar units often make up an eight bar section of the tune
                      in a similar fashion. The tune may repeat that eight bar section twice,
                      followed by another eight bar section similarly constructed
                      that concludes the tune.

                      In the call and answer, there is a build up of melodic tension during the
                      call part, that is then released during the answer, but not completely,
                      until it is all finally released at the end of the last answer at the slowest level.

                      I find you often get that in tunes, to the extent that if you
                      have a seven bar tune, especially if it is repeated a couple of times,
                      it can sound intersting and "unusual", I think because it breaks the
                      usual fractal structure we are used to hearing in tunes.

                      L-systems:.
                      http://en.wikipedia.org/wiki/L-system

                      Robert


                      > 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?


                      [Non-text portions of this message have been removed]
                    • Robert Walker
                      Here are some examples of the fractal tune sloth canons: http://www.robertinventor.com/software/fractal_music_Sloth_canons/index.htm With the first three
                      Message 10 of 27 , Nov 10, 2008
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                        Here are some examples of the fractal tune sloth canons:

                        http://www.robertinventor.com/software/fractal_music_Sloth_canons/index.htm

                        With the first three examples, if you speed the tune up a bit, and remove the quietest part, then it sounds the same (except that the volume of the first note depends on the total number of parts in the tune). The tunes also almost repeat. I made the first three to be as fractal as possible with this method.

                        Anyway if you follow the link there's more there about what makes the tune fractal.

                        Sorry for delay, I've been working on the program and improving the website, had a lot on. Also thanks for the information about fractint's capabilities for generating penrose tilings using L-systems - I'd come across fractint before but had no idea that it could do penrose tilings.

                        Thanks,

                        Robert

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