That's an interesting talk, thanks :).
You might like the Tune Smithy fractal tunes. With some of them you can see the visual shape of the fractal clearly.
This for instance
sounds lke this:
http://robertinventor.com/softwa...
It is a perfect fractal - if you zoom in on it by expanding both pitch and time, then a tiny detail of the tune sounds like the whole tune (except, that in the actual midi clip I stopped construction at a particular number of notes per second, but you could keep going indefinitely with this one)..
But that's an unusual example as the pitches get closer together to make it more like a visual fractal.
More generally in Tune Smithy then the similarity is that the tune sounds the same if you play it several times faster, and leave out some of the notes. You can then repeat that process as often as you like.
The result of that similarity transformation is exactly the same tune as the original, played a lot slower. In fact if you assign a different part or instrument to each of the layers of the construction you get a strict "sloth canon" as a result.
I've got a page about it here:
Seeds and Fractals - - Play & Create Tunes as intricate as Snowflakes - Tune Smithy (software)
Actually, with careful choice of volume levels for each part you can make it so that the entire sloth canon is (almost) completely unchanged (unless you listen to it carefully to the quiet details). In other words - it is a piece of music that sounds almost exactly the same when you play it at, say, a third of the original speed and increase the volume to compensate for the slower speed. You can't hear that the speed has changed or that anything has changed, unless you listen carefully to the quietest details in the tune. The idea you need to use get this to work is to make the faster parts quieter until the fastest and quietest parts in the sloth canon are almost inaudible.
I don't seem to have any videos up to demonstrate this, but have some examples in the Tune Smithy program itself. See the example fractal tunes in the Sloth Canons drop list. I will have a go at making a good quality on-line video of these. and add it to this article,
Often in practise you transform the tune in various ways so obscuring the sloth canon.
Here is a fractal tune, just a solo melody, playing all the notes of a strict sloth canon with many parts, made with Tune Smithy, and with video of the score. In this example it isn't transformed in any way, The sloth canon however probably isn't that obvious however as the faster melody includes all the notes of all the slower melody lines in the canon :).
You aren't really expected to hear this canon - it still works as a unifying structure whether you can pick it out as a canon or not.
Here is a playlist of them all with videos
http://www.youtube.com/playlist?...
Though nearly all of them are based on a sloth canon, you will probably only hear the underlying canon with a few of them as most often it is transformed so much as to be hard to impossible to spot.
But it seems this sloth canon musical structure might be what makes these tunes work.
These are musical fractals that sound quite a bit like composed music - yet they are constructed in a completely different way.
It's a bit of a mystery really, that the tunes work so well, because Tune Smithy doesn't actually use normal composition methods at all to make them. It just uses this musical fractal approach.
Which might suggest that those who say that music is fractal may be onto something. The reason they work might perhaps be because many natural sounds are at least somewhat fractal - such as the wind, waves, streams etc.
Also - though conventional composition isn't explicitly fractal in any obvious way, it is true that composers often use larger and larger structural forms creating fractals in their compositions as well, so might be that one or other of these reasons, or perhaps both, might be why these tunes work and appeal to us in a similar way to composed music.
I've just discovered some more about this.
Sloth canon sequences in the work of a Danish composer
The Danish composer Per Nørgård uses an endless self similar (fractal like) strict sloth canon structure in some of his compositions such as his Symphony number 2. He first discovered his sequence in 1959, so long before I got the idea of making sloth canon sequences for Tune Smithy.
His sequence is constructed in a different way from any of mine.
I've also figured out a general construction you can use to make any possible sloth canon type sequence for endless sloth canon music.
See my article on the Tune Smithy wiki here:
Self Similar Sloth Canon Number Sequences
You might like the Tune Smithy fractal tunes. With some of them you can see the visual shape of the fractal clearly.
This for instance
http://robertinventor.com/softwa...
It is a perfect fractal - if you zoom in on it by expanding both pitch and time, then a tiny detail of the tune sounds like the whole tune (except, that in the actual midi clip I stopped construction at a particular number of notes per second, but you could keep going indefinitely with this one)..
But that's an unusual example as the pitches get closer together to make it more like a visual fractal.
More generally in Tune Smithy then the similarity is that the tune sounds the same if you play it several times faster, and leave out some of the notes. You can then repeat that process as often as you like.
The result of that similarity transformation is exactly the same tune as the original, played a lot slower. In fact if you assign a different part or instrument to each of the layers of the construction you get a strict "sloth canon" as a result.
I've got a page about it here:
Seeds and Fractals - - Play & Create Tunes as intricate as Snowflakes - Tune Smithy (software)
Actually, with careful choice of volume levels for each part you can make it so that the entire sloth canon is (almost) completely unchanged (unless you listen to it carefully to the quiet details). In other words - it is a piece of music that sounds almost exactly the same when you play it at, say, a third of the original speed and increase the volume to compensate for the slower speed. You can't hear that the speed has changed or that anything has changed, unless you listen carefully to the quietest details in the tune. The idea you need to use get this to work is to make the faster parts quieter until the fastest and quietest parts in the sloth canon are almost inaudible.
I don't seem to have any videos up to demonstrate this, but have some examples in the Tune Smithy program itself. See the example fractal tunes in the Sloth Canons drop list. I will have a go at making a good quality on-line video of these. and add it to this article,
Often in practise you transform the tune in various ways so obscuring the sloth canon.
Here is a fractal tune, just a solo melody, playing all the notes of a strict sloth canon with many parts, made with Tune Smithy, and with video of the score. In this example it isn't transformed in any way, The sloth canon however probably isn't that obvious however as the faster melody includes all the notes of all the slower melody lines in the canon :).
You aren't really expected to hear this canon - it still works as a unifying structure whether you can pick it out as a canon or not.
Here is a playlist of them all with videos
http://www.youtube.com/playlist?...
Though nearly all of them are based on a sloth canon, you will probably only hear the underlying canon with a few of them as most often it is transformed so much as to be hard to impossible to spot.
But it seems this sloth canon musical structure might be what makes these tunes work.
These are musical fractals that sound quite a bit like composed music - yet they are constructed in a completely different way.
It's a bit of a mystery really, that the tunes work so well, because Tune Smithy doesn't actually use normal composition methods at all to make them. It just uses this musical fractal approach.
Which might suggest that those who say that music is fractal may be onto something. The reason they work might perhaps be because many natural sounds are at least somewhat fractal - such as the wind, waves, streams etc.
Also - though conventional composition isn't explicitly fractal in any obvious way, it is true that composers often use larger and larger structural forms creating fractals in their compositions as well, so might be that one or other of these reasons, or perhaps both, might be why these tunes work and appeal to us in a similar way to composed music.
I've just discovered some more about this.
Sloth canon sequences in the work of a Danish composer
The Danish composer Per Nørgård uses an endless self similar (fractal like) strict sloth canon structure in some of his compositions such as his Symphony number 2. He first discovered his sequence in 1959, so long before I got the idea of making sloth canon sequences for Tune Smithy.
His sequence is constructed in a different way from any of mine.
I've also figured out a general construction you can use to make any possible sloth canon type sequence for endless sloth canon music.
See my article on the Tune Smithy wiki here:
Self Similar Sloth Canon Number Sequences
About the Author
Robert Walker
Writer of articles on Mars and Space issues - Software Developer of Tune Smithy, Bounce Metronome etc.Studied at Wolfson College, Oxford
Lives in Isle of Mull
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