Yahoo Tuning Groups Ultimate Backup makemicromusic Automated counterpoint

HI there,

Since FTS does a type of automated counterpoint, maybe it might
be interesting to say a bit about how it does it.

It's based on teh idea of passing notes. In the original form,
all the parts start in unison or at octaves (or more generally
non octaves, whateve is the interval of equivalence).

Then the first, fastest part plays its seed above that unison / octave,
as a passing note. The second part then plays its second note,
with the first part joining it to start a new seed.

That unison of second and first part is a poitn of rest, but also
a passing note with respect to the third part.

When the second part finishes its seed, the third part moves on to
its next note, where it is joined by the first two parts, so
now the three parts are all playig a unison / octave passing note
with respect to the fourth part..

So it goes on. When the last part goes onto its second note,
then it is still felt as an intermediate note because the seed
has just started, and there is lots still to go.

Even wtih one part only playing, one hears some kind of
pattern superimposed from the first notes of each seed,
which gives a kind of counterpoint to the tune.

YOu can hear lots of examples in real audio format at
http://www.tunesmithy.connectfree.co.uk/index.htm
or play them in FTS.

For instance, the marimba with string quartet has a very straightforward
fractal tune with the seed just 0 1 0 in scale degrees
in the five parts - it is a kind of demo of the idea to show
how it works.

The Basson solo with harp celesta and glockenspiel
one has a fractal tune, but with the parts playing notes from
any of the layers of ornamentation rather than in strict
succession, and the result is quite an intriguing
feeling of counterpoint - but actually it is still based
on this passing notes / octaves / unison idea. So,
nearly all the fractal tunes are based on it in
one way or another.

For an example in mp3 format (which is best to hear how
they were when I made them, or use an SB LIve!):

http://mp3.com.au/FractalTuneSmithy/Windchimesscale/

All the notes of the seed are the same length, however the notes
are played just a little faster as they get higher in pitch,
- this effect is not very pronounced. It also uses
an echo effect - each phrase staccato as it has
alternate rests and notes, and then if the slower
seed has a rest, the faster seed plays repeats the
previous seed again quietly, and if you have several
simultaneous rests in the parts, the top part will play
very quietly. So, it keeps varying in volume - but not in
a dramatic way either, all quite gentle.

Now, one can go on to do the same thing with non octave scales.
Another idea is to have the parts at some other interval
rather than the octave

If one has a scale like

1/1 6/5 11/8 3/2 7/4 2/1.

which I`ve been exploring recently, one can try placing the
parts three notes apart in the scale like this:

1/1 6/5 11/8 3/2 7/4 2/1 12/5 11/4 3/1 7/2 4/1 24/5 11/2

A B C D E

so A:B is 3/2, B:C is 8/5, C:D is 35/24, D:E is 11/7 etc, so the parts
are at varied intervals and chords at the points of rest where they
come together, so that they aren`t all the same, at octaves (and
don`t have to be "consonances" just because one is resting at them).

Then, lots of other things I explore, like arpeggios in the scale
that ascend and descend in different ways. Here, one could
ascend by 0 1 3 and descend by 0 2 3.

Here it is:
http://www.mp3.com.au/elevenlimitpentatonic

So basically it is a very simple idea. It's not an attempt to
make music following traditional rules of harmony at all, but
making something new that will work with a fractal
tune.

BTW what makes it fractal is that each part plays the same tune
as all the others, with varied speed.

The musical seed gets transformed as it moves up and down in the scale,
but the same thing is happening in all the parts, so they still all
play the same tune - the same notes, at varied speeds.

This corresponds to visual
fractals that look the same at all scales - the fractal tunes
sound the same at all speeds (if one had parts to play for each
of the layers of ornamentation).

There are various notions of fractal, ones that are exactly the
sane at every level, like FTS, or ones that have similar
structures at every level, but not identical - the
word fractal is a general neame for a field of study
rather than a precise mathematical term as such, though
terms like fractal dimension etc. have been given precise
mathematical definitions.

There are lots of fractal music programs, however I wonder if
FTS is unique so far in using _exactly_ similar fractals to make
music?

That's for the basic form of the fractal tune idea. The later
transformations and remappings and fractal rhythms and polyrhythms
make fractal tunes that are no longer exactly self similar,
however, they are still based on the same passing notes idea
for harmony / counterpoint.

I'd be interested to know what other techniques are used for
harmony / counterpoint in fractal tunes. Do
interesting harmonic structures arise naturally from, say,
the structure of the mandelbrot set or whatever?
Or, does the counterpoint need to be added in in some way?

When composing / improvising, I may to some extent use the passing
notes idea, - I think I do while improvising.

Idea is that you let your "mistakes" flow into the piece,
so that you treat them as passing notes, and a source
for inspiration and invention.

Also, I like passing from less to more chromaticism and
back again while improvising. Result is that one
treats the accidentals as passing notes rather than
changes of key, so that is also like some of the fractal
tunes.

Others, I do do kind of key changes, e.g. if yu have
an ordinary type scale, but then make it a non ascending one
that goes up to the 2/1, then down to the 3/2 for the repeat
you will go up one key in the circle of fifths whenever you
go past the end of the repeat of the scale, and down one
when you come back again. "Familiar territory" does this
- no mp3 yet, but its on the real audio page.

Robert

Hi Kraig

> This is quite fascinating. I am not sure i completely follow but it
> sounds like you have a cross between a canon by augmentation and the eastern
> idea of nuclear melody which i believe we discussed recently. Does this
> seem right?

Yes, that's it exactly. The canon works automatically by the fractal construction
method.

> a question also. When you say........

> For instance, the marimba with string quartet has a very straightforward
> fractal tune with the seed just 0 1 0 in scale degrees
> in the five parts -

> I am not sure if 0 means the same note repeated or a reference to the tonic
> as in 0 10
> meaning C D C.

Yes that's it.

> One thing similar I have played with is having a two part counterpuntal line

> played by 3 or four voices in unison but where the unison involve different
> voices.
> the simplest would be one above and one below with a third alternating
> unison between the two. Maybe a fourth alternating unison with the ones the
> third is not playing. The question then becomes what are the two melodies,
> the one above and below or the two alternating. a musical relativity.

Right, that's like the redistribution of the parts. Often the original melody
gets completely lost as often the parts are at octaves or whatever with
each other so each plays a selection of notes from the melody, and the other
selection is transposed to an octave below it or whatever, then
I often do it so that each part sustains its note to the next note it
plays, rather than pausing to let the next instrument play the next
note in the tune.

Robert

Automated counterpoint

🔗Robert Walker <robertwalker@...>

🔗Robert Walker <robertwalker@...>

🔗genewardsmith <genewardsmith@...>

🔗Robert Walker <robertwalker@...>

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