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 Forum index » Clavia Nord Modular » G2 Building Blocks
MathStep - a double stepper arppegiator
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bantri



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PostPosted: Mon May 16, 2005 4:40 pm    Post subject: MathStep - a double stepper arppegiator Reply with quote  Mark this post and the followings unread

An attempt to create arppegios based on a scale and using two steppers with 3 basic inputs each (I increment, N total cycle and M point to reverse cycle)


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mosc
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PostPosted: Mon May 16, 2005 6:41 pm    Post subject: Reply with quote  Mark this post and the followings unread

To me at least, this is abolutely facinating. I love the melodies this thing comes up with. It beats randomness cold. Have you explored these kind of arppegiators before, perhaps with a programming language or something?

I will have to stare at this for a long time before I grasp this, but it's well worth it.

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bantri



Joined: May 15, 2005
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PostPosted: Tue May 17, 2005 6:42 am    Post subject: Reply with quote  Mark this post and the followings unread

mosc wrote:

I will have to stare at this for a long time before I grasp this, but it's well worth it.


Its easier to figure the struture work if you delete the main arpeggiator and play with only 3 sub arpeggiator variables.
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bantri



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PostPosted: Tue May 17, 2005 6:56 am    Post subject: Reply with quote  Mark this post and the followings unread

mosc wrote:
Have you explored these kind of arppegiators before, perhaps with a programming language or something? worth it.


My first experience with melodical patterns was purelly empirical by hearing goa and psy trance music, there are some delightful compositions that can be considered auditive puzzles, making full use of integer positive math to create patterns that need very concentrated hearing to be unlocked and sometimes take 2^4 or more music steps to loop those patterns.

As a practical influence i could recommend the midi arppegio kit demos from Newtronics, Keyfax and Twiddly bits available for free as a good example of carefully crafted melodical patterns.
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bantri



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PostPosted: Tue May 17, 2005 7:42 am    Post subject: Reply with quote  Mark this post and the followings unread

[quote="bantri"]
mosc wrote:
making full use of integer positive math to create melodical patterns


For making those patterns the secret is first to separate the playing sequence from the scale, you should create first a long melodical scale with N notes numbered from 0 to N-1

then you can create some step engines that produce output like:
012301230123... (Inc=+1, N=4, start=0)
210321032103... (inc=-1, N=4, start=2, note that after 0 comes a 3 instead of -1) (if possible, use positive integer math to keep things simple)
9753579753579 (inc=+-1 N=6!!! bounce=4, start=9, initial direction=-)

then if can assure that the SUM of the several steppers is contained in the interval from 0 to N-1 you can play that sequence on the scale.
you can deal with several patterns that are understandable for the hearing like:
012301230123 up loop
3210312103210 dn loop
12345432123345 mirror loop
1234567531 assimetrical updn stages up=+1 dn=-2
0 1 2 4 8 16 8 4 2 1 0 mirrored geometrical progression
0112222333333332222110 temporal doubling mirrored arithmetic progression
091827364554637281 double temporal interleaved +1 and -1 sequences
0414243444546474 double temporal interleaved +1 and starting 4 +0 sequences

all these are much more attractive melodical sequences that the standard linear congruential random generator xn+1=(axn+b) mod c, but its worth noting that this generator also deals with positive integer numbers between 0 and c-1
Very Happy
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mosc
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PostPosted: Tue May 17, 2005 9:50 am    Post subject: Reply with quote  Mark this post and the followings unread

What does the "bounce" do?
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bantri



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PostPosted: Tue May 17, 2005 10:03 am    Post subject: bounce function Reply with quote  Mark this post and the followings unread

the bounce function starts counting from at the same time as totcycle and defines at which point the increment changes signal, if bounce is greater than totcycle then the sequence never enters backward stepping.
On the other hand it is advisable to also set the bounce to be equal or greater than totcycle/2 because if the stepper starts from 0 and bounces before halfway then it will go past zero on its way back into negative values.
example
inc=3
totcycle=8
bounce=5
VBounce on the 5th element (inverting increment)
1 2 3 4 5 6 7 8 9 10
0 3 6 9 12 9 6 3 0 3
^after 8 counts load initial state
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mosc
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PostPosted: Tue May 17, 2005 10:28 am    Post subject: Reply with quote  Mark this post and the followings unread

So, do I understand correctly, bounce is a change in direction after a certain number of steps?
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bantri



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PostPosted: Tue May 17, 2005 10:41 am    Post subject: Reply with quote  Mark this post and the followings unread

mosc wrote:
So, do I understand correctly, bounce is a change in direction after a certain number of steps?


Exactly, you can also do an extra trick by injecting a constant module in the free input of the valsw2-11 module in each stepper to define an initial state different than zero.
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Blue Hell
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PostPosted: Tue May 17, 2005 12:20 pm    Post subject: Reply with quote  Mark this post and the followings unread

lovely patterns indeed and fun to experiment with the settings !

Jan.
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bantri



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PostPosted: Tue May 17, 2005 12:37 pm    Post subject: The On-Line Encyclopedia of Integer Sequences Reply with quote  Mark this post and the followings unread

Once you get to like to arpeggiate with positive integers this site can give an impressive collection of patterns, most of them go outside the 0..127 range of keyboard notes but still a good source for inspiration.

http://www.research.att.com/~njas/sequences/index.html
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bantri



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PostPosted: Tue May 17, 2005 1:06 pm    Post subject: This may turn into an useful integer math module Reply with quote  Mark this post and the followings unread

Theoretically you can build any integer sequence if you have a basic module to cascade like we did analog cascading fm operators in the old dx7 days

The basic module would have those inputs

toggle button for dealing with only positive or positive negative math

rst(yellow input, pos edge) triggers the load of start value in the counter and resets the internal total steps counter to zero

clk(yellow input, pos edge) adds the increment value to the current value

start value(blue input) can be signed but if the math button is toggled for pos math loads the unsigned value to start counting

increment (blue input) can be signed but also obeys the positive math button

total steps (blue input) its our N and should be always positive and is linked to a yellow output that sends a pulse whenever it reaches the count
there should be a number box showing the current step

Current state (blue output) it holds the integer value until receiving the clock input for advancing to the next state

invert increment sign(yellow input, active high) if low adds the increment to current state and if high subtracts the increment from the current state after receiving a clk pos trigger

the bouncing behavior is not interesting to be included in this because it can be done by adding a clock divider in toggled mode to this module to keep it simple.

by cascading some of these modules in theory its possible to construct any integer sequence (my theory though)
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bantri



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PostPosted: Tue May 17, 2005 5:48 pm    Post subject: Second thoughts for creating integer math building blocks Reply with quote  Mark this post and the followings unread

For creating integer sequences the best option would be 2 modules instead of one as follows:

Sum module:
Start Value(Blue Bipolar signed input) Receives the initial value everytime a Rst is clocked

Inc Value (Blue bipolar signed input) Defines the increment to be summed everytime a Clk is clocked

Clk (yellow input, pos edge) triggers the sum

Rst (yellow input, pos edge) triggers the Start value load

Invert sign (yellow input, active high) inverts the sign of the increment when high (optional but useful)

Current State (blue signed output) presents the current sum state

Count module:
Counts from 0 to N-1
N-1 (blue input, rectified to be always positive) defines the point to cycle back to zero

clk (yellow input, pos edge) increment by 1

rst (yellow, pos edge) set counter to zero

LimitReach (yellow output, active high) raises everytime the counter reaches N

by interconnecting multiple copies of these two structures its possible to develop very complex integer sequences for arpeggios

i´ve included a simple structure to show the basis for them


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oXo



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PostPosted: Wed May 18, 2005 1:26 am    Post subject: Reply with quote  Mark this post and the followings unread

Really great, many interesting stuff here ...
Thanks for sharing your knowledge thumb up
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egw
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PostPosted: Wed May 18, 2005 3:56 am    Post subject: Reply with quote  Mark this post and the followings unread

Thanks for the great ideas!
It will be a while before I get a chance to try them out.
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