# Recursive Equations in OM6

Hello,

I’d be grateful for thoughts on how to create a patch for simple recursive equations in OM6. I’m not sure which path to take after looking through the forum and at omloop and tutorial 38 - I’m not so familiar with this side of OM but hoping it’s a trivial task.

I simply want to add two numbers, A to B, and then feed the result back to become B in the next iteration. So I expect I need 2-3 inputs (A and B or a list with them together, and the total number of recursions), and I want the patch output a list that collects the results of the addition for each iteration, so you get a+b, a+(a+b), a+(a+(a+b)) etc (it’s for a basic harmony technique like ring modulation).

Many thanks in advance for any pointers.

Cheers
Nick

hello nick,
i’m not sure if this might help. but surely solves the problem. and there’s probably a better solution.
just check it out.
input: a, b, c (total number of recursions)

(lambda (a b c) (loop for i from 0 to (1- c) collect (om+ (apply '+ (repeat-n a i)) (+ a b))))

or

kind regards,
perti

Many thanks Perti, that looks great.
One question: I’m not sure exactly what’s inside the ‘repeat-n’ omloop as I don’t understand the lisp line you wrote / don’t know lisp itself. Could you clarify it in terms of patching? Thanks in advance!
N

ok nick, i’ll try. english is not my first language so it might be a bit confusing at times.
repeat-n has two inputs: one for ‘how many’ and the other for ‘what’.
you asked for a+b, a+(a+b), a+(a+(a+b))… you can see that ‘a’ is cumulative in each iteration
so, in each iteration in the repeat-n makes a list of repeated a’s which and applying '+ to all elements returns total sum of a’s. i’m not really sure why i put it this way as it is more logical to multiply ‘a’ by the count of cycles in the loop. in this way,
(lambda (a b c) (loop for i from 0 to (1- c) collect (om+ (* i a) (+ a b))))
perhaps because it was late in the evening, but it seems i took a less direct way to solve it. sorry about that. but as i always have thought when programming, right results come first, then comes efficiency and elegance (the difficult part).

hope is clearer now.
regards,
perti

Hi nm0, hi perti,

as the problem has been sketched out, i suppose a and b are single numbers (not lists).
Then in fact the operation is equivalent to: 1a+b, 2a+b, 3a+b…
which would simply go something like this:

If a = {a1, …an} and b = constant then recursion would be appropriate:
a1+b, a2+(a1+b), a3+(a2+(a1+b),…
?

and there it is!.. efficiency and elegance.
thanks for a more logical thought.
best,
perti

Thanks Perti - it works perfectly! I appreciate your insight and elegant solution.

Attached is the actually patch, a simple recursive additive frequency harmonic device.

Many thanks
Nick

recursive-rm.omp (14.5 KB)

Cheers Pre, even simpler. I’ll try this implementation too since I want to also make a subtractive version.
Nick

hi perti,

i think this is the idea behind the OM-versions of arithmetic operators, that you can apply them on lists not only atoms, as with the genuin lisp versions…

hi nick,
i hope thats equivalent to what you did in your patch… i am a bit to tired to check that today…

best
pre

Amazing, thanks for that, I’ll see if i can also do subtraction with your simpler method above, but this looks great in any case
Cheers
Nick

I was curious about the different effects of addition and subtraction, so i already did it on the second output. In fact the difference is just 2 pitches… see x-diff
…?

Anyway, happy chord-finding
Best
Pre

I’d also be curious to ask you both and anyone else - how did you learn about omloop and related features in OM?

I’m asking since I personally don’t find the manual so clear to get started with this topic, but I imagine this is because I’m not familiar with lisp nor computing/maths enough to get the gist of it by myself. The principles seem straight forward once I see example patches but the manual isn’t so user friendly for beginners, I feel.

In my experience:
Good books/websites to go deeper into lisp, but not necessarily always for quickly solving a problem:

Many thanks! I’ll take a look at those.
N

hi nick,

i learned lisp loop firstly (but not deeply enough), then after some research here and there and a lot of effort i came to know (again not entirely) omloop. sometimes i find one preferable over the other, depending on the situation. but who knows why i tend to think more in terms of looping instead of other tools like apply or funcall.
i concur with the bibliography provided by pre. chapter 22 of seibel’s book (loop for black belts) helped me a lot.
i’m not a programmer but a musician with programming needs, though.
cheers,
perti

rethinking your problem: maybe this is the kind of modulation you had in mind…

harm. ser. modulated.omp (18.0 KB)

happy weekend
pre