# resolved Filter for rotational permutations - Rotate-permute

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Dear Janusz and friends,

I´m back to the subject of permutations. The expression below brings all the permutations for a diatonic scale (or any other set you might want to do).

```(setf diat-permute (permute '(1 2 3 4 5 6 7)))

(substitute-map '(c4 d4 e4 f4 g4 a4 b4) '(1 2 3 4 5 6 7) diat-permute)```

But the list is too long and redundant (I got also a stack overflow when trying to make a snippet out of it (but this is another problem...)

The question I´d like to ask is for a function for filtering the rotational variations of a set, to exclude a large number of unnecessary permutations.

For Example:

(1 3 4 2) is rotationally the same as (3 4 2 1 ), (4 2 1 3) and (2 1 3 4), so there is no need of the 4 permutations, since musically you can just use the rotations.

The same goes for other cardinalities

(2 4 3 1 5 6 7) is the rotationally the same that  (4 3 1 5 6 7 2) (3 1 5 6 7 2 4) (1 5 6 7 2 4 3) (5 6 7 2 4 3 1) (6 7 2 4 3 1 5) and (7 2 4 3 1 5 6), there is no need for 7 versions of it.

I´d like to have a function to get only the "parent" of each rotational set,  a kind of rotate-permute function.

It´s a very musical way to think about it.

Can someone help ?

All the best !

Thanks

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Julio,

The easiest procedure for eliminating the rotations is to perform the permutations on all but the first  (or last) item in the list, and then append that item back to the front (or back) of the list.

For example:

```(defun perms-no-rots (lst)
(let ((perms (permute (cdr lst))))
(loop for x in perms
collect (append (list (car lst)) x))))```

I'm still a Lisp rookie, so there might be better, cleaner, more Lisp-y ways to do it, but it seems to work:

```(perms-no-rots '(1 2 3 4))

==> ((1 2 3 4) (1 2 4 3) (1 3 2 4) (1 3 4 2) (1 4 2 3) (1 4 3 2))

(perms-no-rots '(1 2 3 4 5))

==> ((1 2 3 4 5) (1 2 3 5 4) (1 2 4 3 5) (1 2 4 5 3) (1 2 5 3 4) (1 2 5 4 3) (1 3 2 4 5) (1 3 2 5 4) (1 3 4 2 5) (1 3 4 5 2) (1 3 5 2 4) (1 3 5 4 2) (1 4 2 3 5) (1 4 2 5 3) (1 4 3 2 5) (1 4 3 5 2) (1 4 5 2 3) (1 4 5 3 2) (1 5 2 3 4) (1 5 2 4 3) (1 5 3 2 4) (1 5 3 4 2) (1 5 4 2 3) (1 5 4 3 2))```

Edit:

Here's another version I came up with after sending the version above. It is maybe a little nicer to read since I replaced `(append (list....` with `(cons...` :

```(defun perms-no-rots (lst)
(let ((perms (permute (cdr lst))))
(loop for x in perms
collect (cons (car lst) x))))```

Cheers,

Jon

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While playing around with it, I found that this only works reliably when there are no duplicate items in the list to be permuted. So, it's neither perfect nor universally applicable, but as long as the caveat is understood it does the job.

Cheers,

Jon

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```(gen-rotate :left '(1 2 3 4) :type 'list)
=> ((1 2 3 4) (4 1 2 3) (3 4 1 2) (2 3 4 1))

(gen-rotate :left '(1 2 3 4 5 6 7)  :type 'list)
=> ((1 2 3 4 5 6 7) (7 1 2 3 4 5 6) (6 7 1 2 3 4 5)
(5 6 7 1 2 3 4) (4 5 6 7 1 2 3) (3 4 5 6 7 1 2)
(2 3 4 5 6 7 1))```

You should avoid permute function etc...

The best way to pick a possible set is the rnd-order function.

Rotation sets without the starting list:

```(rest (gen-rotate :right '(1 2 3 4) :type 'list))
=> ((2 3 4 1) (3 4 1 2) (4 1 2 3))

(rest (gen-rotate :right '(1 2 3 4 5 6 7) :type 'list))
=> ((2 3 4 5 6 7 1) (3 4 5 6 7 1 2) (4 5 6 7 1 2 3)
(5 6 7 1 2 3 4) (6 7 1 2 3 4 5) (7 1 2 3 4 5 6))```

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If you want only lists starting with 1:

```(loop for i in (combination2 4 '(1 2 3 4))
when (and (equal 1 (first i)) (equal 4 (length (find-unique i))))
collect i)
=> ((1 2 3 4) (1 3 2 4) (1 2 4 3) (1 4 2 3) (1 3 4 2) (1 4 3 2))```

or

```(loop for i in (combination2 4 '(1 2 3 4))
when (and (equal 1 (first i)) (contain-itemsp '(1 2 3 4) i))
collect i)
=> ((1 2 3 4) (1 3 2 4) (1 2 4 3) (1 4 2 3) (1 3 4 2) (1 4 3 2))```

results with 1 in second position:

```(loop for i in (combination2 4 '(1 2 3 4))
when (and (equal 1 (second i)) (contain-itemsp '(1 2 3 4) i))
collect i)
=> ((2 1 3 4) (3 1 2 4) (2 1 4 3) (4 1 2 3) (3 1 4 2) (4 1 3 2))```

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Thanks a lot for your time and patience, my dear friends !

But, actually, I need to remove the redundant permutations, not to generate.

I just wanted to make sure I have all the prime permutations.

Here is the result of the first 720 permutations of the diatonic scale. looks like the algorithm of the function start with all notes begining in C , then in D, then in E. I hope that the batch that starts all on C (the example below), contains all the permutations (the prime ones), but I´m not sure, I would need to check it manually...

Is it rigth ?  The algorithm is doing like this (starting in every note at each 720 permutations) ?

Best !

Julio

Quote
`((c4 d4 e4 f4 g4 a4 b4) (c4 d4 e4 f4 g4 b4 a4) (c4 d4 e4 f4 a4 g4 b4) (c4 d4 e4 f4 a4 b4 g4) (c4 d4 e4 f4 b4 g4 a4) (c4 d4 e4 f4 b4 a4 g4) (c4 d4 e4 g4 f4 a4 b4) (c4 d4 e4 g4 f4 b4 a4) (c4 d4 e4 g4 a4 f4 b4) (c4 d4 e4 g4 a4 b4 f4) (c4 d4 e4 g4 b4 f4 a4) (c4 d4 e4 g4 b4 a4 f4) (c4 d4 e4 a4 f4 g4 b4) (c4 d4 e4 a4 f4 b4 g4) (c4 d4 e4 a4 g4 f4 b4) (c4 d4 e4 a4 g4 b4 f4) (c4 d4 e4 a4 b4 f4 g4) (c4 d4 e4 a4 b4 g4 f4) (c4 d4 e4 b4 f4 g4 a4) (c4 d4 e4 b4 f4 a4 g4) (c4 d4 e4 b4 g4 f4 a4) (c4 d4 e4 b4 g4 a4 f4) (c4 d4 e4 b4 a4 f4 g4) (c4 d4 e4 b4 a4 g4 f4) (c4 d4 f4 e4 g4 a4 b4) (c4 d4 f4 e4 g4 b4 a4) (c4 d4 f4 e4 a4 g4 b4) (c4 d4 f4 e4 a4 b4 g4) (c4 d4 f4 e4 b4 g4 a4) (c4 d4 f4 e4 b4 a4 g4) (c4 d4 f4 g4 e4 a4 b4) (c4 d4 f4 g4 e4 b4 a4) (c4 d4 f4 g4 a4 e4 b4) (c4 d4 f4 g4 a4 b4 e4) (c4 d4 f4 g4 b4 e4 a4) (c4 d4 f4 g4 b4 a4 e4) (c4 d4 f4 a4 e4 g4 b4) (c4 d4 f4 a4 e4 b4 g4) (c4 d4 f4 a4 g4 e4 b4) (c4 d4 f4 a4 g4 b4 e4) (c4 d4 f4 a4 b4 e4 g4) (c4 d4 f4 a4 b4 g4 e4) (c4 d4 f4 b4 e4 g4 a4) (c4 d4 f4 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b4) (c4 d4 a4 g4 f4 b4 e4) (c4 d4 a4 g4 b4 e4 f4) (c4 d4 a4 g4 b4 f4 e4) (c4 d4 a4 b4 e4 f4 g4) (c4 d4 a4 b4 e4 g4 f4) (c4 d4 a4 b4 f4 e4 g4) (c4 d4 a4 b4 f4 g4 e4) (c4 d4 a4 b4 g4 e4 f4) (c4 d4 a4 b4 g4 f4 e4) (c4 d4 b4 e4 f4 g4 a4) (c4 d4 b4 e4 f4 a4 g4) (c4 d4 b4 e4 g4 f4 a4) (c4 d4 b4 e4 g4 a4 f4) (c4 d4 b4 e4 a4 f4 g4) (c4 d4 b4 e4 a4 g4 f4) (c4 d4 b4 f4 e4 g4 a4) (c4 d4 b4 f4 e4 a4 g4) (c4 d4 b4 f4 g4 e4 a4) (c4 d4 b4 f4 g4 a4 e4) (c4 d4 b4 f4 a4 e4 g4) (c4 d4 b4 f4 a4 g4 e4) (c4 d4 b4 g4 e4 f4 a4) (c4 d4 b4 g4 e4 a4 f4) (c4 d4 b4 g4 f4 e4 a4) (c4 d4 b4 g4 f4 a4 e4) (c4 d4 b4 g4 a4 e4 f4) (c4 d4 b4 g4 a4 f4 e4) (c4 d4 b4 a4 e4 f4 g4) (c4 d4 b4 a4 e4 g4 f4) (c4 d4 b4 a4 f4 e4 g4) (c4 d4 b4 a4 f4 g4 e4) (c4 d4 b4 a4 g4 e4 f4) (c4 d4 b4 a4 g4 f4 e4) (c4 e4 d4 f4 g4 a4 b4) (c4 e4 d4 f4 g4 b4 a4) (c4 e4 d4 f4 a4 g4 b4) (c4 e4 d4 f4 a4 b4 g4) (c4 e4 d4 f4 b4 g4 a4) (c4 e4 d4 f4 b4 a4 g4) (c4 e4 d4 g4 f4 a4 b4) (c4 e4 d4 g4 f4 b4 a4) (c4 e4 d4 g4 a4 f4 b4) (c4 e4 d4 g4 a4 b4 f4) (c4 e4 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a4) (c4 f4 d4 b4 g4 a4 e4) (c4 f4 d4 b4 a4 e4 g4) (c4 f4 d4 b4 a4 g4 e4) (c4 f4 e4 d4 g4 a4 b4) (c4 f4 e4 d4 g4 b4 a4) (c4 f4 e4 d4 a4 g4 b4) (c4 f4 e4 d4 a4 b4 g4) (c4 f4 e4 d4 b4 g4 a4) (c4 f4 e4 d4 b4 a4 g4) (c4 f4 e4 g4 d4 a4 b4) (c4 f4 e4 g4 d4 b4 a4) (c4 f4 e4 g4 a4 d4 b4) (c4 f4 e4 g4 a4 b4 d4) (c4 f4 e4 g4 b4 d4 a4) (c4 f4 e4 g4 b4 a4 d4) (c4 f4 e4 a4 d4 g4 b4) (c4 f4 e4 a4 d4 b4 g4) (c4 f4 e4 a4 g4 d4 b4) (c4 f4 e4 a4 g4 b4 d4) (c4 f4 e4 a4 b4 d4 g4) (c4 f4 e4 a4 b4 g4 d4) (c4 f4 e4 b4 d4 g4 a4) (c4 f4 e4 b4 d4 a4 g4) (c4 f4 e4 b4 g4 d4 a4) (c4 f4 e4 b4 g4 a4 d4) (c4 f4 e4 b4 a4 d4 g4) (c4 f4 e4 b4 a4 g4 d4) (c4 f4 g4 d4 e4 a4 b4) (c4 f4 g4 d4 e4 b4 a4) (c4 f4 g4 d4 a4 e4 b4) (c4 f4 g4 d4 a4 b4 e4) (c4 f4 g4 d4 b4 e4 a4) (c4 f4 g4 d4 b4 a4 e4) (c4 f4 g4 e4 d4 a4 b4) (c4 f4 g4 e4 d4 b4 a4) (c4 f4 g4 e4 a4 d4 b4) (c4 f4 g4 e4 a4 b4 d4) (c4 f4 g4 e4 b4 d4 a4) (c4 f4 g4 e4 b4 a4 d4) (c4 f4 g4 a4 d4 e4 b4) (c4 f4 g4 a4 d4 b4 e4) (c4 f4 g4 a4 e4 d4 b4) (c4 f4 g4 a4 e4 b4 d4) (c4 f4 g4 a4 b4 d4 e4) (c4 f4 g4 a4 b4 e4 d4) (c4 f4 g4 b4 d4 e4 a4) (c4 f4 g4 b4 d4 a4 e4) (c4 f4 g4 b4 e4 d4 a4) (c4 f4 g4 b4 e4 a4 d4) (c4 f4 g4 b4 a4 d4 e4) (c4 f4 g4 b4 a4 e4 d4) (c4 f4 a4 d4 e4 g4 b4) (c4 f4 a4 d4 e4 b4 g4) (c4 f4 a4 d4 g4 e4 b4) (c4 f4 a4 d4 g4 b4 e4) (c4 f4 a4 d4 b4 e4 g4) (c4 f4 a4 d4 b4 g4 e4) (c4 f4 a4 e4 d4 g4 b4) (c4 f4 a4 e4 d4 b4 g4) (c4 f4 a4 e4 g4 d4 b4) (c4 f4 a4 e4 g4 b4 d4) (c4 f4 a4 e4 b4 d4 g4) (c4 f4 a4 e4 b4 g4 d4) (c4 f4 a4 g4 d4 e4 b4) (c4 f4 a4 g4 d4 b4 e4) (c4 f4 a4 g4 e4 d4 b4) (c4 f4 a4 g4 e4 b4 d4) (c4 f4 a4 g4 b4 d4 e4) (c4 f4 a4 g4 b4 e4 d4) (c4 f4 a4 b4 d4 e4 g4) (c4 f4 a4 b4 d4 g4 e4) (c4 f4 a4 b4 e4 d4 g4) (c4 f4 a4 b4 e4 g4 d4) (c4 f4 a4 b4 g4 d4 e4) (c4 f4 a4 b4 g4 e4 d4) (c4 f4 b4 d4 e4 g4 a4) (c4 f4 b4 d4 e4 a4 g4) (c4 f4 b4 d4 g4 e4 a4) (c4 f4 b4 d4 g4 a4 e4) (c4 f4 b4 d4 a4 e4 g4) (c4 f4 b4 d4 a4 g4 e4) (c4 f4 b4 e4 d4 g4 a4) (c4 f4 b4 e4 d4 a4 g4) (c4 f4 b4 e4 g4 d4 a4) (c4 f4 b4 e4 g4 a4 d4) (c4 f4 b4 e4 a4 d4 g4) (c4 f4 b4 e4 a4 g4 d4) (c4 f4 b4 g4 d4 e4 a4) (c4 f4 b4 g4 d4 a4 e4) (c4 f4 b4 g4 e4 d4 a4) (c4 f4 b4 g4 e4 a4 d4) (c4 f4 b4 g4 a4 d4 e4) (c4 f4 b4 g4 a4 e4 d4) (c4 f4 b4 a4 d4 e4 g4) (c4 f4 b4 a4 d4 g4 e4) (c4 f4 b4 a4 e4 d4 g4) (c4 f4 b4 a4 e4 g4 d4) (c4 f4 b4 a4 g4 d4 e4) (c4 f4 b4 a4 g4 e4 d4) (c4 g4 d4 e4 f4 a4 b4) (c4 g4 d4 e4 f4 b4 a4) (c4 g4 d4 e4 a4 f4 b4) (c4 g4 d4 e4 a4 b4 f4) (c4 g4 d4 e4 b4 f4 a4) (c4 g4 d4 e4 b4 a4 f4) (c4 g4 d4 f4 e4 a4 b4) (c4 g4 d4 f4 e4 b4 a4) (c4 g4 d4 f4 a4 e4 b4) (c4 g4 d4 f4 a4 b4 e4) (c4 g4 d4 f4 b4 e4 a4) (c4 g4 d4 f4 b4 a4 e4) (c4 g4 d4 a4 e4 f4 b4) (c4 g4 d4 a4 e4 b4 f4) (c4 g4 d4 a4 f4 e4 b4) (c4 g4 d4 a4 f4 b4 e4) (c4 g4 d4 a4 b4 e4 f4) (c4 g4 d4 a4 b4 f4 e4) (c4 g4 d4 b4 e4 f4 a4) (c4 g4 d4 b4 e4 a4 f4) (c4 g4 d4 b4 f4 e4 a4) (c4 g4 d4 b4 f4 a4 e4) (c4 g4 d4 b4 a4 e4 f4) (c4 g4 d4 b4 a4 f4 e4) (c4 g4 e4 d4 f4 a4 b4) (c4 g4 e4 d4 f4 b4 a4) (c4 g4 e4 d4 a4 f4 b4) (c4 g4 e4 d4 a4 b4 f4) (c4 g4 e4 d4 b4 f4 a4) (c4 g4 e4 d4 b4 a4 f4) (c4 g4 e4 f4 d4 a4 b4) (c4 g4 e4 f4 d4 b4 a4) (c4 g4 e4 f4 a4 d4 b4) (c4 g4 e4 f4 a4 b4 d4) (c4 g4 e4 f4 b4 d4 a4) (c4 g4 e4 f4 b4 a4 d4) (c4 g4 e4 a4 d4 f4 b4) (c4 g4 e4 a4 d4 b4 f4) (c4 g4 e4 a4 f4 d4 b4) (c4 g4 e4 a4 f4 b4 d4) (c4 g4 e4 a4 b4 d4 f4) (c4 g4 e4 a4 b4 f4 d4) (c4 g4 e4 b4 d4 f4 a4) (c4 g4 e4 b4 d4 a4 f4) (c4 g4 e4 b4 f4 d4 a4) (c4 g4 e4 b4 f4 a4 d4) (c4 g4 e4 b4 a4 d4 f4) (c4 g4 e4 b4 a4 f4 d4) (c4 g4 f4 d4 e4 a4 b4) (c4 g4 f4 d4 e4 b4 a4) (c4 g4 f4 d4 a4 e4 b4) (c4 g4 f4 d4 a4 b4 e4) (c4 g4 f4 d4 b4 e4 a4) (c4 g4 f4 d4 b4 a4 e4) (c4 g4 f4 e4 d4 a4 b4) (c4 g4 f4 e4 d4 b4 a4) (c4 g4 f4 e4 a4 d4 b4) (c4 g4 f4 e4 a4 b4 d4) (c4 g4 f4 e4 b4 d4 a4) (c4 g4 f4 e4 b4 a4 d4) (c4 g4 f4 a4 d4 e4 b4) (c4 g4 f4 a4 d4 b4 e4) (c4 g4 f4 a4 e4 d4 b4) (c4 g4 f4 a4 e4 b4 d4) (c4 g4 f4 a4 b4 d4 e4) (c4 g4 f4 a4 b4 e4 d4) (c4 g4 f4 b4 d4 e4 a4) (c4 g4 f4 b4 d4 a4 e4) (c4 g4 f4 b4 e4 d4 a4) (c4 g4 f4 b4 e4 a4 d4) (c4 g4 f4 b4 a4 d4 e4) (c4 g4 f4 b4 a4 e4 d4) (c4 g4 a4 d4 e4 f4 b4) (c4 g4 a4 d4 e4 b4 f4) (c4 g4 a4 d4 f4 e4 b4) (c4 g4 a4 d4 f4 b4 e4) (c4 g4 a4 d4 b4 e4 f4) (c4 g4 a4 d4 b4 f4 e4) (c4 g4 a4 e4 d4 f4 b4) (c4 g4 a4 e4 d4 b4 f4) (c4 g4 a4 e4 f4 d4 b4) (c4 g4 a4 e4 f4 b4 d4) (c4 g4 a4 e4 b4 d4 f4) (c4 g4 a4 e4 b4 f4 d4) (c4 g4 a4 f4 d4 e4 b4) (c4 g4 a4 f4 d4 b4 e4) (c4 g4 a4 f4 e4 d4 b4) (c4 g4 a4 f4 e4 b4 d4) (c4 g4 a4 f4 b4 d4 e4) (c4 g4 a4 f4 b4 e4 d4) (c4 g4 a4 b4 d4 e4 f4) (c4 g4 a4 b4 d4 f4 e4) (c4 g4 a4 b4 e4 d4 f4) (c4 g4 a4 b4 e4 f4 d4) (c4 g4 a4 b4 f4 d4 e4) (c4 g4 a4 b4 f4 e4 d4) (c4 g4 b4 d4 e4 f4 a4) (c4 g4 b4 d4 e4 a4 f4) (c4 g4 b4 d4 f4 e4 a4) (c4 g4 b4 d4 f4 a4 e4) (c4 g4 b4 d4 a4 e4 f4) (c4 g4 b4 d4 a4 f4 e4) (c4 g4 b4 e4 d4 f4 a4) (c4 g4 b4 e4 d4 a4 f4) (c4 g4 b4 e4 f4 d4 a4) (c4 g4 b4 e4 f4 a4 d4) (c4 g4 b4 e4 a4 d4 f4) (c4 g4 b4 e4 a4 f4 d4) (c4 g4 b4 f4 d4 e4 a4) (c4 g4 b4 f4 d4 a4 e4) (c4 g4 b4 f4 e4 d4 a4) (c4 g4 b4 f4 e4 a4 d4) (c4 g4 b4 f4 a4 d4 e4) (c4 g4 b4 f4 a4 e4 d4) (c4 g4 b4 a4 d4 e4 f4) (c4 g4 b4 a4 d4 f4 e4) (c4 g4 b4 a4 e4 d4 f4) (c4 g4 b4 a4 e4 f4 d4) (c4 g4 b4 a4 f4 d4 e4) (c4 g4 b4 a4 f4 e4 d4) (c4 a4 d4 e4 f4 g4 b4) (c4 a4 d4 e4 f4 b4 g4) (c4 a4 d4 e4 g4 f4 b4) (c4 a4 d4 e4 g4 b4 f4) (c4 a4 d4 e4 b4 f4 g4) (c4 a4 d4 e4 b4 g4 f4) (c4 a4 d4 f4 e4 g4 b4) (c4 a4 d4 f4 e4 b4 g4) (c4 a4 d4 f4 g4 e4 b4) (c4 a4 d4 f4 g4 b4 e4) (c4 a4 d4 f4 b4 e4 g4) (c4 a4 d4 f4 b4 g4 e4) (c4 a4 d4 g4 e4 f4 b4) (c4 a4 d4 g4 e4 b4 f4) (c4 a4 d4 g4 f4 e4 b4) (c4 a4 d4 g4 f4 b4 e4) (c4 a4 d4 g4 b4 e4 f4) (c4 a4 d4 g4 b4 f4 e4) (c4 a4 d4 b4 e4 f4 g4) (c4 a4 d4 b4 e4 g4 f4) (c4 a4 d4 b4 f4 e4 g4) (c4 a4 d4 b4 f4 g4 e4) (c4 a4 d4 b4 g4 e4 f4) (c4 a4 d4 b4 g4 f4 e4) (c4 a4 e4 d4 f4 g4 b4) (c4 a4 e4 d4 f4 b4 g4) (c4 a4 e4 d4 g4 f4 b4) (c4 a4 e4 d4 g4 b4 f4) (c4 a4 e4 d4 b4 f4 g4) (c4 a4 e4 d4 b4 g4 f4) (c4 a4 e4 f4 d4 g4 b4) (c4 a4 e4 f4 d4 b4 g4) (c4 a4 e4 f4 g4 d4 b4) (c4 a4 e4 f4 g4 b4 d4) (c4 a4 e4 f4 b4 d4 g4) (c4 a4 e4 f4 b4 g4 d4) (c4 a4 e4 g4 d4 f4 b4) (c4 a4 e4 g4 d4 b4 f4) (c4 a4 e4 g4 f4 d4 b4) (c4 a4 e4 g4 f4 b4 d4) (c4 a4 e4 g4 b4 d4 f4) (c4 a4 e4 g4 b4 f4 d4) (c4 a4 e4 b4 d4 f4 g4) (c4 a4 e4 b4 d4 g4 f4) (c4 a4 e4 b4 f4 d4 g4) (c4 a4 e4 b4 f4 g4 d4) (c4 a4 e4 b4 g4 d4 f4) (c4 a4 e4 b4 g4 f4 d4) (c4 a4 f4 d4 e4 g4 b4) (c4 a4 f4 d4 e4 b4 g4) (c4 a4 f4 d4 g4 e4 b4) (c4 a4 f4 d4 g4 b4 e4) (c4 a4 f4 d4 b4 e4 g4) (c4 a4 f4 d4 b4 g4 e4) (c4 a4 f4 e4 d4 g4 b4) (c4 a4 f4 e4 d4 b4 g4) (c4 a4 f4 e4 g4 d4 b4) (c4 a4 f4 e4 g4 b4 d4) (c4 a4 f4 e4 b4 d4 g4) (c4 a4 f4 e4 b4 g4 d4) (c4 a4 f4 g4 d4 e4 b4) (c4 a4 f4 g4 d4 b4 e4) (c4 a4 f4 g4 e4 d4 b4) (c4 a4 f4 g4 e4 b4 d4) (c4 a4 f4 g4 b4 d4 e4) (c4 a4 f4 g4 b4 e4 d4) (c4 a4 f4 b4 d4 e4 g4) (c4 a4 f4 b4 d4 g4 e4) (c4 a4 f4 b4 e4 d4 g4) (c4 a4 f4 b4 e4 g4 d4) (c4 a4 f4 b4 g4 d4 e4) (c4 a4 f4 b4 g4 e4 d4) (c4 a4 g4 d4 e4 f4 b4) (c4 a4 g4 d4 e4 b4 f4) (c4 a4 g4 d4 f4 e4 b4) (c4 a4 g4 d4 f4 b4 e4) (c4 a4 g4 d4 b4 e4 f4) (c4 a4 g4 d4 b4 f4 e4) (c4 a4 g4 e4 d4 f4 b4) (c4 a4 g4 e4 d4 b4 f4) (c4 a4 g4 e4 f4 d4 b4) (c4 a4 g4 e4 f4 b4 d4) (c4 a4 g4 e4 b4 d4 f4) (c4 a4 g4 e4 b4 f4 d4) (c4 a4 g4 f4 d4 e4 b4) (c4 a4 g4 f4 d4 b4 e4) (c4 a4 g4 f4 e4 d4 b4) (c4 a4 g4 f4 e4 b4 d4) (c4 a4 g4 f4 b4 d4 e4) (c4 a4 g4 f4 b4 e4 d4) (c4 a4 g4 b4 d4 e4 f4) (c4 a4 g4 b4 d4 f4 e4) (c4 a4 g4 b4 e4 d4 f4) (c4 a4 g4 b4 e4 f4 d4) (c4 a4 g4 b4 f4 d4 e4) (c4 a4 g4 b4 f4 e4 d4) (c4 a4 b4 d4 e4 f4 g4) (c4 a4 b4 d4 e4 g4 f4) (c4 a4 b4 d4 f4 e4 g4) (c4 a4 b4 d4 f4 g4 e4) (c4 a4 b4 d4 g4 e4 f4) (c4 a4 b4 d4 g4 f4 e4) (c4 a4 b4 e4 d4 f4 g4) (c4 a4 b4 e4 d4 g4 f4) (c4 a4 b4 e4 f4 d4 g4) (c4 a4 b4 e4 f4 g4 d4) (c4 a4 b4 e4 g4 d4 f4) (c4 a4 b4 e4 g4 f4 d4) (c4 a4 b4 f4 d4 e4 g4) (c4 a4 b4 f4 d4 g4 e4) (c4 a4 b4 f4 e4 d4 g4) (c4 a4 b4 f4 e4 g4 d4) (c4 a4 b4 f4 g4 d4 e4) (c4 a4 b4 f4 g4 e4 d4) (c4 a4 b4 g4 d4 e4 f4) (c4 a4 b4 g4 d4 f4 e4) (c4 a4 b4 g4 e4 d4 f4) (c4 a4 b4 g4 e4 f4 d4) (c4 a4 b4 g4 f4 d4 e4) (c4 a4 b4 g4 f4 e4 d4) (c4 b4 d4 e4 f4 g4 a4) (c4 b4 d4 e4 f4 a4 g4) (c4 b4 d4 e4 g4 f4 a4) (c4 b4 d4 e4 g4 a4 f4) (c4 b4 d4 e4 a4 f4 g4) (c4 b4 d4 e4 a4 g4 f4) (c4 b4 d4 f4 e4 g4 a4) (c4 b4 d4 f4 e4 a4 g4) (c4 b4 d4 f4 g4 e4 a4) (c4 b4 d4 f4 g4 a4 e4) (c4 b4 d4 f4 a4 e4 g4) (c4 b4 d4 f4 a4 g4 e4) (c4 b4 d4 g4 e4 f4 a4) (c4 b4 d4 g4 e4 a4 f4) (c4 b4 d4 g4 f4 e4 a4) (c4 b4 d4 g4 f4 a4 e4) (c4 b4 d4 g4 a4 e4 f4) (c4 b4 d4 g4 a4 f4 e4) (c4 b4 d4 a4 e4 f4 g4) (c4 b4 d4 a4 e4 g4 f4) (c4 b4 d4 a4 f4 e4 g4) (c4 b4 d4 a4 f4 g4 e4) (c4 b4 d4 a4 g4 e4 f4) (c4 b4 d4 a4 g4 f4 e4) (c4 b4 e4 d4 f4 g4 a4) (c4 b4 e4 d4 f4 a4 g4) (c4 b4 e4 d4 g4 f4 a4) (c4 b4 e4 d4 g4 a4 f4) (c4 b4 e4 d4 a4 f4 g4) (c4 b4 e4 d4 a4 g4 f4) (c4 b4 e4 f4 d4 g4 a4) (c4 b4 e4 f4 d4 a4 g4) (c4 b4 e4 f4 g4 d4 a4) (c4 b4 e4 f4 g4 a4 d4) (c4 b4 e4 f4 a4 d4 g4) (c4 b4 e4 f4 a4 g4 d4) (c4 b4 e4 g4 d4 f4 a4) (c4 b4 e4 g4 d4 a4 f4) (c4 b4 e4 g4 f4 d4 a4) (c4 b4 e4 g4 f4 a4 d4) (c4 b4 e4 g4 a4 d4 f4) (c4 b4 e4 g4 a4 f4 d4) (c4 b4 e4 a4 d4 f4 g4) (c4 b4 e4 a4 d4 g4 f4) (c4 b4 e4 a4 f4 d4 g4) (c4 b4 e4 a4 f4 g4 d4) (c4 b4 e4 a4 g4 d4 f4) (c4 b4 e4 a4 g4 f4 d4) (c4 b4 f4 d4 e4 g4 a4) (c4 b4 f4 d4 e4 a4 g4) (c4 b4 f4 d4 g4 e4 a4) (c4 b4 f4 d4 g4 a4 e4) (c4 b4 f4 d4 a4 e4 g4) (c4 b4 f4 d4 a4 g4 e4) (c4 b4 f4 e4 d4 g4 a4) (c4 b4 f4 e4 d4 a4 g4) (c4 b4 f4 e4 g4 d4 a4) (c4 b4 f4 e4 g4 a4 d4) (c4 b4 f4 e4 a4 d4 g4) (c4 b4 f4 e4 a4 g4 d4) (c4 b4 f4 g4 d4 e4 a4) (c4 b4 f4 g4 d4 a4 e4) (c4 b4 f4 g4 e4 d4 a4) (c4 b4 f4 g4 e4 a4 d4) (c4 b4 f4 g4 a4 d4 e4) (c4 b4 f4 g4 a4 e4 d4) (c4 b4 f4 a4 d4 e4 g4) (c4 b4 f4 a4 d4 g4 e4) (c4 b4 f4 a4 e4 d4 g4) (c4 b4 f4 a4 e4 g4 d4) (c4 b4 f4 a4 g4 d4 e4) (c4 b4 f4 a4 g4 e4 d4) (c4 b4 g4 d4 e4 f4 a4) (c4 b4 g4 d4 e4 a4 f4) (c4 b4 g4 d4 f4 e4 a4) (c4 b4 g4 d4 f4 a4 e4) (c4 b4 g4 d4 a4 e4 f4) (c4 b4 g4 d4 a4 f4 e4) (c4 b4 g4 e4 d4 f4 a4) (c4 b4 g4 e4 d4 a4 f4) (c4 b4 g4 e4 f4 d4 a4) (c4 b4 g4 e4 f4 a4 d4) (c4 b4 g4 e4 a4 d4 f4) (c4 b4 g4 e4 a4 f4 d4) (c4 b4 g4 f4 d4 e4 a4) (c4 b4 g4 f4 d4 a4 e4) (c4 b4 g4 f4 e4 d4 a4) (c4 b4 g4 f4 e4 a4 d4) (c4 b4 g4 f4 a4 d4 e4) (c4 b4 g4 f4 a4 e4 d4) (c4 b4 g4 a4 d4 e4 f4) (c4 b4 g4 a4 d4 f4 e4) (c4 b4 g4 a4 e4 d4 f4) (c4 b4 g4 a4 e4 f4 d4) (c4 b4 g4 a4 f4 d4 e4) (c4 b4 g4 a4 f4 e4 d4) (c4 b4 a4 d4 e4 f4 g4) (c4 b4 a4 d4 e4 g4 f4) (c4 b4 a4 d4 f4 e4 g4) (c4 b4 a4 d4 f4 g4 e4) (c4 b4 a4 d4 g4 e4 f4) (c4 b4 a4 d4 g4 f4 e4) (c4 b4 a4 e4 d4 f4 g4) (c4 b4 a4 e4 d4 g4 f4) (c4 b4 a4 e4 f4 d4 g4) (c4 b4 a4 e4 f4 g4 d4) (c4 b4 a4 e4 g4 d4 f4) (c4 b4 a4 e4 g4 f4 d4) (c4 b4 a4 f4 d4 e4 g4) (c4 b4 a4 f4 d4 g4 e4) (c4 b4 a4 f4 e4 d4 g4) (c4 b4 a4 f4 e4 g4 d4) (c4 b4 a4 f4 g4 d4 e4) (c4 b4 a4 f4 g4 e4 d4) (c4 b4 a4 g4 d4 e4 f4) (c4 b4 a4 g4 d4 f4 e4) (c4 b4 a4 g4 e4 d4 f4) (c4 b4 a4 g4 e4 f4 d4) (c4 b4 a4 g4 f4 d4 e4) (c4 b4 a4 g4 f4 e4 d4)) `

Dear Janusz

I need the reverse of what you did

From this set of combinations

`((1 2 3 4) (1 3 2 4) (1 2 4 3) (1 4 2 3) (1 3 4 2) (1 4 3 2))`

filter to get only the generator (1 2 3 4)

Best

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4 hours ago, opmo said:
```(loop for i in (combination2 4 '(1 2 3 4))
when (and (equal 1 (first i)) (equal 4 (length (find-unique i))))
collect i)```

YES !!! This is the solution I was searching !

Best !

(loop for i in (combination2 7 '(1 2 3 4 5 6 7))
when (and (equal 1 (first i)) (equal 7 (length (find-unique i))))
collect i)

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will stop the endless printing

```(do-verbose ("rotation")
(loop for i in (combination2 7 '(1 2 3 4 5 6 7))
when (and (equal 1 (first i)) (equal 7 (length (find-unique i))))
collect i))```

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Thanks a lot !! No problem !

This is cool and generate some kind of diatonic version for Hauer stuff

This was my inspiration to this Idea...

WWW.INSTAGRAM.COM

171 likes, 9 comments - schmeinstein on May 31, 2024: "all the notes of C major, once each. you can play these phrases forwards or backwards, even reflect them about the note D, and they still...".

VERY COOL !

Thanks !

```(setf diat-permute (loop for i in (combination2 7 '(1 2 3 4 5 6 7))
when (and (equal 1 (first i)) (equal 7 (length (find-unique i))))
collect i))

(setf diatonic-tropes (substitute-map '(c4 d4 e4 f4 g4 a4 b4) '(1 2 3 4 5 6 7) diat-permute))

(circle-pitch-plot
(flatten (list
(rnd-pick diatonic-tropes
)))
:sort nil
;:remove-duplicates t
:join-first nil

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less computation:

```(setf perm
(do-verbose ("rotation")
(loop for i in (combination2 7 '(c4 d4 e4 f4 g4 a4 b4))
when (and (equal 'c4 (first i)) (equal 7 (length (find-unique i))))
collect i)))

(circle-pitch-plot
(rnd-pick perm)
:sort nil
;:remove-duplicates t
:join-first nil

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Thank you Julio for this cool and fun idea.

As a more general function:

```(defun permu (set)
(do-verbose ("permu")
(let ((n (length set)))
(loop for i in (combination2 n set)
when (and (equal (first set) (first i))
(equal n (length (find-unique i))))
collect i))))```

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And playing a bit around this function:

```(setf melo-set '(d4 fs4 gs4 e4 b4 a4))
(setf res (permu melo-set))

(setf size 24)
(setf mel1.pch (rnd-sample size res))
(setf mel2.pch (rnd-sample size res))
(setf mel3.pch (rnd-sample size res))
(setf mel4.pch (rnd-sample size res))

(setf len-set '(q e e -q s s s s))
(setf lenres (gen-loop 8 (rnd-order len-set)))
(setf len1 (rnd-sample size lenres))
(setf len2 (rnd-sample size lenres))
(setf len3 (rnd-sample size lenres))
(setf len4 (rnd-sample size lenres))

(setf line1 (make-omn :pitch mel1.pch :length len1))
(setf line2 (make-omn :pitch mel2.pch :length len2))
(setf line3 (make-omn :pitch mel3.pch :length len3))
(setf line4 (make-omn :pitch mel4.pch :length len4))

(setf vn1 (ambitus 'violin (pitch-transpose 12 line1)))
(setf vn2 (ambitus 'violin (pitch-transpose 0 line2)))
(setf vla (ambitus 'viola (pitch-transpose -12 line3)))
(setf vlc (ambitus 'cello (pitch-transpose -24 line4)))

(ps 'gm :sq (list vn1 vn2 vla vlc))
```

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wow !! Beautiful feedback !

Yes, Stephane ! This idea is inspiring ! Nice quartet !

Thank you all !!

Best !

Julio

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Dear Friends,

Some continuation here...

Still working with this...

The algorhitm you provided seems not to work with combinations where repetitions are needed.

The find-unique in the function kills the repetitions

(combination2 4 '(0 1 2 3 4 5 6 7 8 9 10 11))))

In this case, I need to optimize these 20736 combinations into something smaller and manageable.

For example (4 0 0 0) will be same as its rotations, like (0 4 0 0) (0 0 4 0) and (0 0 0 4). I just need the (4 0 0 0) or one of its rotations.

So , in this case, there is a lot of repeating numbers that find-unique will kill...

How to filter in this case, to get just the prime of each rotation without killing the repetitions ?

Thanks for the help ! Much needed for creating a library of chord progressions.

All the best !

Julio

```combination2
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11) (2 4 11 11) (3 4 11 11) (4 4 11 11) (5 4 11 11) (6 4 11 11) (7 4 11 11) (8 4 11 11) (9 4 11 11) (10 4 11 11) (11 4 11 11) (0 5 11 11) (1 5 11 11) (2 5 11 11) (3 5 11 11) (4 5 11 11) (5 5 11 11) (6 5 11 11) (7 5 11 11) (8 5 11 11) (9 5 11 11) (10 5 11 11) (11 5 11 11) (0 6 11 11) (1 6 11 11) (2 6 11 11) (3 6 11 11) (4 6 11 11) (5 6 11 11) (6 6 11 11) (7 6 11 11) (8 6 11 11) (9 6 11 11) (10 6 11 11) (11 6 11 11) (0 7 11 11) (1 7 11 11) (2 7 11 11) (3 7 11 11) (4 7 11 11) (5 7 11 11) (6 7 11 11) (7 7 11 11) (8 7 11 11) (9 7 11 11) (10 7 11 11) (11 7 11 11) (0 8 11 11) (1 8 11 11) (2 8 11 11) (3 8 11 11) (4 8 11 11) (5 8 11 11) (6 8 11 11) (7 8 11 11) (8 8 11 11) (9 8 11 11) (10 8 11 11) (11 8 11 11) (0 9 11 11) (1 9 11 11) (2 9 11 11) (3 9 11 11) (4 9 11 11) (5 9 11 11) (6 9 11 11) (7 9 11 11) (8 9 11 11) (9 9 11 11) (10 9 11 11) (11 9 11 11) (0 10 11 11) (1 10 11 11) (2 10 11 11) (3 10 11 11) (4 10 11 11) (5 10 11 11) (6 10 11 11) (7 10 11 11) (8 10 11 11) (9 10 11 11) (10 10 11 11) (11 10 11 11) (0 11 11 11) (1 11 11 11) (2 11 11 11) (3 11 11 11) (4 11 11 11) (5 11 11 11) (6 11 11 11) (7 11 11 11) (8 11 11 11) (9 11 11 11) (10 11 11 11) (11 11 11 11))```

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Don't use permutations, there is no need for it. The simples way is to use rnd-order. It makes no sense to generate 20736 lists and then select few of them at random.

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Thanks, but I need all the results at once, not random. To create a catalog.

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Why you want to generate 20736 lists in catalog. Few examples and description of the process is all you need.

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Opusmodus took 2 minutes to calculate this example on a major 6 diminished scale with 8 notes. So with 12 notes, you can imagine...

(setf perm
(do-verbose ("rotation")
(loop for i in (combination2 8 '(c4 d4 e4 f4 g4 gs4 a4 b4 ))
when (and (equal 'c4 (first i)) (equal 8  (length (find-unique i))))
collect i)))

(circle-pitch-plot
(rnd-pick perm)
:sort nil
;:remove-duplicates t
:join-first nil

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