# PCS Sets Sugestion

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Dear All,

Happy New Year

I´m back to a lot of work with sets, subsets and supersets and I have an idea/suggestion:

When evaluating this

`(pcs-super-sets 7 (pcs '3-1) :forte)`

I get this result

`(7-1 7-2 7-2b 7-3 7-3b 7-4 7-4b 7-5 7-5b 7-6 7-6b 7-7 7-7b 7-8 7-9 7-9b 7-10 7-10b 7-11 7-11b 7-z12 7-13 7-13b 7-14 7-14b 7-15 7-16 7-16b 7-z17 7-z18 7-z18b 7-19 7-19b 7-20 7-20b 7-21 7-21b 7-22 7-23 7-23b 7-24 7-24b 7-25 7-25b 7-26 7-26b 7-27 7-27b 7-28 7-28b 7-29 7-29b 7-30 7-30b 7-33 7-z36 7-z36b 7-z37 7-z38 7-z38b)`

These are all the supersets of cardinality 7 of the 3-1 set.

Would be very nice in this context to have a keyword to invert the result, i.e., actually showing the excluded sets, like all the sets that ARE NOT supersets of the 3-1 set.

Like inverting, like a (pcs-non-super-sets) function. I think that maybe it´s not so difficult, because the algorythm of the function already give the result, the only thing necessary is that the function return exactly the opposite result.

Best,

Julio

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A more specific example

```(pcs-super-sets 4 (pcs '3-1) :forte)
;; (4-1 4-2 4-2b 4-4 4-4b 4-5 4-5b 4-6)

(pcs-super-sets 4 (pcs '3-1) :forte :complementary)
;; (all other 4 note sets, except 4-1 4-2 4-2b 4-4 4-4b 4-5 4-5b 4-6)```

Best,

Julio

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```(let ((out (pcs-cardinal 4 :forte)))
(loop for i in (pcs-super-sets 4 (pcs '3-1) :forte)
do (setf out (remove i out))
finally (return out)))
```
```(let ((rem (pcs-cardinal 7 :forte))
(super (pcs-super-sets 7 (pcs '3-1) :forte)))
(loop for i in super
do (setf rem (remove i rem))
finally (return rem)))
=> (7-31 7-31b 7-32 7-32b 7-34 7-35)```

here it is.

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Thank you, Janusz !

Great !

Julio

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• Dear All,

I´m looking for some way of retrieving musical information from sets of notes.
Some problems, for example:

1) This is the first and more needed now:
Given some UNORDERED amount of pitches, how retrive the prime
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2) How to do this from an existing midi file or XML ? Is t possible to
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Thanks, everyone !

Best,
Julio
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