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In the Wikipedia "Baroque" article I found this quote from "Dictionnaire de Musique" by Jean-Jacques Rousseau:

BAROQUE. Une Musique Baroque est celle dont l’Harmonie est confuse, chargée de Modulations & Dissonances, le Chant dur & peu naturel, l’Intonation difficile, le Mouvement contraint.

Il y a bien de l’apparence que ce terme vient du Baroco des Logiciens.

Being a mathematician, I became intrigued - where to read about this "Baroco des Logiciens"? What is it?

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    $\begingroup$ 'Baraco' is medieval mnemonics for a type of syllogism en.wikipedia.org/wiki/Syllogism#Baroco_(AOO-2) $\endgroup$ – sand1 Sep 30 '18 at 8:08
  • $\begingroup$ @sand1 Spectacular! Why don't you make it an answer? $\endgroup$ – მამუკა ჯიბლაძე Sep 30 '18 at 8:43
  • $\begingroup$ I've now looked up in Encyclopédie: *​​ BAROCO, (Log.)​​ terme qui désigne le quatrieme mode d’argument de la seconde figure. Un syllogisme en baroco a la majeure universelle affirmative, & la mineure & la conclusion particulieres négatives. Voyez Syllogisme. $\endgroup$ – მამუკა ჯიბლაძე Sep 30 '18 at 8:56
  • $\begingroup$ Whereas at universalis.fr, concerning "baroque" they say L'Encyclopédie a cru que le terme venait du baroco des logiciens, alors que la figure du syllogisme ne traduit aucune irrégularité dans le mode de pensée. $\endgroup$ – მამუკა ჯიბლაძე Sep 30 '18 at 9:01
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    $\begingroup$ @MauroALLEGRANZA: The Oxford English Dictionary agrees ... "Littré's suggestion that the word is identical with the logical term baroko seems to rest on no historical evidence; yet form-association with that may have influenced the later English and French use." $\endgroup$ – Gerald Edgar Sep 30 '18 at 12:35
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As noted in the comments, "baroco" is a mnemonic for a certain type of syllogism in classical Aristotlean logic. See Wikipedia

But it is no longer believed that "Baroque" comes from it etymologically.

added In the mnemonic, the three vowels code what type proposition is used for each of the three terms of the syllogism. Here is the key:

A = all S are P, E = no S is P, I = some S are P, O = some S are not P

Baroco in particular is this syllogism:

All X are Y.
Some Z are not Y.
Therefore, some Z are not X.

An example from Wikipedia:

All informative things are useful.
Some websites are not useful.
∴ Some websites are not informative.

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  • $\begingroup$ This is an informative answer, and I accepted it, but - could you also indicate the meaning of this mnemonics? All of these (Barbara, Celarent, etc.) seem to actually mean something, which is obviously helpful for mnemonic purposes. So maybe baroco also means something? $\endgroup$ – მამუკა ჯიბლაძე Oct 2 '18 at 5:29
  • $\begingroup$ I added the meaning of "baroco" in logic. As far as I can tell, the word "baroco" has no other meaning. $\endgroup$ – Gerald Edgar Oct 2 '18 at 10:45

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