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</head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; color: rgb(0, 0, 0); "><div><span style="font-size: 16px;">Hi all,</span></div><div><span style="font-size: 16px;"><br></span></div><div><span style="font-size: 16px;">I would like to have your opinion (that has most probably already been proposed) on a possible analogy. Reading Sebastian Sumjan's linguistic grammar theory (itself derived from Bateson's genetic model, see below), I was wondering if one could draw an analogy between his geno-/phenotype grammars and Set Theory. Could we, for example, consider sets as genotypes that may then give rise to different forms of realizations (phenotypes)? Conversely (and this commutative property of Sumjan's model is crucial), one can of course deduce genotypes from existing phenotypes. Just an idea, but again, not being a music theorist, I suspect many have already explored this avenue: you would be very kind to guide me towards relevant sources.</span></div><div><span style="font-size: 16px;"><br></span></div><div><span style="font-size: 16px;">Here is a quote from Sebastian Shaumyan [Sumjan], <i>A Semiotic Theory of Language</i>, Bloomington, Indiana University Press,
1987.</span></div>
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<p class="MsoNormal"><font face="Calibri"><o:p></o:p></font></p>
<p class="MsoNormal"><o:p><font face="Calibri"> </font></o:p></p>
<p class="MsoNormal"><font face="Calibri">"[97] <span lang="EN-CA">We can
think of the syntactic structure of a sentence as something independent of the
way it is represented in terms of syntagmatic units. In this way we come up
with two levels of grammar, which I call <i>genotype
grammar</i> and <i>phenotype grammar</i>.
Genotype grammar comprises functional units—predicates, terms, modifiers—and
abstract operator-operand relations between these units. Phenotype grammar
comprises syntagmatic units—morphemes and words—and connections between them in
terms of linear order and their morphological properties. […]<o:p></o:p></span></font></p>
<p class="MsoNormal"><span lang="EN-CA"><font face="Calibri"> </font></span></p>
<span style="font-size: 16px;"><span lang="EN-CA">The rules of genotype grammar are invariant with
respect to various possibilities of their realization by phenotype grammar. The
terms <i>genotype</i> and <i>phenotype</i> are borrowed from biology,
where genotype means a definite set of genes that is invariant with respect to
its different manifestations called phenotype."</span><!--EndFragment--></span><div><span style="font-size: 16px;"><br></span></div><div><span style="font-size: 16px;">Thanks for your help,</span></div><div>s</div><div style="font-size: 14px; font-family: Calibri, sans-serif; "><div><font class="Apple-style-span"><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000">_____________________</font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000"><br></font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000">Serge Lacasse</font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000"><br></font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000">Professeur titulaire de musicologie</font></span><font class="Apple-style-span" color="#00000000"><br></font><font class="Apple-style-span" color="#00000000"><font class="Apple-style-span" face="Times New Roman">Directeur de l'OICRM-Laval</font></font></font></div><div><font class="Apple-style-span"><font class="Apple-style-span" color="#00000000"><font class="Apple-style-span" face="Times New Roman">et du LARC<br></font></font><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000"><br></font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000">Pavillon Louis-Jacques-Casault</font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000"><br></font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000">1055, avenue du Séminaire</font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000"><br></font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000">Local 4355</font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000"><br></font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000">Université Laval</font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000"><br></font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000">Québec QC G1V 0A6</font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000"><br></font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000"><br></font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000">Bureau/Office : 418 656-2131, poste 15113</font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000"><br></font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000">Studio : 418 656-2131, poste 11367</font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000"><br></font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000">Télécopieur/Fax : 418 656-7365</font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000"><br></font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><a href="http://www.mus.ulaval.ca/lacasse"><font class="Apple-style-span" color="#00000000">www.mus.ulaval.ca/lacasse</font></a></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000"><br></font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000"> </font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000"><br></font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000">===================</font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000"><br></font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000">Avis relatif à la confidentialité</font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000"><br></font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000"><br></font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span" color="#00000000">Ce message contient des renseignements qui peuvent être confidentiels ou protégés. Il s'adresse au destinataire prévu ou à une personne autorisée à le recevoir en son nom. Si vous l'avez reçu par erreur, nous vous prions d'en informer l'auteur dans les meilleurs délais, de ne pas divulguer son contenu et de le supprimer de votre système.</font></span></font></div></div></body></html>