<html><head><base href="x-msg://182/"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Prof Lacasse,<div><br></div><div>Prof Dora Hanninen has made excellent use of the concepts of genotype and phenotype in her work for some years now, and has just published A Theory of Musical Analysis with the University of Rochester Press. Among many virtues of this work is that it engages the biological concepts without the encumbrance of the metaphor of grammar.</div><div><br></div><div>Best,</div><div>Joseph Dubiel</div><div>Columbia University</div><div><br></div><div><br><div><div>On Jan 12, 2013, at 11:43 AM, Serge Lacasse wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><span class="Apple-style-span" style="border-collapse: separate; font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; font-size: medium; "><div 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],<span class="Apple-converted-space"> </span><i>A Semiotic Theory of Language</i>, Bloomington, Indiana University Press, 1987.</span></div><div class="MsoNormal" style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 12pt; font-family: Cambria; "><font face="Calibri"><o:p></o:p></font></div><div class="MsoNormal" style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 12pt; font-family: Cambria; "><o:p><font face="Calibri"> </font></o:p></div><div class="MsoNormal" style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 12pt; font-family: Cambria; "><font face="Calibri">"[97]<span class="Apple-converted-space"> </span><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<span class="Apple-converted-space"> </span><i>genotype grammar</i><span class="Apple-converted-space"> </span>and<span class="Apple-converted-space"> </span><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></div><div class="MsoNormal" style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 12pt; font-family: Cambria; "><span lang="EN-CA"><font face="Calibri"> </font></span></div><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<span class="Apple-converted-space"> </span><i>genotype</i><span class="Apple-converted-space"> </span>and<span class="Apple-converted-space"> </span><i>phenotype</i><span class="Apple-converted-space"> </span>are borrowed from biology, where genotype means a definite set of genes that is invariant with respect to its different manifestations called phenotype."</span></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">_____________________</font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; "><font class="Apple-style-span"><br></font></span><span class="Apple-style-span" style="font-size: medium; font-family: 'Times New Roman'; 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