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'''Menzerath's law''', or '''Menzerath–Altmann law''' (named after Paul Menzerath and Gabriel Altmann), is a [[linguistics|linguistic]] law according to which the increase of a linguistic construct results in a decrease of its constituents, and vice versa
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<ref>{{cite book | author = Gabriel Altmann, Michael H. Schwibbe  | title =  Das Menzerathsche Gesetz in informationsverarbeitenden Systemen| edition =  | publisher =  Olms |location=Hildesheim/Zürich/New York| year =  1989 | isbn = 3-487-09144-5  }}</ref>
.<ref>{{cite book | author = Luděk Hřebíček    | title = Text Levels. Language Constructs, Constituents and the Menzerath-Altmann Law  | edition =  | publisher = Wissenschaftlicher Verlag Trier  |location= | year =  1995  | isbn = 3-88476-179-X  }}
</ref>  


E.g., the longer a sentence (measured in terms of the number of clauses) the shorter the clauses (measured in terms of the number of words), or: the longer a word (in syllables or morphs) the shorter the syllables or words in sounds.
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According to Altmann (1980),<ref>
{{cite journal| author=Gabriel Altmann |year=1980 |title=Prolegomena to Menzerath's law |journal=Glottometrika |volume=2 |pages=pp. 1–10}}
</ref> it can be mathematically stated as:
 
<math>y=a \cdot x^{-b} \cdot e^{-c x}</math>
 
where:
 
* <math>y</math> is the constituent size (e.g. syllable length)
* <math>x</math> size of the linguistic construct that is being inspected (e.g. number of syllables per word)
* <math>a</math>, <math>b</math>, <math>c</math> are the parameters
 
Beyond [[quantitative linguistics]], Menzerath's law can be discussed in any
multi-level complex systems. Given three levels, <math>x</math> is the
number of middle-level units contained in a high-level unit, <math>y</math>
is the averaged number of low-level units contained in middle-level units,
Menzerath's law claims a negative
[[Correlation and dependence|correlation]] between <math>y</math> and <math>x</math>.
Menzerath's law is shown to be true for both the
[[nucleotide|base]]-[[exon]]-[[gene]] levels in the [[human genome]]
,<ref>
{{cite journal| author=Wentian Li |year=2012 |title= Menzerath's law at the gene-exon level in the human genome|journal=Complexity |volume=17 |issue=4|pages=49–53 |doi=10.1002/cplx.20398}}
</ref>
and [[nucleotide|base]]-[[chromosome]]-[[genome]] levels in genomes from a collection of species
.<ref>
{{cite journal| author= Ramon Ferrer-I-Cancho, Núria Forns |year=2009 |title=  The self-organization of genomes|journal=Complexity |volume=15 |issue=5|pages=34–36 |doi= 10.1002/cplx.20296}}
</ref>
 
==References==
{{Reflist}}
 
[[Category:Quantitative linguistics]]

Latest revision as of 04:00, 4 January 2015

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