# Menzerath's law

The Menzerathsche Act (often Menzerath-Altmann-law , English Menzerath's law ) is one of the results of Quantitative Linguistics . It means that the complexity of the direct components of a linguistic unit depends on the complexity of the unit itself.

Using the example of the ratio of the syllables to the words of which they are components: The length of the syllables of a word depends on the number of syllables that the word has. This means that if you examine a large number of words, it can be shown that the length of the syllables of these words changes with the length of the words. However, this law applies not only to the relationship between word and syllable, but in general also to smaller and larger linguistic units.

## On the development of the Menzerath law

As early as the 19th century it was hypothesized that the duration of the sounds in a word decreases with its length. Menzerath & de Oleza (1928) expanded this hypothesis to include the statement that as the number of syllables in the words increases, the syllables themselves become shorter on average.

The following hypothesis developed from this:

The bigger the whole, the smaller the parts.

Specified in the field of linguistics :

The larger a linguistic construct, the smaller its constituents.

Altmann, Heups and Köhler showed early 80s with quantitative methods that this postulate to larger constructs of the natural language can be applied, the larger the rate is, the smaller the individual subsets ( Clauses ), etc. is a prerequisite for such connections that a relationship between units (here: sentence) and their direct constituents (here: sub-clause) is investigated. If one looks at the relationship between units that are connected to one another via an intermediate level (i.e.: indirect constituents), their relation changes: the more complex the sentence, the more complex / larger the words (intermediate level: partial sentence / clause). This relation is known as Arens ' law , named after Hans Arens , who made a study of it.

From the hypothesis that the change in the constituent length is proportional to the change in the construct length, and the additional assumption of a disturbance variable, Altmann & Schwibbe (1989: 6-7) can derive the following mathematical model: with the special cases (for ) and for . ${\ displaystyle y = ax ^ {b} e ^ {cx}}$${\ displaystyle ae ^ {cx}}$${\ displaystyle b = 0, c \ neq 0}$${\ displaystyle y = ax ^ {b}}$${\ displaystyle b \ neq 0, c = 0}$

## Example: Morph length depending on the word length

In order to check the validity of Menzerath's law, Gerlach (1982) completely evaluated a dictionary of German with around 15,000 headwords. The adaptation of the model resulted in the following: ${\ displaystyle y = ax ^ {b}}$

${\ displaystyle x}$ ${\ displaystyle n}$ ${\ displaystyle y}$ ${\ displaystyle y ^ {*}}$
1 2391 4.53 4.33
2 6343 3.25 3.37
3 4989 2.93 2.91
4th 1159 2.78 2.62
5 112 2.65 2.42
6th 13 2.58 2.26

Where is : number of morphs per word, the number of words in the dictionary with the length ; the observed average length of the morph (number of phonemes per morph); the length of the morph, which is calculated by fitting the given form of Menzerath's law to the observed data; the F-test gave me a very good result. You can see very clearly that the morphological length decreases as the word length increases. Result: Menzerath's law is a good model for this text. For more detailed explanations, please refer to the literature given. ${\ displaystyle x}$${\ displaystyle n}$${\ displaystyle x}$${\ displaystyle y}$${\ displaystyle y ^ {*}}$${\ displaystyle P = 0 {,} 001}$

Asleh & Best (2004/5) dedicate themselves to the length of syllables depending on the word length for German and Italian examples; a new study deals with the subject using the example of Greek.

## For the designation and performance of the law

The Menzerathsche law is since its mathematical formulation and generalization by Altmann (1980) as Menzerath-Altmann-law or Menzerath-Altmann's Law refers. It structures the language from the so-called "sentence aggregates" (Hřebíček: groups of sentences with the same lexemes) as the largest units down to the sounds / phonemes. At least with a subclass of Japanese Kanji characters, this law also seems to be working.

## To the validity of the law

The Menzerath law has proven itself in many studies on a wide variety of linguistic phenomena in a number of languages. In addition, however, it can also be used in areas other than linguistics . Studies have shown that the social behavior of baboon groups also corresponds to Menzerath's law: the larger the entire group, the smaller the subordinate social groups.

## literature

• Gabriel Altmann : Prolegomena to Menzerath's Law. In: R. Grotjahn (ed.): Glottometrika 2, Brockmeyer, Bochum 1980, pp. 1-10. ISBN 3-88339-104-2 .
• Gabriel Altmann, Michael Schwibbe : The Menzerath law in information processing systems. Olms, Hildesheim, Zurich, New York 1989, ISBN 3-487-09144-5 .
• Laila Asleh, Karl-Heinz Best : To review the Menzerath-Altmann law using German (and Italian) words as an example. In: Göttingen Contributions to Linguistics. 10/11, 2004/05, pp. 9-19.
• Irene M. Cramer: The Menzerath law. In: Reinhard Köhler, Gabriel Altmann, Rajmund G. Piotrowski (eds.), Quantitative Linguistics - Quantitative Linguistics. An international manual. de Gruyter, Berlin / New York 2005, ISBN 3-11-015578-8 , pp. 659-688.
• Peter Grzybek & Gabriel Altmann, Gabriel: Oscillation in the frequency-length relationship. In: Glottometrics 5, 2002, pp. 97-107 (PDF full text ).
• Peter Grzybek, Emmerich Kelih & Ernst Stadlober: The relation between word length and sentence length: an intra-systemic perspective in the core data structure. In: Glottometrics 16, 2008, pp. 111–121 (PDF full text ).
• Luděk Hřebíček : Lectures on Text Theory. Academy of Sciences of the Czech Republic, Oriental Institute, Prague 1997, ISBN 80-85425-26-2 .
• Luděk Hřebíček: Variation in Sequences. Academy of Sciences of the Czech Republic, Oriental Institute, Prague 2000, ISBN 80-85425-37-8 .
• Paul Menzerath: The architecture of the German vocabulary. Dümmler, Bonn / Hanover / Stuttgart 1954.
• Paul Menzerath, JM de Oleza: Spanish sound duration. An experimental study. de Gruyter, Berlin / Leipzig 1928.

Wiktionary: Menzerath's law  - explanations of meanings, word origins, synonyms, translations

## Individual evidence

1. ^ Karl-Heinz Best : Eduard Sievers (1850-1932). In: Glottometrics 18, 2009, , pp. 87-91. (PDF full text ).
2. See the overviews in Altmann & Schwibbe 1989.
3. Gabriel Altmann : H. Arens' "Hidden Order" and the Menzerath Law. In: Manfred Faust, Roland Harweg, Werner Lehfeldt, Götz Wienold (eds.): General linguistics, language typology and text linguistics. Festschrift for Peter Hartmann. Narr, Tübingen 1983, ISBN 3-87808-215-0 , pp. 31-39.
4. Rainer Gerlach: To review Menzerath's law in the field of morphology. In: Werner Lehfeldt, Udo Strauss (eds.): Glottometrika 4. Brockmeyer, Bochum 1982, ISBN 3-88339-250-2 , pp. 95-102. Gerlach had successfully used the form of the Menzerath law. The newly calculated data can be found on page 49 at: Gabriel Altmann, Michael H. Schwibbe: The Menzerath Law in Information Processing Systems. Olms, Hildesheim / Zurich / New York 1989, ISBN 3-487-09144-5 .${\ displaystyle y = ax ^ {b} e ^ {cx}}$${\ displaystyle y = ax ^ {b}}$
5. It's about: Gerhard Wahrig (Hrsg.): Dtv dictionary of the German language. Deutscher Taschenbuch Verlag, Munich 1978, ISBN 3-423-03136-0 .
6. Georgios Mikros, Jiří Milička: Distribution of the Menzerath's law on the syllable level in Greek texts. In: Gabriel Altmann, Radek Čech, Ján Mačutek, Ludmila Uhlířová (eds.): Empirical Approaches to Text and Language Analysis dedicated to Luděk Hřebíček on the occasion of his 80th birthday. RAM-Verlag, Lüdenscheid 2014, ISBN 978-3-942303-24-8 , pp. 180-189.
7. lql.uni-trier.de ( Memento of the original from December 29, 2015 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice.
8. ^ Claudia Prün: Validity of Menzerath-Altmann's Law: Graphic Representation of Language, Information Processing Systems and Synergetic Linguistics. In: Journal of Quantitative Linguistics 1, 1994, pp. 148-155.
9. Altmann & Schwibbe 1989, p. 99 ff.