Combinatorics of Rhyming Variants in Sonnets by R. M. Rilke: A Quantitative and Typological Approach

Abstract
Combinatorial analysis of the German sonnet corpus based on mathematical study of verse was carried out on poetic works by Rainer Maria Rilke. Sonnets rhyming methods classification based on their symmetry relations in quatrain and tercet parts was constructed. According to this classification, which does not take into consideration the so-called irregular sonnets, the concepts of symmetric, partially symmetric and asymmetrical sonnets are introduced and the possible quantity of sonnets of each type is calculated by means of the combinatorial method. Taking into account these notions, the unique combinatorial potential of the poet has been revealed, and the evolution of Rilke’s sonnets structure from “New poems” (“Neue Gedichte”) to “Sonnets to Orpheus” (“Sonette an Orpheus”) is also investigated. The notions of symmetrical and independent sonnets are introduced. Using these notions, it is shown that “New poems” contain just independent sonnets, which have non-recurring rhyming variants, while in “Sonnets to Orpheus” this principle is not respected. The nuclear part of sonnets, consisting of those independent sonnets that generate the whole amount of Rilke’ sonnets (i. e., the entire collection of independent and dependent sonnets), has been determined. Eight sonnets adjacent to the “Sonnets to Orpheus” are also taken into account in the corresponding calculations, too. Special attention is paid to symmetrical sonnets. The structure of all 18 symmetric Rilke’s sonnets is described, among which 11 are independent (four sonnets in “New poems”, and seven sonnets in “Sonnets to Orpheus”). As an example, the stylometric analysis of the rhythmic field of one of the symmetrical sonnets was performed. It is shown that its internal rhythm is close to the structure of the golden section. A hypothesis is expressed concerning the influence of rhyming variants on the external and internal rhythms of the sonnet.

Keywords 
mathematical study of verse, combinatorics, German sonnet, Rilke, rhyming methods, quatrain, tercet, rhyme classification, symmetry, symmetrical sonnets, asymmetrical sonnets, independent sonnets, dependent sonnets, evolution, harmony