Representational model of modulation in modal works: Cycle Mode Space

Abstract

In music analysis in the 20th century, different approaches were developed to examine the harmonic progression of works composed with a chord or scale-based approach. In tonal music, Riemann's tonnetz, Tonal Pitch Space (Lerdahl, 2001), Modal Pitch Space (Tsougras, 2003) and Tymoczko's (2011) cube representation approaches are used to represent modulation regions. As an alternative to tonnetz, the Tonal Pitch Space was created with a psycho-acoustic approach in the context of the proximity-distance relationship. Inspired by the Tonal Pitch Space, the Modal Pitch Space is limited to seven diatonic modes (Phrygian, Lydian, Myxoldian, Ionian, Eolian, Dorian, Lokrian). Tymoczko's approach is chord-based and limited to octatonic, heptatonic and diatonic scales. In addition to diatonic modes, tetratonic and pentatonic scales and non-diatonic modes, which are similar to the scales used at Turkish Maqam Music in the Western music sound system, have been used by local and foreign composers, including the Turkish Mighty Five. There is no model in the literature that includes non-diatonic modes and tetratonic and/or pentatonic modes for representation of modal modulation region. Accordingly, this study will develop existing approaches and propose a Cycle Mode Space limited to tetratonic, pentatonic, hexatonic, heptatonic and octatonic modes in Western music equal-tempered system. The aim of the study is to propose a mode space to represent the modulation progression in works composed with a scalar tradition in the 20th century. In this direction, it will be tried to obtain data about modal regions preferred by the composer, the modal 'path' applied by the composer and the modal centers. The qualitative research method will be applied in the study, and in this direction, literature review, musical style analysis and purposive sampling method will be used. It will be stated which modes the proposed model will cover, the proximity-distance relationship between these modes will be defined and the visual representation of the model will be introduced. Mode regions will be represented by colors in model. In this study, excerpts from Bartók's Piano Sonata (1st movement), Stravinsky's The Soldier's Story (March Royal), Hindemith's Six Schansons (Schanson 2) and A. Adnan Saygun's Op. 15 Sonatin (1st movement), which are described in the literature as composed with a scalar tradition, will be analyzed in the context of modal transformation (modulation). The modal 'path' in the related works will be represented by the ÇMA model. Cycle Mode Space include 873 diatonic and synthetic modes, containing 33 tetratonic, 185 pentatonic, 299 hexatonic, 261 heptatonic and 94 octatonic modes. The whole cycle is divided into twelve slices and the axis regions are represented in these slices by modeling the cycle of fifths. While determining the scope of the defined modes, synthetic modes with at most two consecutive minor 2nd intervals were created. Modes with at most major 3rd intervals in their structure were limited. In this model, 'maximal proximity value' is proposed to define the distance-closeness relationship between the modes. In order to calculate this value, the number of common pitches between the modes and the coordinate system in mathematics were used. It is noteworthy that the works we analyzed predominantly utilized the hypermodulation type by composer in which the axis and mode regions change in the context of modulation. Thanks to the mode space we have proposed, a holistic visual representation of the modulation has been provided; it is possible to obtain data and comment on the axis regions, modes and modal plan preferred by the composer in the work. In this way, information about the composer's style and aesthetic characteristics can be obtained. With the proposed model, it is possible to make comparative analysis between the works of any composer in the scalar tradition or with the works of another composer. In this way, data on composer’s stylistic characteristics in a historical or spatial context can be provided. The model can be improved by adding different modal structures preferred by composers.