Introduction of an automatized analysis method of musical tension as a response to musical form

Understanding, describing and displaying musical tension as a complex and multidimensional phenomenon, especially that of contemporary music, requires new analytical methods. In order to explore musical tension (also musical intensity, temporal dynamics etc.) through music psychological perception experiments using complete musical examples in a variety of styles from baroque to contemporary music (including post-tonal music and jazz, an overview of the repertoire used in tension studies see Farbood 2012) have used continuous data (or self-report) recording methods and technology since the 1980ies (an overview see Gabrielsson & Lindström 2010, Schubert 2010). The participants have been musicians and non-musicians as well as children, adolescents, adults and older people. Among the analytical approaches to interpret data have been e.g. correlation and ANOVA analysis, comparison of time series, descriptive approaches, functional data analysis, averaging methods (moving window, Fourier), and trend/regression analysis, but, in our opinion and underlined also by Gabrielsson and Lindström (2010) and Schubert (2010) several problems concerning the adequacy of treatment and interpretation of the data remain. We think that analyzing those curves based on the principle of preserving important reverse points (high-points and low-points) emerging during the listening process offers the possibility to gain more valid analytical conclusions in relation to musical form than individual (verbal) cognitive subjective descriptions or mathematical-statistical methods. In this paper we introduce the automatized version of a new reduction method analyzing curves derived from perception tests on Erkki-Sven Tüürs (b. 1959) symphony no. 4 (2002) and no. 6 (2007) conducted as a pilot study in 2010 (N=7, musicians and non-musicians). The reduction and averaging principles applied to the curves were developed as a manual method during 2011 and 2012 (see Lock & Kotta 2012), and thanks to Toby Gifford automatized in Java script implemented into a Max/MSP patch in 2012 and 2013. Through a number of reductional stages (down to a one-minute-moving-window allowing only three reverse points included) applied for the individual curves of each participant we are able to average the curves of all participants (including as much as possible tension points within a 15-second-moving-window) into an Average Reliability (AR) curve showing a generalized curve of the perception of the musical tension perceived by the participants which allows us to analyze more appropriately musical tension as a response to musical form.