Abstracts

Structural Features of a Class of Musical Scale Systems in World Music

The subfield within mathematical music theory concerned with scale systems has engaged most intensively with diatonic and pentatonic scales and their modes, and the class of all scales that satisfy certain conditions: Myhill’s Property (MP) or, equivalently, non-degenerate well-formedness (WF). A variation on these conditions gives rise to a class of scale systems where there are three distinct scale step-interval types, among which are a number of important examples from world music: the Japanese In-scale (e.g., hira-joshi mode) or hemitonic pentatonic; the heptatonic subset within octatonic (Vieru’s “Romanian major”); the ancient Indian ma-grama; and the various modes of so-called Hungarian minor or gypsy minor, which include the North Indian that Bhairav (Afghan Beiru), among others.

The Georgian triad: Theoretical reflections on a characteristic feature in West-Georgian contrapuntal polyphony

Well-formed Mode Theory is a refinement of the theory of well-formed scales and has been developed and explored by David Clampitt, Manuel Dominguez and myself mainly with respect to aspects of common practice western music. The well-formedness property involves two mutually dual manifestations of the modal structure, namely (1) a characteristic step interval pattern and (2) a folding of the mode into its octave range by means of the generator and the co-generator of the scale (e.g. fifth and fourth in the case of the diatonic modes). An interesting class of well-formed modes are the diazeuctic modes. They are defined by the Rameau equation, i.e. by the condition that the difference interval between generator and cogenerator (the diazeuxis) coincides with one of the two step intervals of the mode. It follows from that definition that the other step interval occurs precisely twice. The simplest diazeuctic modes have 3 tones and are exemplified by the (fifth-generated) structural modes and by the (thirdgenerated) generic triads. Both of them serve as elementary constituents for harmonic tonality. However, apart from this interpretation it is challenging to look for different manifestations of the diazeutic modes. West-Georgian contrapuntal polyphony offers a particularly interesting case. Dmitri Arakishvili coined the term „Georgian triad“ for the first structural mode C-F-G as a vertical unit. The Gurian song „Misdevs Mela Lomsa“ is a good example, where close and open positions of this chord occur in contrapuntal contexts, where they serve as stable sonorities. I my talk I will therefore explore some differences in the interaction of Georgian Triads and Usual Triads between West-Georgian Polyphony and Common-Practice Styles.

A single dual-stream framework for syntactic computations in music and language

This study is the first to compare in the same subjects the specific spatial distribution and the functional and anatomical connectivity of the neuronal resources that activate and integrate syntactic representations during music and language processing. Combining functional magnetic resonance imaging with functional connectivity and diffusion tensor imagingbased probabilistic tractography, we examined the brain network involved in the recognition and integration of words and chords that were not hierarchically related to the preceding syntax; that is, those deviating from the universal principles of grammar and tonal relatedness. This kind of syntactic processing in both domains was found to rely on a shared network in the left hemisphere centered on the inferior part of the inferior frontal gyrus (IFG), including pars opercularis and pars triangularis, and on dorsal and ventral long association tracts connecting this brain area with temporo-parietal regions. Language processing utilized some adjacent left hemispheric IFG and middle temporal regions more than music processing, and music processing also involved right hemisphere regions not activated in language processing. Our data indicate that a dual-stream system with dorsal and ventral long association tracts centered on a functionally and structurally highly.

Neural correlates of high-level musical syntax

Listening to music is a process that happens over time. In this process the musical elements (notes, chords, intervals, etc.) don´t sound in random order but follow certain regularities, which are called musical syntax. Against the backdrop of these regulations, the musical elements start to relate to each other (see e.g. - Hugo Riemann's theory of harmonic function) and hereby larger musical units are created which themselves also stand in relation with each other. This structure can be found on several hierarchical levels. Every listener internalizes those rules as an implicit knowledge. Adding then the attempt of human perception to form 'Gestalten', both principles are causing expectations of the continuation of the structure and course of the piece they are listing to and are thereby closely linked to the generation of musical tension-resolution patterns. On the level of musical elements, an independent branch of research has already been developed. Less studied are so far the underlying processes of neural mechanisms, concerning the question of how those structural units at a higher level are assembled to form a piece of music. In a first EEG-experiment to study those neural correlates of those processes by using the example of electronic dance music, the following could be shown: The synchronization of rhythmic neuronal activity of several globally distributed, cortical regions increases in the range of the gamma-band [30-80Hz] before the expected segmentation points of the hierarchically highest structure units occur. At this point it reaches its maximum and then decreases again. The resulting synchronization pattern could represent both, the structure of musical ‘Gestalten’ based on syntactic rules as well as the resulting tension-resolution pattern.

Temperament in Tonal Systems of Southeast Asian and ancient Indian music

Tonal systems of Southeast Asian music are often very diverse and seldom fits into a pure tone system. Additionally, the literature about music theory discussing tonal systems is sparse in these cultures. Exceptions are investigations of the music of the Bama in todays Myanmar and Indian and Tamil music theories. Examples of tonal systems of Cambodia, Myanmar, Thailand, Bali and Sri Lanka collected and analyzed by the author are therefore discussed in terms of their context of instrument building, musical practice and physical as well as physiological constraints. It appears in many cases that the musicians try to match a pure one system but need to deviate from it because of several constraints. Also the equidistant Ayutthaya scale may be understood in this sense when comparing  it with ancient Indian sruti systems of 22 equidistant tones which allow to play in many scales with only small deviations from a pure tone system. All these cases are similar to the Western notion of temperament where a compromise is used to build a tuning system allowing to play in many tonalities like the Werkmeister or Kirnberger suggestions. Therefore the tuning systems of Southeast Asia and ancient India may also be caused by temperaments as compromises meeting instrument and playing constraints.

Topoi in Japanese music: The »kakezume-Pattern« and Yoshizawa Kengyô’s »Chidori no kyoku«

Musical topoi have become a major focus in German music theoretical discourse; they offer an optional, non-binding link between structural and semantic aspects of music. Similarily, in-depth analysis of the music in non-western cultures could benefit from a close look at the musical topoi of these cultures.

A good example is the »kakezume pattern«, one of the best-known topoi in Japanese music, and its highly idiosyncratic usage in Yoshizawa Kengyo’s »Chirodri no kyoku«. This famous Sôkyoku piece, composed a few years before the arrival of Perry’s Black Ships, was (intendedly) revolutionary while at the same time reflecting the long history and the varying meanings and functions of the kakezume pattern. Thus, an exploration of the historical background may help to understand the structural and semantic complexity of the piece and its singular place in the Jiuta-Sôkyoku-tradition.

The ESRA Project - Challenges in the Operationalization of Highly Diverse Musics

Central to the content-related objectives of digital audio databases, especially to those dedicated to music as a global, trans-cultural phenomenon, is the requirement to formulate a comprehensive and coherent conceptual framework, adequately interrelating structural analysis with descriptive typology.

Frequently, efforts at culture-independent objectification of musical utterances have met with a fair share of skepticism from ethnomusicologists and cultural anthropologists. Likewise, attempts at parametrically correlating intrinsic musical structures with extrinsic cultural phenomena have been criticized as merely generating reductionist homologies by deriving ontology from methodology.

Abstract formal-structural representations of musical sound, however, constitute a fundamental prerequisite for the computational utilization of large bodies of digital audio files, as present in the world’s sound archives. On the other hand, interactive contextualization of such analytical datasets with descriptive and interpretative metadata poses an essential desideratum for audio databases as practice-oriented research utilities, to allow for sustainable, on-topic access to relevant data concerning a wide range of causative musicological issues.

Current approaches will be illustrated by exemplary case studies, with reference to select recordings from the ESRA collections.

Neural maps and Hidden-Markov models classifying ethnographic sound archives

The University of Hamburg Ethnographic Sound Recordings Archive (E.S.R.A.) provides access to a large corpus of historical music recordings from all over the world. Since most meta information got lost during the world wars, there is no reasonable chance to utilize the data using tag based retrieval techniques. We therefore propose a knowledge discovery method, which processes audio data only. The system is built on two levels: feature extraction of each recording yields meaningful high-dimensional representations, which are then clustered on a low-dimensional space. Visualization of the space depicts musical similarities among the recordings. Theoretical issues and results are discussed.

Extended Chromatic Tonality and Music Cognition

A fundamental component of Western music is harmony, a complex rule system featuring a point of reference (the tonal center or tonic). Tonal harmony allows listeners and performers to experience dynamic streams of tension and to build up patterns of expectations. Strikingly, in the late-romantic period, the reference to a single tonic becomes increasingly less important, while sequential patterns of harmonic progressions prevail. Although precise mathematical descriptions of these harmonic phenomena can be made, the integration into cognitive models that account for the processes of expectation building and tension formation lacks groundwork in both the theoretical and empirical domain. This talk will outline the conceptual framework (Theory of Tonal Fields, Neo-Riemannian Theory) and draw connections to current cognitive models of tonal harmony (Generative Syntax Model) to approach important challenges, such as the relationship between harmony and chromatic voice-leading, and between sequential and hierarchical descriptions. Building on established research lines in music cognition,
avenues for experimental investigation will be indicated which in turn will point at further implications for theoretical and empirical research on tonal harmony.

Generalized Probabilistic Parsing of Musical Syntax

In general, the parsing of a sequence is the process to infer its underlying structure given a computational model. A musical sequence may be conceptualized, for example, of chord symbols, sets of pitch classes, notes, or audio data, depending on the purpose of the analysis. Harmonic sequences are often analyzed in  a  hierarchical way following traditions by Keiler or Steedman, or recent approaches by Rohrmeier or Granroth-Wilding. The cognitive reality of such hierarchical representations has also been supported by experimental research (e.g. Koelsch et al. 2013). At present there are few approaches with full implementations of such models and they do not capture the complexity of musical phenomena like half-cadences or modulation, and a plain context-free parser architecture might not be general enough to implement them.In this talk, a generalized probabilistic parsing architecture is presented that is homogeneous and can be used for implementing and comparing mildly context-sensitive generative  models.

The basis of this approach is the transitive closure chart-parsing algorithm, described by Kay (1973), described for example by Grune and Jacobs (2008), which is extended to a probabilistic parsing model by Klein and Manning (2005) called generalized (bottom up) chart parsing algorithm (GCP). One of the core advantages of this approach is the possibility of using arbitrary forms of categories in the parsing process. While context-free grammars only allow symbols without any kind of relational informations as categories, GCP allows almost any data type. Furthermore, a GCP implementation of the model in Rohrmeier (2011) is presented that includes modulation and basic metrical aspects.

References:

Granroth-Wilding, M., & Steedman, M. (2012). Statistical parsing for harmonic analysis of jazz chord sequences. Ann Arbor, MI: MPublishing, University of Michigan Library.

Grune, D., & Jacobs, C. J. (2008). Parsing Techniques: A Practical Guide. Springer, New York.

Kay, M. (1973). The MIND system. Natural Language Processing, 155-188. Algorithmic Press, New York.

Keiler, A. (1978). Bernstein's" The unanswered question" and the problem of Musical competence. Musical Quarterly, 64(2), 195-222. Koelsch, S., Rohrmeier, M., Torrecuso, R., & Jentschke, S. (2013).

Processing of hierarchical syntactic structure in music. Proceedings of the National Academy of Sciences, 110(38), 15443-15448.

Klein, D., & Manning, C. D. (2005). Parsing and hypergraphs. In New developments in parsing technology (pp. 351-372). Springer Netherlands.

Rohrmeier, M. (2011). Towards a generative syntax of tonal harmony. Journal of Mathematics and Music, 5(1), 35-53.

Steedman, M. J. (1984). A generative grammar for jazz chord sequences. Music Perception, 52-77.

Architecture of a distributed Sound Archive Database Application

Modeling a sound archive database application forces the developer to deal with multiple requirements and constraints such as accessibility from diverse environments and devices, ability to store and search efficiently through complex datasets of musical parameters and meta data, flexible user-management and -roles, asynchronous background process service to interact with server-side analysis tools and the ability to connect with other distributed applications and services through a robust API. This lecture will discuss the current architecture of E.S.R.A. and outlines prospective refactorings and optimizations.