Analytic signal processing in music computation

1996

The purpose of this thesis is to develop a sound model that can be used as a creative tool by professional musicians. Post-production editing suites are used for compiling and arranging music tracks, and for creating soundtracks and voice-overs for the radio, television and film industries. A sound model would bring a new dimension of flexibility to these systems, allowing the user to stretch and mould sounds as they please.

The Fast Fourier Transform (FFT) is a powerful general-purpose algorithm widely used in signal analysis. FFTs are useful when the spectral information of a signal is needed, such as in pitch tracking or vocoding algorithms. The FFT can be combined with the Inverse Fast Fourier Transform (IFFT) in order to resynthesize signals based on its analyses.This application of the FFT/IFFT is of great interest in electro-acoustic music because it allows for a high degree of control of a given signal's spectral information (an important aspect of timbre) allowing for flexible, and efficient implementation of signal processing algorithms. Real-time implementations of the FFT and IFFT are of particular interest since they may be used to provide musicians with highly responsive and straight-forward means for generating and controlling sound in live-performance situations. This paper presents musical applications using the IRCAM Signal Processing Workstation (ISPW) that make use of FFT/IFFT-based resynthesis for timbral transformation in real time. An intuitive and straightforward user interface, intended for use by musicians, has been developed by the authors in the Max programming environment. Techniques for filtering, cross-synthesis, noise reduction, dynamic spectral shaping, and resynthesis are presented along with control structures that allow for fine timbral modification and control of complex sound transformations using few parameters. Emphasis is also placed on developing control structures derived from real-time analyses (time and frequency domain) of a musician's input. The ideas and musical applications, discussed in this paper, offer composers an intuitive approach to timbral transformation in electro-acoustic music, and new possibilities in the domain of live signal processing that promise to be of general interest to musicians.

University of York, 1992

It has been said more than once that the advent of computer technology and its application to music has given the electroacoustic composer command over a vast universe of sound that could only be the dream of his predecessors. While, at least in theory, it is reasonable to assume the validity of this statement, it is also important to bear in mind that the same developments have given rise to new problems confronting anyone willing to take full advantage of the new developments. For instance, the psychoacoustic effects of sound perception within a musical context are immediately apparent and much more significant than when dealing with traditional instruments: A concept like timbre, which is reasonably defined within the orchestral palette, takes new significance as a time-varying, multidimensional entity, in which there is no one to one correspondence between the spectrum and timbral identity. Another well known difficulty is that involved in achieving sounds that are 'alive', rather than of neutral 'electronic' quality, experienced by anyone that has used a synthesizer, regardless of whether it is implemented as a piece of hardware or in a software package.

1987

Abstract This paper describes a peak-tracking spectrum analyzer, called Parshl, which is useful for extracting additive synthesis parameters from inharmonic sounds such as the piano. Parshl is based on the Short-Time Fourier Transform (STFT), adding features for tracking the amplitude, frequency, and phase trajectories of spectral lines from one FFT to the next.

One of the goals of the study of music theory is to develop sets of rules to describe different styles of music. By formalising these rules so that their semantics are machine intelligible, it is possible to use computers to reason about and analyse these rules – computational music theory. ANTONis an automatic composition system based on this approach. It formalises the rules of Renaissance Counterpoint using AnsP rolog and uses an answer set solver to compose pieces. This paper discusses ANTON, presenting the ideas behind the system and focusing on the challenges of modelling and synthesis-ing rhythm.

Musical sounds are produced by vibrating structures. The motion of such structures can be modeled using mechanical equations. Nevertheless, these models are not adapted to the real-time synthesis of sounds. This paper addresses the design of synthesis models for musical sounds, in particular the ones produced by a vibrating string. We describe the relationship between the mechanical model and the synthesis model that must satisfy the hearing.

Ph.D. dissertation, Tel-Aviv University, 2012

""Subdivision schemes are multi-resolution analysis (MRA) methods commonly used in computer aided geometric design to generate curves or surfaces with specified smoothness degrees. This work offers new insights into the synthesis and analysis of musical structures based on subdivision schemes theory. The work proposes certain generalizations to the subdivision schemes theory in a way that offers analogies between the mathematics of subdivision schemes (or MRA) and musical hierarchical structures. Based on these observations, new methods for music synthesis and analysis are developed. These methods also reveal certain symmetry patterns and pitch-and-rhythm interrelationships that have a cognitive foundation. The approach proposed and the new tools developed are also shown to be of value in accelerating the convergence and smoothness analysis of subdivision schemes. The work first proposes several mathematical models generalizing the subdivision operation and allowing a more flexible synthesis and a subdivision-based approach to data analysis. These models enable data synthesis and analysis based on both smooth and non-smooth schemes, using perturbations, permutations and varying resolutions. The ‘varying-resolution’ synthesis model allows a structured access to the various resolutions of the refined data and yields desired patterns. The model is based on two dual rules trees, the ‘primal’ and the ‘adjoint’, proposed for the representation of subdivision schemes. It is also shown that the newly proposed ‘adjoint rules tree’ poses a different, operator-oriented, view on the subdivision process and has improved and appealing properties. These properties are shown to extend the standard MRA and to have the potential of accelerating the convergence and smoothness analysis of subdivision schemes. The ‘generalized perturbed schemes’ synthesis model can be viewed as a special multiresolution representation that allows a more flexible control on adding the details. The two analysis models proposed are the respective inverse of those two synthesis models: The ‘subdivision regression’ analysis model can be viewed as a special MRA decomposition inverting the ‘generalized perturbed schemes’ synthesis model, whereas the ‘tree regression’ analysis model allows the identification of certain patterns within the data and it inverts the ‘varying-resolution’ synthesis model. The work then draws analogies between the mathematics of subdivision schemes (or wavelets), as reflected by these mathematical models and hierarchical structures of music. Based on these observed analogies, new methods are proposed for music synthesis and analysis through MRA, which provide a different perspective on music composition, representation and analysis. It is demonstrated that the structure and recursive nature of the generalized subdivision models above are well suited to the synthesis and analysis of monophonic and polyphonic musical patterns, doubtless due in large part to the strongly hierarchical nature of traditional musical structures. The music synthesis methods create patterns that bear a special meaning of interrelations between pitch and rhythm. The music analysis methods enable the compression and decompression (reconstruction) of musical pieces and the extraction of useful features of the pieces. In particular, the analysis identifies and derives certain symmetry patterns and pitch-and-rhythm interrelationships, showing the importance of these interrelationships as features for music analysis and classification. Such attributes were not used so far as features for music analysis and classification. Our approach to pitch-and-rhythm interrelationships points out an interesting phenomenon, according to which the relations between neighbor pitches may be related to their timing through a relatively simple subdivision model. The work discusses the cognitive foundation of this model and demonstrates its significance in several case studies. The work is accordingly divided into three major parts. The mathematical part (Part II, Chapters 5 and 6) presents the generalized subdivision models for synthesis and analysis. The musical part (Part III, Chapters 7–10) presents the respective methods for music synthesis and analysis. An additional mathematical part (Part IV, Chapters 11 and 12) deals with accelerating the convergence analysis of subdivision schemes, by reformulating the discussion in Chapter 5 in terms of matrices or operators. Parts I (Chapters 1–4) and V (Chapters 13 and 14 and appendices) include the introduction and the closure chapters, respectively.""

2009

We present a new basis for anal- ysis of music. The basis vectors are sam- pled real waveforms of fixed frequency inside a Gaussian envelope. Their frequencies and time localizations are induced by a tiling of the time-frequency plane well adapted to mu- sic. Through a careful investigation of their properties they are subsequently slightly mod- ified in order to give a stable system, without losing their time-frequency localization. Our new basis discriminates semitones, detects the overtones as well as the attack of notes, and gives a sparse representation of the signal. It will enhance the performance of all kinds of dig- ital audio processors, and provide a useful tool for numerous multimedia applications.

IEEE Journal of Selected Topics in Signal Processing, 2000

2020

In the last century, two trends have increased the scope of musical analysis: music theorists have provided mathematical insight into specific musical scenarios, while musicologist have examined the nature of musical analysis as a cultural, cognitive, and scholarly endeavor [1] [2] [3] [4] [5]. This paper intends to bring these two strands of research together by providing a constructive mathematical foundation for the process of musical analysis. By establishing a mathematical description of the generation of an analysis of a piece of music, useful mathematical tools for performing operations frequently used in analysis, and possible precise definitions for loaded terms such as “musical similarity” and “musical form”, I will extend the analyst and the meta-analyst’s ability to create abstractions from musical surfaces, the core of every process of analy-