Traditional Notation Research Articles

Helical Collapse of a Whirling Elastic Rod Forced to Lie on a Cylinder

Helical Collapse of a Whirling Elastic Rod Forced to Lie on a Cylinder

Pitch Spelling: A Computational Model

In this article, cognitive and musicological aspects of pitch and pitch interval representations are explored via computational modeling. The specific task under investigation is pitch spelling, that is, how traditional score notation can be derived from a simple unstructured 12-tone representation (e.g., pitch-class set or MIDI pitch representation). This study provides useful insights both into the domain of pitch perception and into musicological aspects of score notation strategies. A computational model is described that transcribes polyphonic MIDI pitch files into the Western traditional music notation. Input to the proposed algorithm is merely a sequence of MIDI pitch numbers in the order they appear in a MIDI file. No a priori knowledge such as key signature, tonal centers, time signature, chords, or voice separation is required. Output of the algorithm is a sequence of "correctly" spelled pitches. The algorithm is based on an interval optimization approach that takes into account the frequency of occurrence of pitch intervals within the major-minor tonal scale framework. The algorithm was evaluated on 10 complete piano sonatas by Mozart and had a success rate of 98.8% (634 pitches were spelled incorrectly out of a total of 54,418 notes); it was tested additionally on three Chopin waltzes and had a slightly worse success rate. The proposed pitch interval optimization approach is also compared with and tested against other pitch-spelling strategies.

Documentation in orthopaedic surgery - do integrated care pathways work?

Integrated care pathways (ICPs) are being widely adopted in orthopaedic surgery. This study compares the quality of medical notation in an ICP with traditional record keeping. During a 3-month period, 53 total hip replacements (ICP notation) and 30 total knee replacements (traditional notation) were performed. The records of each patient were scrutinised using a standardised scoring system, based on The Royal College of Surgeons of England guidelines on medical record keeping. Each set of records (83) was scored for: admission clerking, subsequent entries, consent form, operation note, and discharge letters. The time taken to retrieve this information was recorded. The overall score for traditional records (mean, 70%) was significantly higher (P = 0.001 ) than for the ICP records (mean, 62%). The mean scores for initial clerking, subsequent entries and consent form were higher in the traditional record group. It took 35% longer to retrieve information from the ICP group (P < 0.001). In this study, the quality of record keeping was higher when using the traditional notation than an established ICP. In both groups, the frequency of omissions was high.

Case Study on Algebraic Software Methodologies for Scientific Computing

The use of domain specific languages and appropriate software architectures are currently seen as the way to enhance reusability and improve software productivity. Here we outline a use of algebraic software methodologies and advanced program constructors to improve the abstraction level of software for scientific computing. This leads us to the language of coordinate free numerics as an alternative to the traditional coordinate dependent array notation. This provides the backdrop for the three accompanying papers: Coordinate Free Programming of Computational Fluid Dynamics Problems, centered around an example of using coordinate free numerics, Machine and Collection Abstractions for User-Implemented Data-Parallel Programming, exploiting the higher abstraction level when parallelising code, and An Algebraic Programming Style for Numerical Software and its Optimization, looking at high‐level transformations enabled by the domain specific programming style.

Stretching Traditional Notation

Stretching Traditional Notation

Alternatives to Traditional Notation

Alternatives to Traditional Notation

A general pitch interval representation: Theory and applications

Abstract Pitch and pitch‐intervals are most often represented — in the western tradition — either by the traditional pitch naming system and the relating pitch‐interval names, or as pitch‐classes and pitch‐class intervals. In this paper we discuss the properties, relationships and limits of these two representations and propose a General Pitch Interval Representation (GPIR) in which the above two constitute specific instances. GPIR can be effectively used in systems that attempt to represent pitch structures of a wide variety of musical styles (from traditional tonal to contemporary atonal) and can easily be extended to other microtonal environments. Special emphasis will be given to the categorisation of intervals according to their frequency of occurrence within a scale. Two applications of the GPIR will be presented: a) in a system that transcribes melodies from an absolute pitch number notation to the traditional staff notation, and b) in a pattern‐matching process that attempts to discover repetition...

Multidimensional representation of electroacoustic music*

Abstract A five‐layered system of graphical representation has been created for the analysis of electroacoustic compositions. Electronic music often contains spectral changes and other timbral aspects that make traditional music notation inadequate. The sonogram is a useful representation of the frequency spectra and their evolutions. Additional layers have been included to clarify various aspects such as pitch relationships, phrasing, overall dynamic levels and processing techniques. Pitch notation, a phrase analysis, amplitude lines and a text line of comments have been combined to form more accurate visual representations of music.

Extending music notation through programming

Traditional notation has led to the continuation of a traditional musical approach in which scores are static descriptions to be realized by performers. Borrowing programming concepts from computer science leads to score-like descriptions with the capability of expressing dynamic processes and interaction with performers. The implications for composition, performance, and future research are discussed.

Weighted norm estimates for oblique derivative problems

Estimates of the Caccioppoli-Schauder type are proven for a class of regular oblique derivative problems in Holder function spaces with weights. Previous restrictions on the range of admissible weights are showed to be unnecessary. 1. NOTATION Let c be a bounded open subset of a finite-dimensional Euclidean space. We adopt traditional notation for (real) function spaces such as Ck (ni), Ck, (j), Cck(co) , LP(c) , which need not be illustrated. We do however specify that Wk,P(co) denotes the Sobolev space of order k and exponent p on c. Next, as in [1], we set Ho (co) = CO (U0) 1 Io; norm in CO(U), H() = Cka-k(), IIa; = norm in Ckak(,k) for k (a nonnegative integer) O to, being the set of points of c whose distance from 0c is > a. Of course, Ha)(ca ) -= H a (H )(C) c Ha7)(co) if b' 0}, So{x E R N: lxI < 1, XN = O}, S+ = OB+ISa H(-b) = H(-b)(B+) , I b = Ia ,Received by the editors August 8, 1993 and, in revised form, January 27, 1994. 1991 Mathematics Subject Classification. Primary 35D10, 35J25; Secondary 35B45, 35B65, 46E35. )1995 American Mathematical Society

Color-Encoded Music Scores: What Visual Communication Can Do for Music Reading

N ot long ago, a group of adventurous young people-three girls and a boy-accepted my invitation to play a Bach chorale together on the piano. Why adventurous? Because none of them could play the piano or read music. Two hours later, the whole piece was played, from start to finish, by these four musical novices. For this to be possible, the traditional musical score had to be transformed to better communicate the music. Established early in the present millennium, traditional musical notation was clearly not meant by its creators-Christian monks transcribing sacred music-to be accessible to a wide public. So the system developed, becoming ever more abbreviated and complex, always aiming at faithfulness to the composition, but entirely neglecting the other half of the communicative process-namely, the reading, or decoding, of this complex notation. Now, however, as the end of the millennium draws near, two factors make the present time particularly ripe for a critique of the music-reading process: the advent of visual communication as a field of study and Piaget's pedagogical theory. The purpose of this article is to present the genesis of a new musical notation system geared to expanding the musicliterate public-a self-evident musical score. My intention is to encourage readers to try this bold experiment for themselves-that is, to try to play Mozart's Sonata XVI or Satie's Gymnopedies while reading scores written with this musical notation system.

Systems for nonlinear instruments and notation

Abstract Linear notation when applied to sculptural, or nonlinear instruments is mutually obstructive. Take for example a sound sculpture which has been designed to link the visual and aural arts in a balanced representation — how does one score for an instrument where the pitched elements may only be a by‐product of visual and timbral or even logistical considerations; where sound parameters do not operate along a convenient continuum; where resonators are not presented in panel format for easy access; where traditional percussion mallets may be wholly unsuitable? The symbiotic nature of nonlinear instruments is the stuff of compromise as the spatial position of resonant objects, relative to human limitations, impose a set of physically possible or convenient musical gestures. These considerations extend beyond the limits of traditional notation and bring to the fore the question as to whether new systems should be devised or whether, perhaps, it is best for such performances to remain within an improvis...

Musical notation for the keyboard: An examination of stimulus‐response compatibility

AbstractA recent stimulus‐response compatibility model was used to provide a performance evaluation of an experimental notation for the keyboard in which pitch varies horizontally in visual space. One hundred and twenty subjects performed a choice reaction time task using either the horizontal notation or a more traditional vertical notation. Half the subjects in each notation group received white noise and half received pitch‐varying feedback with responses. A horizontal display advantage was revealed when rules of the model were applied to data analyses. Further, the horizontal display advantage was not dependent on the nature of the feedback. In a second experiment, performance of musicians and non‐musicians was compared using the horizontal and vertical notations. Musicians' performance was uniformly better than that of non‐musicians, and did not differ with notation orientation. The findings support the use of non‐traditional horizontal notations for novice performance on a keyboard instrument.

Linking Different Cultures by Computers: A Study of Computer-Assisted Music Notation Instruction

CAMNI, which stands for Computer-Assisted Music Notation Instruction, is self-educational software designed and developed with HyperCard. This program features interactive hypermedia (inter-linked musical notation knowledge, musical tempo controlled by the user, the use of digital sounds and animation), multiple representation mode (the staff notation, the number notation, the letter name of notes and the piano keyboard, four representations are linked and can be switched from one to another easily or presented at the same time in terms of a user's need), graphical user interface “GUI,” context-sensitive-sound icon (the use of a sound icon in lesson navigation and sub-index design), direct manipulation (pointing and clicking objects to interact with the program), and self-directed but computer-context-sensitive-guided environment (multi-path navigation characterized by an author-designed but user-defined and individualized learning approach). The CAMNI was specifically designed for Chinese students who would like to study the staff notation whether or not they have background with the number notation (the traditional Chinese musical notation system).

The UPIC System: Origins and Innovations

T HE IDEA OF THE UPIC system goes back to 1953-54, when Iannis Xenakis wrote music for orchestra, using graphic notation for representing musical effects that were too complicated to be specified with traditional staff notation. The work Metastasis (written in 1953-54 and premiered at Donaueschingen in 1955) makes systematic use of glissandi (continuous transition between two notes of different pitches). Xenakis drew the glissandi as straight lines in the pitch-versus-time domain. The score is written for sixty-one different instrumental parts. The great number of glissandi creates a sound space of continuous evolution comparable to the ruled surfaces and volumes that he used in architecture.

Musical Notation for the Keyboard: An Examination of Stimulus–Response Compatibility

The principles of stimulus-response compatibility were used to provide a performance evaluation of an experimental notation for the keyboard in which pitch varies horizontally in visual space. Subjects performed a choice reaction time task using either the horizontal notation or a more traditional vertical notation. Half the subjects in each notation group were provided white noise and half pitch-varying feedback with responses. Responses were reliably faster with the horizontal display. Further, the superiority of the horizontal display was not dependent on the nature of the feedback. In a second experiment, performance of musicians and nonmusicians was compared using the horizontal and vertical notations. Performance by musicians was equivalent with horizontal and vertical displays and uniformly better than nonmusicians. The findings fail to support the argument that horizontal visual representations will be less useful in musical tasks because they will be incompatible with the mental representation of pitch as varying vertically from ‘low’ to ‘high’.

Korean Musical Instruments: A Practical Guide

The first and most comprehensive English language account of Korean musical instruments. Designed as a 'show and tell' guide, two overview chapters on history and al instruments currently used or reported in Korea precede seven chapters devoted to the seven most important current instruments. Each instrument is considered in its historical, regional, and contemporary context, in respect to notation types and systems, instrument construction, and playing techniques. THe book includes copious notations in both traditional mensural notation and Western staff notation.

A mathematical expression language for imaging applications

The language of image processing is predominantly the language of discrete mathematics. Image processing texts are written using its notation, as are articles for conferences and journals. While math formulae are appropriate for communicating the traditional algorithmic relationships among parts of a process, they have not been used for a complete description of procedures implemented on a computer. This is largely because iteration, assignment and complete description of object shape has been traditionally deemed outside of mathematics and so has been supplied instead by “glue text” surrounding the formulae. We propose an Expression Language, a set of conventions for construction of compilable math expressions, for providing these complete descriptions by extending only slightly the traditional notation of mathematics. The impetus for the Expression Language arose from the need to describe precisely a large number of image processing functions in the context of national and international standards, but the language is also appropriate to graphics and to visualization.

A graphical environment for user-interface design and development

This paper presents a new approach to the design of an easy-to-use and flexible user-interface management system (UIMS). We identify two major problems for UIMSs. The first problem is to find a way to make the UIMS easier to use without sacrificing important functionality. A new design concept, behaviour abstraction, is described which allows important gains in ease-of-use, while retaining the kind of flexibility needed by user-interface designers. The second problem is to provide a user-interface design tool that allows easy and flexible runtime configuration. A traditional notation, the data-flow diagram, proves to be an adequate and appropriate organising principle for the design of the runtime connection between a user-interface module and application modules. An implementation, called the graphical specification system (GSS), provides an integrated environment for designing the user-interface component of interactive embedded system software. GSS provides two tools; an application display generator (ADG) for designing screen objects and a data-flow editor (DFE) for specifying runtime connections. The ADG uses behaviour abstraction in a what-you-see-is-what-you-get (WYSIWYG) drawing environment. The designer can easily create arbitrary graphical presentations and assign behavioural roles for these presentations to build functional user-interface objects. In the DFE, the designer can specify sources, transformations and destinations of data by selecting user-interface objects designed in ADG, attaching functions to internal nodes or using special intermodule connection icons called ports. The DFE allows a limited programming capability through the diagrams to accommodate the needs of an evolving user interface. GSS demonstrates the smooth integration of a drawing environment for display design and a data-flow editor for runtime specification. The specifications can be executed for testing during the design process and saved for stand-alone execution. Our results provide a platform for future work in extending the behaviour abstraction concept and for building in usability engineering tools.

Set notation as a language to specify data transformation programs

AbstractTo allow tools in a computer‐based working environment to share data, it is sometimes necessary to transform the data from the form used by one tool to the form expected by another. An application generator has been developed that generates data transformation programs from high‐level descriptions of the required transformations. The transformation specifications are expressed in traditional set notation, which combines features of functional and logic programming. The system thus offers a powerful declarative language for expressing data transformations.