Comparison Structure Analysis

This study presents an automatic, computer-aided analytical method called Comparison Structure Analysis (CSA), which can be applied to different dimensions of music. The aim of CSA is first and foremost practical: to produce dynamic and understandable representations of musical properties by evaluating the prevalence of a chosen musical data structure through a musical piece. Such a comparison structure may refer to a mathematical vector, a set, a matrix or another type of data structure and even a combination of data structures. CSA depends on an abstract systematic segmentation that allows for a statistical or mathematical survey of the data. To choose a comparison structure is to tune the apparatus to be sensitive to an exclusive set of musical properties. CSA settles somewhere between traditional music analysis and computer aided music information retrieval (MIR). Theoretically defined musical entities, such as pitch-class sets, set-classes and particular rhythm patterns are detected in compositions using pattern extraction and pattern comparison algorithms that are typical within the field of MIR. In principle, the idea of comparison structure analysis can be applied to any time-series type data and, in the music analytical context, to polyphonic as well as homophonic music. Tonal trends, set-class similarities, invertible counterpoints, voice-leading similarities, short-term modulations, rhythmic similarities and multiparametric changes in musical texture were studied. Since CSA allows for a highly accurate classification of compositions, its methods may be applicable to symbolic music information retrieval as well. The strength of CSA relies especially on the possibility to make comparisons between the observations concerning different musical parameters and to combine it with statistical and perhaps other music analytical methods. The results of CSA are dependent on the competence of the similarity measure. New similarity measures for tonal stability, rhythmic and set-class similarity measurements were proposed. The most advanced results were attained by employing the automated function generation – comparable with the so-called genetic programming – to search for an optimal model for set-class similarity measurements. However, the results of CSA seem to agree strongly, independent of the type of similarity function employed in the analysis.

The Compositional Aesthetic of Rodolfo Coelho de Souza in Paradise Station: an analysis

This article focuses on the compositional aesthetics of Rodolfo Coelho de Souza (1952-), a Brazilian fine art composer and active researcher, whose concerns surpasses the musical composition isolated from the social communication aspect. This is particularly evident in his piece Paradise Station, which, when analyzed, features the structural depth of its compositional process without disregarding the dialog with the listener and the Brazilian character, according to pitch, rhythm, texture, timbre and dynamics. The present analysis reveals a modular structure based on set classes, worked through a transformation network, which follows the David Lewin model.

C(k)-solvability near the characteristic set for a class of planar complex vector fields of infinite type

This paper deals with semi-global C(k)-solvability of complex vector fields of the form L = partial derivative/partial derivative t + x(r) (a(x) + ib(x))partial derivative/partial derivative x, r >= 1, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), epsilon > 0, where a and b are C(infinity) real-valued functions in (-epsilon, epsilon). It is shown that the interplay between the order of vanishing of the functions a and b at x = 0 influences the C(k)-solvability at Sigma = {0} x S(1). When r = 1, it is permitted that the functions a and b of L depend on the x and t variables, that is, L = partial derivative/partial derivative t + x(a(x, t) + ib(x, t))partial derivative/partial derivative x, where (x, t) is an element of Omega(epsilon).

Gevrey solvability near the characteristic set for a class of planar complex vector fields of infinite type

We study the Gevrey solvability of a class of complex vector fields, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), given by L = partial derivative/partial derivative t + (a(x) + ib(x))partial derivative/partial derivative x, b not equivalent to 0, near the characteristic set Sigma = {0} x S(1). We show that the interplay between the order of vanishing of the functions a and b at x = 0 plays a role in the Gevrey solvability. (C) 2008 Elsevier Inc. All rights reserved.

Solvability near the characteristic set for a special class of complex vector fields

This work deals with the solvability near the characteristic set Sigma = {0} x S-1 of operators of the form L = partial derivative/partial derivative t+(x(n) a(x)+ ix(m) b(x))partial derivative/partial derivative x, b not equivalent to 0 and a(0) not equal 0, defined on Omega(epsilon) = (-epsilon, epsilon) x S-1, epsilon > 0, where a and b are real-valued smooth functions in (-epsilon, epsilon) and m >= 2n. It is shown that given f belonging to a subspace of finite codimension of C-infinity (Omega(epsilon)) there is a solution u is an element of L-infinity of the equation Lu = f in a neighborhood of Sigma; moreover, the L-infinity regularity is sharp.

On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials

In this paper we provide the proof of a practical point-wise characterization of the set RP defined by the closure set of the real projections of the zeros of an exponential polynomial P(z) = Σn j=1 cjewjz with real frequencies wj linearly independent over the rationals. As a consequence, we give a complete description of the set RP and prove its invariance with respect to the moduli of the c′ js, which allows us to determine exactly the gaps of RP and the extremes of the critical interval of P(z) by solving inequations with positive real numbers. Finally, we analyse the converse of this result of invariance.

Unit, intermediate (field) (direct and general support) and depot maintenance repair parts and special tools list : generator set, aviation, gas turbine engine driven, integral trailer mounted, 10KW, 28 volts : DoD model MEP 362A, class precise, mode DC, NSN 6115-01-161-3992.

Includes index.

Operator/crew and organizational maintenance manual : generator set, gas turbine engine driven, skid mounted, 150 KW, alternating current, tactical, model D424A, class precise, hertz 400, NSN 6115-01-113-1093.

"8 October 1982."

Intermediate (field) (direct and general support) and depot level maintenance manual : generator set, diesel engine driven, tactical skid mtd 5kw, 1 phase - 2 wire, 1 phase - 3 wire, 3 phase - 4 wire, 120, 120/240 and 120/208 volts, DoD model MEP-002A, class utility, hertz 60, NSN 6115-00-465-1044.

"July 1977."

Operator and organizational maintenance manual : generator set, diesel engine driven, tactical skid mtd 5kw, 1 phase - 2 wire, 1 phase - 3 wire, 3 phase - 4 wire, 120, 120/240 and 120/208 volts : DoD model MEP-002A, class utility, hertz 60, NSN 6115-00-465-1044.

"July 1977."

Organizational, intermediate (field) (direct and general support) and depot maintenance repair parts and special tools list : generator set, gasoline engine driven, skid mounted, tubular frame, 10KW, AC, 120/208V, 3 phase and 120/240V, single phase, (less engine) : DoD model MEP-018A, MEP-023A, class utility, precise ... 6115-00-926-0843.

"June 1977."

Operator and organizational maintenance manual : generator set, diesel engine driven, tactical skid MTD 10KW, 1 phase-2 wire, 1 phase-3 wire, 3 phase-4 wire, 120, 120/240 and 120/208 volts, DoD model MEP-003A, class utility, Hertz 60, NSN 6115-00-465-1033.

Includes index.

Operator, organizational, intermediate (field), (direct support and general support), and depot level maintenance manual : generator set, tactical, gasoline engine, air cooled, 5 KW, AC, 120/240V single phase, 120/208V 3 phase, skid mounted, tubular frame (less engine) military design ; DoD model MEP-017A, MEP-022A, class utility ... 6115-00-017-8241.

"December 1977."

Intermediate (field) (direct and general support) and depot level maintenance manual : generator set, diesel engine driven, tactical skid MTD 5KW, 1 phase-2 wire, 1 phase-3 wire, 3 phase-4 wire, 120, 120/240 and 120/208 volts, DoD model MEP-002A, class utility, hertz 60, NSN 6115-00-465-1044.

"July 1977."

Intermediate (field) (direct and general support) and depot level maintenance : generator set, diesel engine driven, tactical skid MTD., 200 KW, 3 phase, 4 wire, 120/208 and 240/416 volts : DoD model MEP009A, MEP108A, class utility, precise ... 6115-00-403-3762.

"20 October 1977."