Ternary Form

2019 ◽  
pp. 158-194
Author(s):  
David Beach
Keyword(s):  
Ternary Form

Webern's New Quartet

Tempo ◽  
1939 ◽  
pp. 52-53
Author(s):  
Erwin Stein
Keyword(s):  
String Quartet ◽  
Structural Elements ◽  
The Third ◽  
Ternary Form

Anton Webern's String Quartet, Op. 28 (1938), is in three movements, the structural elements of which are related to classical forms. The first movement is designed as an adagio (ternary form), the second is a kind of scherzo and trio en miniature, in which neither part contains a second section or development. The third movement is an elaborate scherzo form without trio.

Characteristic Analysis As An Oil Exploration Tool

1994 ◽  
Author(s):  
H. A. F. Chaves
Keyword(s):  
Set Theory ◽  
Mineral Resources ◽  
Sedimentary Facies ◽  
Petroleum Exploration ◽  
Mineral Deposits ◽  
Characteristic Analysis ◽  
A Value ◽  
Ternary Form ◽  
Exploration Tool ◽  
Individual Variables

Characteristic analysis is well known in mineral resources appraisal and has proved useful for petroleum exploration. It also can be used to integrate geological data in sedimentary basin analysis and hydrocarbon assessment, considering geological relationships and uncertainties that result from lack of basic geological knowledge, A generalization of characteristic analysis, using fuzzy-set theory and fuzzy logic, may prove better for quantification of geologic analogues and also for description of reservoir and sedimentary facies. Characteristic analysis is a discrete multivariate procedure for combining and interpreting data; Botbol (1971) originally proposed its application to geology, geochemistry, and geophysics. It has been applied mainly in the search for poorly exposed or concealed mineral deposits by exploring joint occurrences or absences of mineralogical, lithological, and structural attributes (McCammon et al., 1981). It forms part of a systematic approach to resource appraisal and integration of generalized and specific geological knowledge (Chaves, 1988, 1989; Chaves and Lewis, 1989). The technique usually requires some form of discrete sampling to be applicable—generally a spatial discretization of maps into cells or regular grids (Melo, 1988). Characteristic analysis attempts to determine the joint occurrences of various attributes that are favorable for, related to, or indicative of the occurrence of the desired phenomenon or target. In geological applications, the target usually is an economic accumulation of energy or mineral resources. Applying characteristic analysis requires the following steps: 1) the studied area is sampled using a regular square or rectangular grid of cells; 2) in each cell the favorabilities of the variables are expressed in binary or ternary form; 3) a model is chosen that indicates the cells that include the target (Sinding-Larsen et al, 1979); and 4) a combined favorability map of the area is produced that points out possible new targets. The favorability of individual variables is expressed either in binary form— assigning a value of +1 to favorable and a value of 0 to unfavorable or unevaluated variables—or in ternary form if the two states represented by 0 are distinguishable—the value +1 again means favorable, the value —1 means unfavorable, and the value 0 means unevaluated.

Two into Three Won't Go? Poetic Structure and Musical Forms in Mozart's Idomeneo

2012 ◽  
Vol 24 (3) ◽  
pp. 229-248
Author(s):  
Tim Carter
Keyword(s):  
Eighteenth Century ◽  
The Other ◽  
Poetic Structure ◽  
Ternary Form ◽  
Before And After ◽  
Rational Inquiry ◽  
Musical Forms

AbstractBy the last quarter of the eighteenth century, the typical Metastasian two-stanza aria text could be set to music in one of two ways: in the ternary form typical of the earlier da capo aria (stanzas 1–2–1) or in a binary one (stanzas 1–2–1–2). Why did Mozart choose one form over the other in Idomeneo (1781); what does this tell us about the role of his librettist, Giovanni Battista Varesco, both before and after the composer left Salzburg for Munich to finish composing the opera and to prepare its performance; and how might these issues enable some rational inquiry into questions of music and drama?

Handel's Recomposed Return Arias and Romantic Attraction in Alexander Balus

2016 ◽  
Vol 69 (3) ◽  
pp. 651-698
Author(s):  
David Ross Hurley
Keyword(s):  
Romantic Attraction ◽  
Ternary Form ◽  
The Subject ◽  
Comprehensive Study

Among the various formal structures employed in the arias of Handel's oratorios is a ternary form in which the last section is newly written, rather than being a verbatim repeat of the first section, as in the ubiquitous da capo aria. This form, for which I propose the term “recomposed return aria,” is rarely mentioned by scholars, and has never been the subject of a comprehensive study, despite its considerable aesthetic interest. In this article I focus on Handel's use of the recomposed return aria, exploring in particular the array of recapitulatory designs that it encompasses, and the reasons why Handel may sometimes have chosen this form instead of the regular da capo. I then turn to the oratorio Alexander Balus, as a case study through which to show how the compositional freedom intrinsic to the recomposed return aria allows for the portrayal of various aspects of erotic attraction experienced by the protagonists.

scholarly journals Ligeti's ‘third way’: ‘Non–atonal’ elements in the Horn Trio

Tempo ◽  
2001 ◽  
pp. 17-23 ◽  
Author(s):  
Mike Searby
Keyword(s):  
Major Elements ◽  
Musical Language ◽  
Third Way ◽  
Avant Garde ◽  
The Past ◽  
Ternary Form ◽  
Harmonic Language ◽  
As If

It is perhaps curious that only a year after this exchange took place in 1981, Ligeti completed his Horn Trio – which uses traditional ternary form, a passacaglia (although a disguised one), a strong melodic focus, and a harmonic language which contains clear triads and dominant sevenths in abundance. In spite of his assertions above, it does seem as if Ligeti, in addition to rejecting the Avant-garde, is looking to the past for major elements of his musical language.

Determinantal representations of x4+y4+z4

1938 ◽  
Vol 34 (1) ◽  
pp. 6-21 ◽  
Author(s):  
W. L. Edge
Keyword(s):  
Theoretical Description ◽  
Fourth Degree ◽  
Linear Forms ◽  
Ternary Form ◽  
Quartic Form ◽  
Fourth Root

A ternary form of degree n can be expressed as a symmetrical determinant, of n rows and columns, whose elements are linear forms; furthermore, not only is such a mode of expression known to be possible, but A. C. Dixon, in 1902, gave* a process by which the determinant can be obtained when the ternary form is given. This process, however, although it admits of such a straightforward theoretical description, cannot be carried through in practice, for a general ternary form, without the introduction of complicated algebraical irrationalities, even if we restrict ourselves to forms of the fourth degree; consequently no application of Dixon's process to an actual example seems to have been published. If then a choice can be made of a quartic form for which the reduction to a symmetrical determinant can be carried out without undue complication, it seems fitting to give some account of it. The following pages are therefore devoted to the study, from this aspect, of the form x4+y4+z4, for which the reduction can be accomplished without introducing any irrationality other than the fourth root of − 1.

Determinantal representations of elliptic curves via Weierstrass elliptic functions

2018 ◽  
Vol 34 ◽  
pp. 125-136 ◽  
Author(s):  
Mao-Ting Chien ◽  
Hiroshi Nakazato
Keyword(s):  
Elliptic Curves ◽  
Algebraic Curve ◽  
Theta Functions ◽  
Elliptic Functions ◽  
Determinantal Representation ◽  
Ternary Form ◽  
Riemann Theta Functions

Helton and Vinnikov proved that every hyperbolic ternary form admits a symmetric derminantal representation via Riemann theta functions. In the case the algebraic curve of the hyperbolic ternary form is elliptic, the determinantal representation of the ternary form is formulated by using Weierstrass $\wp$-functions in place of Riemann theta functions. An example of this approach is given.

Thinking Materialistically with Locke, Lonzi, and Cavarero

2021 ◽  
pp. 93-106
Author(s):  
Olivia Guaraldo
Keyword(s):  
John Locke ◽  
The Body ◽  
Musical Piece ◽  
Political Dimension ◽  
The Third ◽  
Ternary Form ◽  
The Subject ◽  
Adriana Cavarero ◽  
The Given ◽  
Bodily Condition

A “scherzo” is a musical piece which traditionally retains the ternary form of the minuet but is considerably quicker. This is a materialist scherzo, since it treats three different authors that are all significantly concerned with the body. John Locke, Carla Lonzi, and Adriana Cavarero present three different modes of narrating sex: the first implicitly, the second explicitly, the third creatively. Cavarero’s relationality, whilst giving a provocatively creative account of orgasm, attributes to sex a grounding function in rethinking the subject. Yet that there is also a political dimension in this carnal account of orgasm. By exploring the possibilities of the given of our bodily condition—an anatomical destination to pleasure that is always relational—this etude defends relational ethics as providing a different perspective on how to imagine social and political forms of co-existence and non-violence, beyond and apart from the naturalized claim to “fundamental hostility.”

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