Reticulum Klumpenhouweranum

Reticulum Klumpenhouweranum, ex Henrico Klumpenhouwer, theorista musicus Canadiensi et olim discipulo doctorali Davidis Lewis in Universitate Harvardiana appellatum, est "quodque reticulum quod operationibus T et/vel I (transpositione vel inversione) utitur ad interpretandas coniunctiones inter copias classium soni.Anglice: "any network that uses T and/or I operations [transposition or inversion] to interpret interrelations among pcs" [pitch-class sets].David Lewin, "Klumpenhouwer Networks and Some Isographies that Involve Them," Music Theory Spectrum 12 (1990)(1):83-120. Secundum Georgium Perle, "Reticulum Klumpenhouwerianum est chorda per eius summas et differentias dyadicas" explicata, et "hoc genus explicationis coniunctionum triadicarum in notione copiarum cyclicarum ab initio intellegebatur,Anglice: "A Klumpenhouwer network is a chord analyzed in terms of its dyadic sums and differences," et "this kind of analysis of triadic combinations was implicit in [the] concept of the cyclic set from the beginning." In George Perle, "Letter from George Perle," Music Theory Spectrum, 15(1993):300-303. in quo copiae cyclicae sunt copiae quarum elementa alterna complementarios unius intervalli circulos aperiunt."Anglice: "sets whose alternate elements unfold complementary cycles of a single interval." In George Perle, Twelve-Tone Tonality (1996), p. 21. ISBN 0-520-20142-6. 

"Notio Klumpenhouwerana, in eius significationibus ambo simplex et profunda, est quod sinit coniunctiones inversionales una cum transpositionales in reticulis sicut eis figurae primae,"Anglice: "Klumpenhouwer's idea, both simple and profound in its implications, is to allow inversional, as well as transpositional, relations into networks like those of Figure 1." quae sagittam monstrat desuper a B ad F# nominatum T7, desuper a F# ad A nominatum T3, et sursum ab A ad B, nominatum T10, quod sinit ut repraesentatur a figura 2a, exempli gratia, nominatum I5, I3, et T2. In figura 4, hoc est (b) I7, I5, T2 et (c) I5, I3, T2.


 Classis intervallorum
 Coniunctio similitudinis
 Isographia
 Ordo tonorum
 Prolongatio
 Transformatio (musica)
 Theoria transformationalis Lewiniana

Notae

Bibliographia
 Forte, Allen. 1973. The Structure of Atonal Music. Portu Novo: Yale University Press.
 Lewin, David. 1987. Generalized Musical Intervals and Transformations. Portu Novo et Londinii: Yale University Press.
 Martino, Donald. 1961. The Source Set and Its Aggregate Formations, Journal of Music Theory 5(2): 224–273.
 Morris, Robert. 1987. Composition with Pitch Classes, p. 167. Portu Novo et Londinii: Yale University Press. ISBN 0-300-03684-1.
 Rahn, John. 1980. Basic Atonal Theory. Novi Eboraci et Londinii: Longman's.
 Roeder, John. 1989. Harmonic Implications of Schonberg's Observations of Atonal Voice Leading, Journal of Music Theory 33(1):27–62.

Categoria:Chordae
Categoria:Modernismus (musica)
Categoria:Theoria musica posttonalis