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.^[1]^[2] 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,^[3] in quo copiae cyclicae sunt copiae quarum elementa alterna complementarios unius intervalli circulos aperiunt."^[4]

"Notio Klumpenhouwerana, in eius significationibus ambo simplex et profunda, est quod sinit coniunctiones inversionales una cum transpositionales in reticulis sicut eis figurae primae,"^[5]^[2] 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.^[2] In figura 4, hoc est (b) I₇, I₅, T₂ et (c) I₅, I₃, T₂.

Nexus interni

Notae[recensere | fontem recensere]

↑ Anglice: "any network that uses T and/or I operations [transposition or inversion] to interpret interrelations among pcs" [pitch-class sets].
↑ ^2.0 ^2.1 ^2.2 David Lewin, "Klumpenhouwer Networks and Some Isographies that Involve Them," Music Theory Spectrum 12 (1990)(1):83-120.
↑ 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.
↑ 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.
↑ 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."

Bibliographia[recensere | fontem recensere]

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.

Haec stipula ad musicam spectat. Amplifica, si potes!

[1] Anglice: "any network that uses T and/or I operations [transposition or inversion] to interpret interrelations among pcs" [pitch-class sets].

[Lewin-2] 2.0 ^2.1 ^2.2 David Lewin, "Klumpenhouwer Networks and Some Isographies that Involve Them," Music Theory Spectrum 12 (1990)(1):83-120.

[3] 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.

[4] 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.

[5] 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."

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