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

↑ 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

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.

Musica

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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