FZMw Jg. 6 (2003) S. 65 [24]; Corrigenda to/zu


The Shapes of Indeterminacy:
John Cage's Variations I and Variations II

 

by David P. Miller

 


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then mark off the actual, asymmetrical units of time into which the total performance length was divided, with starting times of e.g. 3'57", 13'7", etc. The maximum duration of each event (equivalent to a measurement of 100%) was also determined by the differences between subsequent beginning points. In the case of clusters, or multiple-sound events, the beginning point of each sound was mapped to the subunit of time available for the cluster, rather than the total length of the performance. This also determined the order of sounds within a cluster.

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B. Differing Procedures

As mentioned, I used a millimeter ruler to make all measurements for Variations I. For the first realization, these measurements took the form of fractions. The denominator of each fraction was the distance in millimeters from the given point, through the line, and beyond to the furthest edge of the overlaid or juxtaposed transparencies (the sheet of points and the chosen sheet of lines). The numerator of each fraction was the distance from the line to the point. (See Figure 2.)

Fig. 2:

Variations I: fractional measurement technique. Values obtained: a/b and x/y.

_Variations I_: fractional measurement technique. Values obtained: a/b and x/y.



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Dokument erstellt am 14. Februar 2003