By David Armentrout
Publication through Armentrout, David, Armentrout, Patricia
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Extra info for Anika Sorenstam: Discover the Life of a Sports Star
So long as all proportions are referred to unity, there is a single tempo. indd 15 15 8/31/06 3:37:41 PM both slower and faster than their member durations. These can result either from additive durations or from different simultaneous subdivisions of the same whole duration (Figure 1). A linear scale of tempos exists in practice but is not customarily described as such. Between any two given tempos there can be a scale of gradually accelerated tempos. The normal way to perform such an increase is by graduating “equal” increments of tempo between the two limiting tempos.
The Pythagorean twelve-tone scale can also be derived from cyclic tuning in perfect fifths (Figure 8). If cyclic tuning in perfect fifths is extended further, enharmonic equivalents are multiplied until we obtain a fifty-threetone scale, all but eleven of whose adjacent intervals are Pythagorean commas (Figure 9). The Pythagorean scale provides a very limited amount of consonance. Only its perfect octaves, its fifths and fourths, and its major seconds and minor sevenths have no near interval equivalents which are more consonant.
For example, if general pitch contour is the main design element, then precise melodic interval patterns should be relatively hard to measure by ear. Similarly, if the composer intends simultaneous interval combinations to be heard as “vertical melody,” then it should be made hard to hear these combinations as chords subordinated to roots: blend should be underemphasized, rhythmic displacement, timbre contrast, and dissonance perhaps emphasized. Many of the devices (especially the prohibitions) of serial and “atonal” composition are explicable most satisfactorily by reference to this principle.