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Arithmetic Operation Grammar. User Interfaces. Conclusions and Further Work. Article Navigation. April 05 This Site. Google Scholar. Author and Article Information. Guido Kramann. Online Issn: Computer Music Journal 44 1 : 17— Cite Icon Cite. Figure 1. View large Download slide.
The next step is to show how this basic element can be represented audibly. The source code in Figure 3 simply goes through the natural numbers and filters the powers of the first four prime numbers out of each number. This is done with a kind of selective division. For this purpose, first the number B is calculated as the product of the maximum powers of the individual prime numbers 2, 3, 5, and 7.
Each natural number currently under consideration divides B only with the prime factors 2, 3, 5, and 7, and this with a maximum exponent of 3 for the number 2, a maximum exponent of 2 for 3, and a maximum exponent of 1 for both 5 and 7.
Figure 2. Figure 3. Figure 4. But for the operation of division, this is only the case if one excludes all the division results that have a remainder. Several formulas can be used simultaneously to generate multiple voices. This will be illustrated using a simple, concrete example. Similarly, rather consonant relationships are created by the addition of numbers that are rich in the prime factors 2, 3, 5, and 7, because such shifts are widely in phase with the rhythms in which just these divisors appear.
Figure 5. Figure 6. Figure 7. The balls can be designed according to compositional considerations. For example, there is a ball in which a pompom is pasted with colored areas. Whenever the pompom flips, a new variant of the musical structure appears. The resulting balls are placed on a motorized support that slowly rotates the balls around two axes, while a webcam continuously records the changing view and passes it on to the software as a pixel image.
In this software the image is filtered in such a way that there is only a black background and colored shapes in red, green, blue, and yellow Figure 9 a. In the next step, single-colored contiguous areas are segmented. Several such areas can be connected again and form a colorful contiguous area.
Alternately, they may exist separately without connection to other areas. For areas that are composed of several colored areas, the number of areas in each color is counted.
Using a color coding in which blue represents 2 red 3 green 5 and yellow 7 a multiplication of all the prime numbers assigned to the areas with each other is performed, and one obtains exactly one number for each individual contiguous colored area Figures 9 b, c. Figure 8. Figure 9. Figure While a transparent sphere is spinning smoothly, and if the shape of the object inside is more cuboid rather than spherical, it can happen that the inside shape suddenly falls from one side to another.
Such a change in the shape of an object leads to sudden changes. For this type of twisting, areas can be covered by others and new combinations of colored areas can emerge. Moving elements within the ball can gradually combine with other elements of the ball surface through the ball's rotation, and thus vary the sound event. The colors determine which instrument dominates. Isolated, single-color areas are used to influence the base number.
There may be, for instance, areas with more- or less-complex patterns; see Figure From the perspective of a person who has just started with TFP, all this happens at the beginning, either by chance or by intentional reference to the visual form rather than the sonic one. In the best case, however, over time these relationships become increasingly clear and can be taken advantage of by the user. On the level of the facade design model, this would mean that instead of an initial, simplified method of accessing the functionality of the subsystem, methods of greater sophistication would gradually emerge, passing more parameters.
Or these parameters have always been passed, but gradually the user becomes aware of them. The Flippin' Pompoms can be used to convey the meaning of what it is like to compose and to make the experience of holding one's own composition as a ball in one's hand and making it heard whenever desired.
Decorating transparent and opaque spheres as a compositional method.
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