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Twelve-Tone Musical Scale. Sonantometry or music as math discipline. Music: A Mathematical Offering by Dave Benson. Nicolaus Mercator use of Ratio Theory in Music at Convergence; The Glass Bead Game Hermann Hesse gave music and mathematics a crucial role in the development of his Glass Bead Game. Harmony and Proportion. Pythagoras, Music and Space.
Examples include a 3-dimensional scale model of a building or the scale drawings of the elevations or plans of a building. [1] In such cases the scale is dimensionless and exact throughout the model or drawing. The scale can be expressed in four ways: in words (a lexical scale), as a ratio, as a fraction and as a graphical (bar) scale.
An architect's scale is a specialized ruler designed to facilitate the drafting and measuring of architectural drawings, such as floor plans and Multi-view orthographic projections. Because the scale of such drawings is often smaller than life-size, an architect's scale features multiple units of length and proportional length increments. [1]
Some scales use a different number of pitches. A common scale in Eastern music is the pentatonic scale, which consists of five notes that span an octave. For example, in the Chinese culture, the pentatonic scale is usually used for folk music and consists of C, D, E, G and A, commonly known as gong, shang, jue, chi and yu. [14] [15]
Academic research on video game music began in the late 1990s, [3] and developed through the mid 2000s. Early research on the topic often involved historical studies of game music, or comparative studies of video game music and film music (see, for instance, Zach Whalen's article "Play Along – An Approach to Videogame Music" which includes both). [4]
For example, the batik of Cirebon has a fractal dimension of 1.1; the batiks of Yogyakarta and Surakarta (Solo) in Central Java have a fractal dimension of 1.2 to 1.5; and the batiks of Lasem on the north coast of Java and of Tasikmalaya in West Java have a fractal dimension between 1.5 and 1.7.
3D graphics became more popular in the 1990s in video games, multimedia, and animation. In 1995, Toy Story , the first full-length computer-generated animation film, was released in cinemas. Since then, computer graphics have become more accurate and detailed, due to more advanced computers and better 3D modeling software applications, such as ...
The Mandelbrot set, one of the most famous examples of mathematical visualization. Mathematical phenomena can be understood and explored via visualization. Classically, this consisted of two-dimensional drawings or building three-dimensional models (particularly plaster models in the 19th and early 20th century).