Musical Geometry
Simple but powerful presentation that links musical theory with geometry, Carl Munck’s THE CODE, cymatics, A440, the pyramids and much more.
Simple but powerful presentation that links musical theory with geometry, Carl Munck’s THE CODE, cymatics, A440, the pyramids and much more – http://youtube.com/watch?v=LJVO-FcxDio Edgar Cayce: ‘…the pyramids were built on a song.’
http://milbert.com/articles#james_furia
Musical geometry refers to the exploration of geometric patterns, structures, and relationships found within music. This interdisciplinary field examines the mathematical principles underlying musical compositions, harmonies, rhythms, and scales. It seeks to uncover the inherent order and symmetry within music, as well as the connections between geometry, mathematics, and musical expression.
Some key aspects of musical geometry include:
1. Harmonic Ratios: Musical intervals, such as the octave, fifth, and fourth, are based on simple frequency ratios that exhibit geometric patterns and relationships. For example, the octave represents a doubling of frequency, the fifth corresponds to a 3:2 frequency ratio, and the fourth corresponds to a 4:3 frequency ratio.
2. Geometric Progressions: Musical scales and sequences often follow geometric progressions, where each successive note or interval is derived from a geometric transformation of the previous one. This can include geometric sequences, series, and progressions that create patterns and structures within musical compositions.
3. Fractal Music: Fractals are geometric shapes or patterns that exhibit self-similarity at different scales. In music, fractal patterns can be found in compositions that repeat motifs or themes at various levels of complexity. This can create intricate and recursive structures that echo the geometric properties of fractal geometry.
4. Spatial Representation: Some composers and theorists explore the spatial representation of musical elements using geometric shapes and forms. This can involve visualizing musical structures in two or three dimensions, mapping pitch, rhythm, and dynamics onto geometric shapes, or using geometric patterns to represent musical concepts.
5. Mathematical Analysis: Musical geometry also involves mathematical analysis techniques to study the mathematical properties of musical compositions and structures. This can include Fourier analysis, which decomposes complex waveforms into simpler sine waves, as well as graph theory, topology, and other mathematical tools for analyzing musical patterns and relationships.
Overall, musical geometry offers a rich and interdisciplinary approach to understanding the mathematical and geometric underpinnings of music. By exploring the connections between geometry, mathematics, and music, researchers and musicians can gain insights into the fundamental principles that govern musical compositions and enhance their understanding and appreciation of music as a mathematical and artistic expression.