Geometry in music?? Part 1

 What would our lives be without music? And what would music be without geometry?

Did you know that some classics composers  composed their works based, sometimes intuitively, on structures mathematics and aesthetic and geometric patterns? For example, Bach, whose work is full of structures geometric and numerical keys, or Chopin, who used modular arithmetic by putting into a
dodecagon the 24 existing shades. Bartók also used geometry to "write" music for stringed, percussion, and celesta instruments. Look at the picture, isn't it amazing?:



You can also look his Fibonacci scale:
The writing of music, universal language, part of geometry. The base element is the pentagram, which is a construction of five horizontal parallel lines. This staff must be filled or completed with musical figures that are formed with spheres, circles or lines. The combination of these geometric elements will determine the duration of this musical figure formed. The position on the staff will determine the pitch of the note. The spheres or circles of the musical figures can be placed so that the staff lines are tangent or intersecting. It is also aesthetically important that the measurements of the figures are equivalent, as is the space between them. In order to understanding what I mean, I gave you an image:





Are you able to notice de geometry explained?? 😁


Comentarios

Publicar un comentario

Entradas populares de este blog

Geometry in astronomy

Imagen
 As I said, I am a lover of nature, which is why I love landscapes, the sky... and astronomy, in which geometry abounds. Geometry plays a crucial role in the field of astronomy, enabling us to understand and study the structures and phenomena of the universe. Here are some examples of how geometry is applied in astronomy: 1. Planetary Positions and Trajectories: Geometry is used to determine the positions and trajectories of planets in the solar system. The study of planetary orbits and Kepler's laws of motion are based on geometric concepts such as ellipses, circles, and angles. 2. Distance Measurement: Geometry is used to measure distances in space. For example, stellar parallax is used to determine the distance to nearby stars by measuring the apparent shift in position of the observed star from two different viewpoints on Earth. 3. Celestial Shapes and Structures: Geometry helps us understand the shapes and structures of celestial objects. For instance, the shapes of galaxies, ...
Leer más

Geometry to be fit! Part 1

Imagen
 Geometry also plays a fundamental role in various aspects of the sport. Here are some examples of how geometry is applied in sports: 1. Field and track design: Geometry is used in the design and construction of sports fields, tracks, and stadiums. Architects and designers use geometric principles to create playing fields with precise dimensions and proportions, such as the shape and size of a soccer field, the dimensions of a running track, or the layout of the lines on a tennis court. 2. Trajectories and Angles in Throwing Sports: In sports such as discus, javelin, or baseball, athletes must understand the trajectories and angles necessary for a successful throw. Geometry helps determine the direction, height, and force required for the thrown object to reach the desired distance or location. 3. Strategy and tactics: Geometry also plays a role in sports strategy and tactics. Teams use geometric concepts to establish specific formations, positions, and movements in sports such as ...
Leer más

Geometry in music?? Part 5

 Wind Instrument Construction. Just as exploring the golden ratios in string instruments has been suggested, it would be interesting to investigate the construction proportions of wind instruments to determine if there are any applicable relationships in the classroom. Which measurements impact the sound? The holes, their distance from the end of the tube, their diameter, the height of the toneholes, the spacing between open holes, proportion ratios, distances, diameters... all depending on the pitch produced by each hole. This is a truly fascinating topic to explore in the classroom as it involves hands-on and practical activities. However, it can be challenging to find specific information to pursue this investigation, so we will not delve into the development of this subject. Nonetheless, a practical and hands-on activity can be proposed, combining the subjects of Technology and Music, such as constructing a flute. Various tutorials can be found online, primarily in English, by ...
Leer más