Geometry in music?? Part 4

 As we mentioned before, the use of geometric transformations is a widely used and recurring technique in any document that links music and mathematics. Therefore, it is not considered necessary to delve into it, and we will address the issue of musical geometry from other perspectives:

1. Its application in dance through the geometric figures present in a choreography. The students propose and execute various positions that are captured on paper or captured in photographs, thus generating a visual resource with which the geometric shapes they have created can be explored. From there, concepts such as perimeters, areas, geometric figures, angles and vertices can be addressed. In addition, in the musical field aspects such as rhythm, phrasing and body expression are worked on.

2. The handling of musical instruments, considering their dimensions and the geometric peculiarities they possess, gives them different sound qualities that are related to the study of waves. The following table shows the relationship between the geometry of wind instruments and the wavelength as a function of the length of the tube:







These specific characteristics confer different sound qualities that can be studied through mathematical relationships. Specifically, they determine the timbre and harmonic series, which are qualities that make each instrument sound unique. Based on their geometry, we can determine the length of the tube and its relationship with the emitted wavelength. With this information, and assuming an air velocity of 330 m/s, we can calculate the frequency (Hz) of the instrument's fundamental note using the formula 𝑓 = 330/𝜆, where 𝜆 represents the wavelength.

Furthermore, the measurements of certain instruments can also be used to apply geometric knowledge in calculating areas and volumes. For instance, the neck of a saxophone can serve as an example for such calculations:






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