Musical notes and scales

Today we know that the possibility of using sound waves to transmit information has led human beings to develop skills and instruments for the production of sounds. Sounds that we can hear (audible) are used for our direct communication, through speech and also through music. Inaudible sounds have many applications in engineering, basic sciences and medicine, mainly in the form of ultrasound.

We can say that music is a perfect example of the integration of art with mathematics and technology. Musical notes are sounds with determined frequencies, in such a way that there is an exact mathematical relationship between them.

The musical scale is nothing more than a sequence of sounds, arranged in an ascending or descending way, according to the frequency, on which the music is based. Musical scales are obtained through a well-defined mathematical relationship between the frequencies of each musical note.

The division into intervals with a mathematical relationship has been used since the time of Pythagoras, although the scales are different, as human hearing perceives simultaneous sounds that have multiple frequencies of each other as pleasant. That is, a frequency of 261.6 Hz when played simultaneously with a frequency of 523.3 Hz produces a pleasant effect.

The Greeks used a five-note scale, which was also used by the Chinese and later by the Scots. Therefore, it is possible to play music from these cultures using only the black keys of a piano. The Chinese also created a scale with twelve notes.

In Western culture, we also use a twelve-note scale. Arabic music uses a 16-note scale and Indian music uses a 22-note scale. The scales used today have a basic frequency (440 Hz) and, from this, the other notes are obtained by multiplying or dividing the previous note by a constant factor as in a geometric progression.

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