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Imagine a stretched string tied in its extremities.When we touch this string, it vibrates (look the drawing below): Pythagoras decided to divide this string in two parts and touched each extremity again.
Thus, he continued doing subdivisions and combining the sounds mathematically creating scales that, later, stimulated the creation of musical instruments that could play this scales.
The tritone interval, for example, was obtained in a relation 32/45, a complex and inaccurate relation, factor that makes our brain to consider this sound unstable and tense.
We decided to create this topic to show Mathematics is related to Music, because many people ignore the fact the there is Mathematics in music.
Maybe you don’t like Math, but don’t worry; we will try to explain each concept in a simple way, just for you to know that our sensitivity to sound is connected to the logic in our brains. If this wheel completes a turn in 1 second, we say that the frequency of this wheel is “one turn per second”, or “one Hertz”.
This is really interesting, so let your prejudices aside. Before going to the subject of Mathematics in music, let’s remember some basic concepts. Hertz is just a name to represent a frequency unit, and normally is abbreviated by “Hz”.
Ok, in the first topics here in the website, we commented that sound is a wave, and that the frequency of the sound is what defines the music note. If this wheel of our example completes 10 turns per second, its frequency would be 10 Hertz (10 Hz). Well, sound is a wave, and this wave oscillates with a certain frequency.For example, the A (440 Hz) multiplied by 2 = 880 Hz is also an A, but just one octave above.If the goal was to lower one octave, it would be enough just dividing by 2.This note had a pleasant harmony with G and also with C.This procedure was then repeated starting in D, resulting in A. When they repeated this procedure of dividing the string in three parts once again, resulting in B, there was a problem, because B didn’t fit well when played with C (the first note of the experiment).For each frequency, we will have a different sound (a different note).A note, for example, corresponds to a frequency of 440 Hz. It was observed that when a frequency is multiplied by 2, the note still the same.Since its creation until today, the Pentatonic Scale represents a good option to melodies, as we already said in the topic “Pentatonic Scale”.But let’s return to the subject of notes and frequencies, because we just showed 5 notes of the scale.In other words, between C and D, for example, should exist an intermediate note, because the distance between C and D (one tone) was bigger than the distance of C and B (one semitone).Through an analysis of frequency, it was discovered that multiplying the frequency on the note B by the number 1.0595 we would arrive in the frequency of C.