If the smallest form of this fraction results in small numbers, it means that the rhythmic pattern can be more easily interpreted. When we play two notes at the same time, we are comparing a sound that hits X times per second with another that hits Y times per second, resulting in a X/Y fraction. In practice, as we have already seen, a musical note is formed by beats played quickly in succession (for example: 220 beats per second = 220 Hz). If this idea is not very clear, consider the following: However, two sounds that played in the proportions of 32 by 45 would form a rhythmic pattern more difficult to decipher. The pattern resulting from this combination of two rhythms could be quickly identified. For example, imagine a sound that plays every two seconds, along with another sound that plays every 3 seconds (resulting in a 2/3 fraction). The fraction 32/45 sounds “unpleasant”.Īlthough there is no scientific evidence to justify this, the reason may be the combination of periods, where very misaligned periods are more difficult to interpret. Interestingly enough, in general, the human brain interprets sounds as “pleasant” from small values in the numerator and denominator of a fraction, such as the 2/3, 4/5, 8/5, etc. Over time, the notes were given the names we know today. The tritone interval, for example, was obtained from the 32/45 ratio, a complex relationship, a factor that leads our brain to consider this sound unstable and tense. So, he continued making subdivisions and mathematically combined the sounds creating scales that later stimulated the creation of musical instruments that could reproduce these scales. This sound, despite being different, combined well with the previous sound, creating a pleasant harmony to the ear, because these divisions shown until now have 1/2 and 2/3 mathematical relationships (our brain likes well-defined logical relationships). This time, it was not the same note an octave higher, but a different note, which needed to be renamed. He noticed that a new sound appeared, different from the previous one. He decided to try what the sound would look like if the string was divided into 3 parts: The sound produced was exactly the same, only higher (since it was the same note an octave higher): Pythagoras decided to divide this string into two parts and touched each end again. When we play this string, it vibrates (see the drawing below): Imagine a stretched rope, attached to its ends. This we have just shown about octaves, he discovered while “playing” with a taut string. At that time, there was a man named Pythagoras who made very important discoveries for mathematics (and for music). Okay, so before we continue, let’s go back to the past, to Ancient Greece. We can then conclude that a note and its respective octave maintain a ratio of ½. If the goal was to lower an octave, it would be enough to divide it by 2. For example, the A note (440 Hz) multiplied by 2 = 880 Hz is also an A note, just one octave above. The A note, for example, corresponds to a frequency of 440 Hz.Īnd where does mathematics come into play here? It has been observed that when a frequency is multiplied by 2, the note remains the same. For each frequency, we have a different sound (a different note). If a sound wave completes 10 oscillations in 1 second, its frequency will be 10 Hz. If a sound wave completes one oscillation in 1 second, its frequency will be 1 Hz. Great, but what does that have to do with sound? Well, sound is a wave, and that wave oscillates with a certain frequency. If this wheel in our example completed 10 revolutions in 1 second, its frequency would be 10 Hertz (10 Hz). Hertz is just a name given to represent the unit of frequency, and is often abbreviated to “Hz”. If this wheel completes one revolution in 1 second, we say that the frequency of that wheel is “one revolution per second”, or “one Hertz”. Very well, in the first topics here in the website, we mentioned that sound is a wave and that the frequency of the sound is what defines the musical note.īut what is frequency? It is a repetition with time reference. This is very interesting, so let go of your prejudices. Maybe you don’t like math, but don’t worry, we will try to explain each concept in a simple way, so that you realize that our sensitivity to sound is linked to the logic of our brains. We decided to build this topic to show you how mathematics is related to music.
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