[Un article de The Conversation écrit Jean-Pierre Dalmont – Professeur des Universités, spécialiste des guides d”ondes acoustiques et de la physique des instruments de musique, Le Mans Université]
If it often happens that we perceive in various circumstances that some people, even alone, sing false, it is because they very significantly move away from the expected musical scale. To fix the ideas, if in a melody, the expected note is a LA3 (the there In the middle of the keyboard) its frequency should be around 440 Hz, that is to say 440 oscillations per second.
If it deviates from more than 10 Hz, it will be far enough from the expected to shock the listeners who know the melody. Musical scales have a large share of arbitrariness and their perception is therefore a matter of the achievement.
Someone who has no musical culture will in no case be shocked by these deviations. Moreover, the musical scales which do not fall under our culture such as the eastern scales or the scales in quarter tones seem false, because they are not familiar to us.
The correctness is therefore a very relative notion, and it is when you make music with many that it really takes on its meaning. Indeed, two musicians who play together must be “agreed”, that is to say that the notes they will play together must agree. And there, our ear is intractable: if two musicians are not granted, the result is extremely unpleasant, it sounds false. We therefore leave the area of acquired to enter that of physics.
Music, a matter of physicists?
What phenomenon does it hold? The answer to this question has been known for quite a short time in view of the history of music since it is only in the middle of the 19th centurye Century that Hermann von Helmholtz gave a scientific explanation of the notion of dissonance, which he names ” Rauhigkeit “(” RUGURY “).
It associates the notion of dissonance with the concept of beats. Indeed, mathematics tell us that when we superimpose two pure sounds of the same amplitude and neighboring frequencies, this results in a single sound whose frequency is their average and whose amplitude is modulated periodically by a frequency equal to their difference. For example, if we superimpose two pure sounds of the same amplitude and frequencies 439 Hz and 441 Hz, we obtain a 440 Hz sound which goes out twice per second (2 Hz). It is a fairly unpleasant feeling, because our brain does not appreciate the quickly repeated events which mobilize its attention too much.
Hermann von Helmholtz subjectively estimated that the feeling was the most unpleasant for beats around 30 Hz. When this frequency increases, the feeling of beating disappears and the unpleasant feeling with.
Things get complicated when bunk two complex sounds. A complex sound is a periodic sound which we know, from Joseph Fourier, that it can be broken down into a sum of pure sounds – the harmonics -, the frequencies of which are multiple of its frequency, called fundamental frequency. When you superimpose two complex sounds, then all the harmonics of the first sound are likely to beat with one or even several harmonics of the second. The probability that the two sounds sound well together is almost zero.
The rare situations without beat correspond to the consonant intervals: the octave which corresponds to a frequency ratio equal to 2 exactly, the quinte which corresponds to a 3/2 ratio, the quarter 4/3, the major third 5/4 and, at the limit, the minor third 6/5.
These intervals, if the fundamental note is not too low, do not create beats since the superposition of two sounds of a just interval results from a single, whose fundamental frequency is the difference between the two. Thus a 440 Hz la3 and an 880 Hz (Octave) give a 440 Hz frequency la3, but with a different stamp. A LA3 at 440 Hz and a MI4 to 660 Hz (fifth) give a La2 to 220 Hz. Likewise, a 440 Hz la3 and a D#4 to 550 Hz (major third) give a la1 to 110 Hz.
In any case, the ear does not perceive beats because they are too fast. On the other hand, if we consider an octave lower at 220 Hz and a do#3 to 275 Hz (major third), we get a 55 Hz that begins to be perceived as rough. At this height, the third is almost dissonant. This is undoubtedly why in the Middle Ages, the major third was rejected, because considered to be dissonant, not to mention the minor third. These two intervals are also always considered by specialists as imperfect consonances, as opposed to the Octave and the fifth which are perfect consonances.
These intervals are the basis of Western music since they make it possible to build the UT natural range (do)) re mi fa solwhich will allow, by combining different non -joint notes, to define the bases of musical harmony. Over time, composers and listeners will be more and more accommodating vis-à-vis the accuracy and, currently, on a digital keyboard, only octaves are rigorously just.
Finally, nowadays, sing just is singing not too false!
With an unwavering passion for local news, Christopher leads our editorial team with integrity and dedication. With over 20 years’ experience, he is the backbone of Wouldsayso, ensuring that we stay true to our mission to inform.
