Harmony is the "organization" of sounds, with the help of which you can "cook" various harmonic sound mixtures. It is meant harmony of sounds of different pitches. That is, their simultaneous sound. To bake a cake, you need to take flour, water, eggs, butter, sugar, salt, and the like. The products are different, and if you mix them, you will get something single, whole, even though we mixed different ingredients.
Perfumes consist of dozens of odorous substances. Each of them has its own constant smell, but in different compounds they give a new single smell. The seven main colors of the solar spectrum in the most diverse combinations give new colors and shades. Since school years, we have known an interesting experiment that shows that the color white is a chord of the seven colors of the rainbow. In other words, new structures can be created from the details of the designer.
Taste, smell, color... And hearing? Our musical ear? He also strives for harmony. He is attracted by the harmony of sounds. Musical harmony is a whole science. This concept is capacious and broad. But now we will talk about only one of its sources, about one of its bases is the combination of sounds that differ in pitch.
Musical ear and harmony
Musical "dish" for the ear must also be prepared according to special recipes. They are suggested to us by the laws of physics and our musical taste, which has been cultivated for thousands of years. It is not so easy to become a "musical chef", it is not so easy to "cook" a musical mixture of sounds of different pitches so that it is "edible".
It is possible to come up with a simple melody by typing sounds one by one. However, it is unlikely to be original. This melody will resemble familiar motifs. And to connect sounds in simultaneous sound, that is, to connect them into chords, and to make these chords sound one after the other, lining up in a slender harmonic series, requires very precise recipes.The simultaneous sounding of various musical instruments in ancient times had nothing to do with the present harmony of sounds. A long time musical instruments could not even sound in unison, because they were in different moods.
Previously, the distances between sounds of different pitches were quite approximate, they were determined, as they say, by ear, and not according to the strict rules of musical acoustics. The human ear, of course, listened to these rules and regularities, but the insidious "barely" nullified all efforts to harmonize sounds. Here and there, false chords awaited the musician. As soon as the musicians did not tune their instruments, hoping to accidentally find the "golden mode", nothing came out. Therefore, the ancient Greek scientist Pythagoras decided to call on numbers for help.
The great discovery of Pythagoras
According to legend, he pulled a string and took the first sound. Then he divided the string in the middle, that is, he made it twice as short. The sound of twice the shorter string is similar to the sound of a long string. And if they sounded together, they merged in such a way that it was difficult to distinguish them from one another. This consonance was called the octave...Then the scientist began to divide the string into three or four parts. He again delved into the world of numbers...Thus, the first steps were taken on the way to the discovery of the laws of musical order. Dividing the string each time into equal parts, Pythagoras received a whole set of sounds, different in pitch. All that remained was to line them up according to the pitch, one by one, and a mathematically precise arrangement of sounds was ready.
It seemed that he had to come out, because among these sounds there was not one, so to speak, "invented". All of them are the result of careful calculation. What unit of measurement can be used to arrange a series of sounds in height? What is the distance between two neighboring sounds, that is, what is the interval? After all, it must be strictly the same to become a unit of measurement.
Build Pythagorean mathematical sounds, and between them this "golden" desired interval - a unit of measurement - will appear by itself. Between the two notes of the octave, the upper and the lower, perfectly merging, the whole set of sounds had to fit like centimeters in a meter, without a remainder. Then take a few octaves of different heights, say seven octaves, like the present-day grand piano, and you already have a wonderful and pure set of a hundred sounds.
But what is surprising! — the precise, mathematically verified sounds of the Pythagorean scale did not want to line up in such a way. In the middle register, they gave the desired melodious chords. But in the lower and higher they made the musicians shudder. there were not very many of them, these false sounds that "howled", and therefore got the name "wolves". This, of course, is a pity, but do not cross out because of this extremely great discovery of Pythagoras.
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PS: Czytam, ale już na początku bzdura na bzdurze i bzdura pogania.