The fifth circle helps to conveniently memorize musical harmony and learn parallel keys. It allows you to effectively learn modes and key characters, so understanding the principle of its work is extremely important for all students who master musical theory.
The concept of a quarto-fifth circle
The quarto-fifth circle is a special arrangement system according to the degree of kinship, that is, differences in the number of characters of one from another of different keys. In graphical form, it is graphically depicted in the form of a circuit of a closed circle, in which, on the one right, the sides are on the ascending fifth line of key with sharps, and on the left, on the descending line, with flats.
If you move clockwise in a fifth circle, the first step (tonic) of subsequent major keys will be up from the previous ones by an interval equal to five steps, that is, by a pure fifth. At the same time, one sign will always be added in the key - a sharp. In the counterclockwise direction, the downward interval will also be 3.5 tones. Moreover, in each subsequent tonality the number of flats will increase.
What is this system used for?
The quarto-fifth circle of keys is used to determine the number of characters (sharps, flats) with a key. It is also used to search for related keys and determine the degree of their proximity. Related tones of the first degree include majors and minors, which differ from the original by one sign of alteration. They also include those located in a circle in the neighborhood, parallel to them and to the original one. The closer the keys are to each other in the circle, the higher the degree of their relationship. In the event that there are more than three or four steps between them, then there is no proximity. Many composers used the principle of circular motion when writing their works, for example F. Chopin ("24 Preludes") and I. S. Bach ("The Well-Tempered Clavier"). In the XIX-XX centuries, it was reflected in jazz compositions and rock music, but was used in a transformed form called the "golden sequence" (not only a fifth, but also a quart was used to build chords).
The principle of finding major keys with sharps
So, let's see how the fifth circle “works” and how the alteration signs are added in different keys. The principle of the system is as follows: first, one initial tonality is taken. We know her tonic. To determine the first step of the next key, count five notes up. The tonic of related tonality will be at the fifth level of the original, that is, at its dominant. Thus, the interval for calculations is the fifth. It is because of the use of the five steps for determining the tonality that the fifth circle got its name. Now consider the signs of alteration. The rule is this: they are transferred from the original key to the next, plus one sign (sharp) is added to them (to the sixth step).
Let's look at the key in C major, in which there are no signs of alteration (sharps and flats). Its tonic is note do, and dominant is salt. Therefore, according to the principle of the fifth circle, the next key will be G major (aka G-dur). Now let's decide on the sign of alteration. In the resulting related tonality, step 6 is the fa. It is on it that the sharp will be. To determine the next tonality from salt, we postpone the interval equal to five steps. Its dominant is re. This means that the next key will be D major (D-dur). There will already be two signs of alteration in it: from the previous key (F-sharp) and joining at the sixth step, C sharp. By analogy, you can find all the other keys. In determining the one that has seven signs in the key, the circle will be closed anharmonically.
Major fifth circle with flats
Flat major keys are, unlike sharp keys, on the contrary, in pure quarts down. The tonic in C major is taken as the starting point, since C-dur has no alteration signs. Counting down five steps, we get the tonic of the second key after it - F major. In the flat tonalities, the signs of alteration appear not on the sixth, but on the fourth step of the fret, that is, on the subdominant. In F major this is B flat. Passing the entire fifth circle, we get the following major flat keys: C major, F major, B flat major, E flat major, A flat major, G flat major, C E flat major. Moreover, the latter has as many as seven flat. Further, the circle closes anharmonically. Of course, after that, other tonalities appear in a spiral - with a double-flat, but they are rarely used because of their complexity.
Minor keys in a fifth circle. What is their construction principle?
So, we examined 12 major keys. Each of them has related minor. You can see this in the fifth circle shown in the picture above. The scale of the related key of the minor is based on the same sounds as the major. But it starts with a different note. For example, related tonalities without signs of alteration in C major and A minor are built on simple sounds. In C-dur, steady sounds come before, mi and salt. They make up a major tonic triad.
The interval between the tonic and the third stage is a big third. At the first step in note A, the sounds of a, do and mi form a stable triad. The interval between the first and third stage is equal to 1.5 tones (small third). This makes a-moll a minor key. A minor and C major are parallel: the tonic of the first is separated by a small third down from the tonic of the second. Their important characteristic is the same number of signs of alteration. For example, in G minor and B flat major contain two flats when key, and in E minor and G major - one sharp. In parallel keys, the same scale is used, so a melody that sounds in a major fret can easily be transformed into a minor, and vice versa. This technique is often used in Russian folk songs (see "And we sowed millet"). Thus, if we lower the tonics of all major keys to a minor third down, we get a minor fifth circle. The figure shows the signs of alteration that are present in each sharp and flat minor keys.
Instead of a conclusion
So, in this article we examined the fifth circle and found out that it is a system of arrangement of all tonalities, taking into account the degree of their relationship. Thanks to the anharmonism in music, the circle closes, forming sharp and flat, major and minor keys. Knowing the principle of the system, you can easily build any chords and find out the number of alteration marks in harmony.