Quantum circle. Key

Circle of fifths helps you remember conveniently musical harmony It allows you to effectively learn scales and key signatures, so understanding how it works is extremely important for all music theory students.

The concept of the quarto-fifth circle

The quarto-fifth circle is a special system of arrangement according to the degree of kinship, that is, the difference in the number of signs of one from another of different tonalities. IN graphical form it is clearly depicted in the form of a diagram of a closed circle, in which on one side - the right - there are an ascending row of fifths with sharps, and on the left - along a descending row - with flats.

If you move clockwise around the circle of fifths, the first degree (tonic) of subsequent major keys will be upward from the previous ones by an interval equal to five steps, that is, by a perfect fifth. In this case, one sign will always be added to the key - sharp. In a counterclockwise direction, the descending interval will also be 3.5 tones. In this case, in each subsequent key 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 signs (sharps, flats) in the key. It is also used to search for related tonalities and determine the degree of their proximity. Related keys of the first degree include majors and minors, which differ from the original by one accidental sign. They also include those in the circle in the neighborhood, parallel to them and to the original one. The closer the tones are to each other in the circle, the higher the degree of their relationship. If there are more than three or four steps between them, then there is no proximity. Many composers used the principle of movement in a circle when writing their works, for example F. Chopin ("24 Preludes") and J. S. Bach ("The Well-Tempered Clavier"). IN XIX-XX centuries it was reflected in jazz compositions and rock music, but was used in a transformed form, which is called (not only the fifth, but also the fourth was used to build chords).

The principle of finding major keys with sharps

So, let's figure out how the circle of fifths “works” and how accidentals are added in different keys. The principle of operation of the system is as follows: first, one initial key is taken. We know her tonic. To determine the first step of the next key, count five notes upward. The tonic of a related key will be on the fifth degree of the original one, that is, on its dominant. Thus, the interval for calculations is the fifth. It is because of the use of five degrees to determine keys that the circle of fifths got its name. Now let's consider the Rule: they are transferred from the original key to the next one, plus one sign is added to them (to the sixth degree) - sharp.

Let's look at the key of C major, which does not have accidentals (sharps and flats). Its tonic note is C and its dominant note is salt. Therefore, according to the principle of operation of the circle of fifths, the next key will be G major (otherwise G-dur). Now let's decide on the alteration sign. In the resulting related tonality, step No. 6 is F. This is where the sharp will be. To determine the next key from G, let’s move up an interval equal to five steps. Its dominant is re. This means that the next key will be D major. It will already have two accidental signs: from the previous key (F-sharp) and C-sharp, which joins on the sixth degree. By analogy, you can find all other tones. When determining the one that has seven signs in the key, the circle will close enharmonically.

Major circle of fifths with flats

Flat major keys, unlike sharp keys, are valued down in perfect fourths. The tonic of C major is taken as the starting point, since C major does not have accidentals. Counting down five degrees, we get the tonic of the second key after it - F major. In flat keys, accidental signs appear not on the sixth, but on the fourth degree of the mode, that is, on the subdominant. In F major it is B flat. Having gone through the entire circle of fifths, we get the following major flat keys: Moreover, the latter has as many as seven flats. Then the circle closes enharmonically. Of course, after this, other keys appear in a spiral - with double flats, but they are used quite rarely due to their complexity.

in the circle of fifths. What is their design principle?

So, we looked at 12 major keys. Each of them has related minor ones. You can see this in the circle of fifths shown in the picture above. The scale of the related minor key is built on the same sounds as the major one. But it starts on a different note. For example, related tonalities without accidental signs C major and A minor are built on simple sounds. In C major, the stable sounds are do, mi and salt. They form a major tonic triad.

The interval between the tonic and the third degree is a major third. At the first step in the note A, the sounds A, C and E form a stable triad. The interval between the first and third degree is equal to 1.5 tones (minor third). This makes A minor a minor key. A minor and C major are parallel: the tonic of the first is a minor third down from the tonic of the second. Their important characteristic is same number alteration signs. For example, G minor and B flat major contain two flats in the key, and E minor and G major contain one sharp. Parallel keys use the same scale, so a melody sounding in a major mode can quite easily transform into a minor one, and vice versa. This technique is often used in Russian folk songs(See “And we sowed millet”). Thus, if we move the tonics of all major keys down a minor third, we get a minor circle of fifths. The figure shows accidental signs that are present in each sharp and flat minor key.

Instead of a conclusion

So, in this article we looked at the circle of fifths and learned that it is a system for arranging all tonalities, taking into account the degree of their relationship. Thanks to enharmonism in music, the circle closes, forming sharp and flat, major and minor keys. Knowing the principle of operation of the system, you can easily construct any chords and find out the number of accidentals in a scale.

This lesson is more intended for those who are already studying in music school or even school. From many years of practice, I can say that the circle of fifths is a topic that is not mastered by students, which is why problems arise with mastering the material and performing any piece. Yes, yes, without knowing what key we are playing in, it is extremely difficult to navigate, and for some reason it is difficult to play. Therefore, before performing any piece, you need to determine in what key it is written. Believe me, then you will understand it much faster.

So, we discussed in detail what tonality is in, and now I will explain to you the system by which they are arranged. If we talk in simple language- then in each key there are some signs, that is, when playing a scale or piece, we also use the black keys. But what - a harmonious and logical system - the circle of fifths of tonalities - will help.

In studying music theory, there are moments that need to be understood, and there is information that just needs to be memorized like a rhyme. Here is the rule below in the picture that you need to memorize.

The order of attaching key characters is always the following:

If you noticed, this is the same sequence, which is read from both sides - sharps in one direction, flats in the opposite direction. Here it needs to be memorized in both directions. On the staff it looks like this

Now let's answer the first question - why fifth?

Here is the next rule that you just need to understand.

For every fifth raised, one sharp is added.

In the picture it looks like this:

We start from C major (or A minor, more on that below) and go clockwise.

We know that there are no signs in C major and A minor. This is an axiom that must be remembered. However, all beginners already know C major, because it is played only on white keys, which is very convenient. So, C major. If we build a fifth from “C” up, we get the note G. So, in G major there will already be one sharp. Which? We look above at the order of adding sharps - first sharp - F. This means that in G major there is F sharp. And when we play the G major scale, we raise the F note in it and instead of the white key we will play the black one.

Now we build a fifth from G up (we stopped in the key of G major). The resulting note is D. There are already two sharps in D major - which ones? We look at the order of sharps - the first two are F and C.

From re we build another fifth, we get the note A. There are already three sharps in A major - F, C, G. These are the first three.

From A - the next fifth - the note E is obtained. In E major there are already the first four sharps - F, C, G, D.

From E - a fifth upwards you get the note B - in B major there are 5 sharps - F, C, G, D, A.

A fifth from B - and a new key of F sharp (read why not F - read here) - F sharp major - 6 sharps - F, C, G, D, A, E.

And the last fifth from F sharp to sharp. So the key is C sharp major - 7 sharps - F, C, G, D, A, E, B. Oh how. To be fair, I want to say that keys with 7 sharps are not common in practice, but they do happen.

The same thing will happen if we build fifths in minor keys, taking the note A as the starting point - that’s where the 0 signs are.

We build a fifth from A - we get the key of E minor. There is one sharp in E minor. Which? Let's look at the order - F - first sharp.

From E one more fifth and we get B minor, in which there will already be two sharps - F and C.

From B, after 5 steps, the note F sharp is formed (be careful - not F, but F sharp). In F sharp minor there are 3 sharps – F, C, G.

From F# fifth to C# minor, which already has 4 sharps.

From up to # 5 steps we skip - and we get new key with 5 sharps – G# minor.

From G# fifth – D# minor – 6 sharps.

From re# fifth – A#. And in A sharp # there are 7 sharps.

Keys with flats in the key

In this picture we go counterclockwise.

For each downward fifth, one flat is added.

From C down to the fifth we get the note F. There is one flat in the key of F major. Which? Let's look at the order of the flats. We see that this is B flat.

From F we build down another fifth and get the note B flat. In the key of B major there are already two flats - B and E.

From B b we build another fifth and end up on the note E b. And in E b major there are already 3 flats - B, E, A. And so on.

If you understand this principle, then determining the number of characters in any key will not be difficult. Now it’s clear why “fifth”? Because it is built in fifths. Why a circle? Look carefully at the pictures above - we start with the keys C major, and end with C major or C major - not quite, of course, a circle, but still. It’s the same with minor keys – it starts from A and ends with A# or Ab minor.

For ease of perception, I divided the keys and showed sharp and flat ones separately. In theory textbooks, the circle of fifths of tonality is presented in the form of such a picture.

And finally, I suggest you listen to the Waltz in C minor by Frederic Chopin. Very famous work, beautiful, flying and superbly performed by Alexander Malkus.

The circle of fifths is a fairly well-known concept. music theory, but, unfortunately, not everyone knows what it is for and how it can be used in their musical practice.

Usually the circle of fifths is described as a spiral of tones located clockwise in fifths up from the note C, and counterclockwise in fifths down or in fourths up (hence another name quarto-fifth circle keys).

Although the circle of fifths is indeed a circle of keys, its use is much broader than just finding the number of signs in a particular key.

Since my goal is to give you the most rich information, which is not in most textbooks, then I need to tell you everything about the circle of fifths that I know or could find in additional sources.

So, the first thing you should know is that the circle of fifths reflects the interaction of all 12 sounds of the chromatic scale.

As is known, the chromatic scale is an artificially created modal structure that is practically never found in pure form, since it has no tonal or modal center.

Displaying notes in the circle of fifths is closer to musical reality.

Chromatics displays the smallest possible division in our music system coordinates (tempered tuning) and is a mathematical structure, and the circle of fifths reflects the mathematical ratio of 3:2 and is based on physical laws.

Look at the circle representing the interaction of chromatics and the circle of fifths

The fifth is the most perfect interval after the octave, which is the 3rd in the overtone series.

As you know, the fifth movement in the bass and melody sounds most complete and is the basis of cadences, and the movement from the 5th degree to the first (fourth - inversion of the fifth) is the basis of hymnic intonation.

Another interesting fact for those who didn't know. Pianos are most often tuned in fifths.

We can say that this is the most important interval in music :). Well, guitarists also love to play fifths, since they sound perfectly clear when played through distortion.

AND last fact– the circle of fifths was first described by our compatriot Nikolai Pavlovich Diletsky, which cannot but rejoice. Russians invented the circle of fifths :)

If we move from the note C through fifths, then we will inevitably encounter the phenomenon of tonal anharmonicity. When tones consist of identical sounds, but different notes. I recorded a special video lesson about this.

A little about the most obvious things for those who are hearing about the circle of fifths for the first time.

Moving in a circle, we find ourselves in a new key, in which the number of signs is always one more than in the previous one. The names of keys and signs are written on the circle itself. But in order to remember the signs themselves, you can also use the fifth scheme.

Sharps start from F# and go up in fifths.

And flats start from Bb and go down fifths.

For example, you considered that the note B is a 5th step in fifths from the note C - this means that the number of sharps in the key is 5 and you need to build 5 fifths from the note F# - F#-C#-G#-D#-A# these will be the sharps we need.

Now let's talk about more interesting features circle.

Let's take a look at the circle itself and see what notes surround the C note:

Right is G

Left is F

And these are S and D tonalities.

That is, the circle can be used as a hint to find the main functions in any key!

This is its first hidden property.

Tonality and modulations

Another important property of the circle of fifths is that it clearly shows the harmonic gravity of chords. We can see it if we move in a circle counterclockwise. You may notice that the IV or F chord for C major is located after the tonic, that is, directed beyond the key to the Bb major chord.

For this reason, most classic revolutions are based on movement from stage II to stage V, rather than from stage IV. The IV stage, as a rule, is introduced at the beginning of formations, for example, I-IV-viio-III-VI-II-V. Many theorists even propose to consider stage IV as stage II without tonic.

Because this interpretation is more logical from the point of view of physics and musical perception.

Using the circle of fifths, you can build modulations in progressions, since the next 7 keys are the most used for modulations (including minor ones).

Moving around the circle of fifths and replacing chords with corresponding keys allows you to get the well-known harmonic swing.

For example, Em-Am-D7-G-C-F#7b5-B7

progression from the song Shadows in your smile and hundreds of others. The movement is characteristic of jazz. Reverse movement also possible.

Also more complex species The fourth-fifth movement can be used to create modern sequences, but I will write about this in a separate article.

Also, if you move from any note 5 times clockwise, you get all the notes of the pentatonic scale.

As you can see, the circle of quarto-fifths is an excellent cheat sheet for theory, modulation and memorizing keys.

Greetings to all readers of our music blog! I have already said more than once in my articles that for good musician It is important to have not only playing technique, but also to know theoretical basis music. We already had an introductory article about it. I highly recommend that you read it carefully. And today the object of our conversation is signs in.
I would like to remind you that there are major and minor keys in music. Major keys can be figuratively described as bright and positive, while minor keys can be described as gloomy and sad. Each tonality has its own characteristics in the form of a set of sharps or flats. They are called tonality signs. They can also be called key signs in keys or key signs in keys because before writing any notes and signs, you need to depict a treble or bass clef.

Based on the presence of key signs, keys can be divided into three groups: without signs, with sharps in the key, and with flats in the key. There is no such thing in music that the signs in the same key will be both sharps and flats at the same time.

And now I give you a list of tonalities and the key signs corresponding to them.

Key Chart

So, after carefully considering this list, there are several important points to note.
In turn, one sharp or flat is added to the keys. Their addition is strictly stipulated. For sharps the sequence is as follows: fa, do, sol, re, la, mi, si. And nothing else.
For flats the chain looks like this: si, mi, la, re, salt, do, fa. Note that it is the reverse of the sharps sequence.

You probably noticed the fact that the same number of characters have two tones. They're called . There is a separate section about this on our website. detailed article. I advise you to read it.

Determination of key signs

Now follows important point. We need to learn to determine by the name of the key what key signs it has and how many there are. First of all, you need to remember that signs are determined by major keys. This means that for minor keys you will first have to find a parallel major key, and then proceed according to the general scheme.

If the name of a major (except for F major) does not mention any signs at all, or only a sharp is present (for example, F sharp major), then these are major keys with sharp signs. For F major, you need to remember that B flat is in the key. Next, we begin to list the sequence of sharps, which was defined above in the text. We need to stop the enumeration when the next note with a sharp is a note lower than the tonic of our major.

• For example, you need to determine the signs of the key A major. We list the sharp notes: F, C, G. G is a note lower than the tonic of A, therefore the key of A major has three sharps (F, C, G).

For major flat keys the rule is slightly different. We list the sequence of flats up to the note that follows the name of the tonic.

• For example, our key is A flat major. We begin to list the flats: B, E, A, D. D is the next note after the name of the tonic (A). Therefore, there are four flats in the key of A flat major.

Circle of fifths

Circle of fifths- This graphic image connections between different tonalities and their corresponding signs. We can say that everything that I explained to you before is clearly present in this diagram.

In the circle of fifths table of keys, the starting note or reference point is C major. Clockwise from it are sharp major keys, and counterclockwise are flat major keys. The interval between adjacent keys is a fifth. The diagram also shows parallel minor keys and signs. With each subsequent fifth we add signs.

As a rule, representatives musical sphere all this system They simply call it the circle of fifths, so as not to complicate pronunciation. There is another name - the diquint system.

Operating principle and device

For many years, this system of the musical sphere has been commonly depicted as a ball or circle, which has a spiral inside. The most top point symbolizes the notes, and moving in a clockwise direction, they already place the remaining notes in accordance with the sequence. Considering the system in the opposite direction, one can already observe F, B-flat, and so on. Moreover, this established order is considered generally accepted and standard, and all because in “C” major there simply cannot be a single sign in the treble clef.

Quarters and fifths

Again, it is worth referring to the generally accepted design of this system. Namely, the highest point represents a marked note, which cannot always be denoted by syllables; marking with a single letter is acceptable. This tradition It was the circular system that took root due to the fact that the major key is devoid of any symbols, that is, it is simple.

The note indicated on the circle fully symbolizes the major key. For greater convenience, as a rule, another note can be placed next to it, which will already symbolize the opposite key - minor. As for the distance between them within a circle, the interval will be equal to either a fifth or a quart.

A little theory

In fact, the entire system of the circular quarto-fifth device is a spiral. Moreover, it does not connect in any place, but increases to infinity. But in practice, this tendency is considered inappropriate, because the entire tonality is distributed over eight or nine steps. It starts with “C” major, which is then no longer used. Moreover, if you take a tonality with a lower indicator, then the gamma will still completely coincide.

No one will develop the spiral to a larger number, because a tonality, for example, with thirteen symbols, is even difficult to pronounce. Such concepts as “g-double-sharp” and so on appear.

The main purpose of the circle of fifths

As a rule, this system is used to solve several problems at once. There are three main ones:

• search for identical keys;
• recognition of the number of characters in an existing or specified key;
• determining the maximum similarity of tones.

Considering the first problem and its solution, it can be noted that there are several degrees of relationship or similarity of tones. In simple words, similar tones are those that differ from each other by one sign. And what is most characteristic is that in this system the differences are visible, as they say, to the naked eye, since the entire system is built as clearly as possible.

Related tonalities are also those that are from starting point located close to each other. That is, the so-called neighbors.

The second solution to the problem involves determining the number of characters relative to the key. As a rule, their number can be from zero to seven, but in practice keys with a large number of signs are rarely used.

As for determining the degree of kinship, it is very simple to recognize it: the closer they are located relative to each other, the closer the degree of kinship itself will be. For example, a distance equal to one step implies the first degree and so on. But if there are already more than three steps, then there can be no talk of any relationship at all.

A little history

It is worth noting that musicians over the years have strived to find a special and universal system. It was she who ultimately became this circle, which represents simple diagram. This system allows short time recognize the relationships between keys, chords, and other necessary moments. Each musician, using this circle, can independently determine the features of a given tonality, because directly on musical instrument this is inconvenient to do.

The emergence of the diquintic system

The first publications about her appeared in 1678. The author of the publication was a Russian composer with Ukrainian roots named Nikolai Diletsky. By the way, he is also the author of many other techniques related to musical direction.

Almost a century later, this system was recognized abroad. As for the implementation of the system in the work of musicians, it can be observed in many single compositions. Initially, the system was used in classical performance, but our contemporaries were able to introduce it into jazz and even rock.