Tonal circle. Circle of fifths in minor keys

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How to perform the same major music from sounds of different heights?

We know that major keys use both fundamental steps and derivatives. In this regard, the necessary accidentals are set with the key. In previous articles, we compared C-dur and G-dur (C major and G major) as an example. In G-dur, we have F-sharp in order to keep the correct intervals between the steps. It is he (F-sharp) in the key of G-dur that is indicated with the key:

Figure 1. Key signs of G-dur tonality

So how do you determine which tone corresponds to which accidentals? It is this question that the fifth circle of keys helps to answer.

Sharp circle of fifths major keys

The idea is as follows: we take a key in which we know the number of accidentals. Naturally, the tonic (base) is also known. Tonic next to sharp circle of fifths tonality will become the fifth step of our tonality (an example will be below). In the accidental signs of that next key, all the signs of our previous key will remain, plus a sharp VII degree of the new key will appear. And so on, in a circle:

Example 1. We take C-dur as a basis. There are no accidentals in this key. The note sol is the fifth degree (the fifth degree is the fifth, hence the name of the circle). It will be the tonic of the new key. Now we are looking for an accidental sign: in the new key, the seventh step is the note F. For her, we set the sharp sign.

Figure 2. Found the key sign of the sharp key G-dur

Example 2. Now we know that in G-dur the key is F-sharp (F#). The tonic of the next key will be the note re (D), since it is the fifth step (the fifth from the note sol). One more sharp should appear in D-dur. It is set for the 7th degree of D-dur. This is a C note. This means that D-dur has two sharps at the key: F# (remained from G-dur) and C# (VII step).

Figure 3. Key accidentals for the key of D-dur

Example 3. Let's completely switch to the letter designation of the steps. Let's define the next key after D-dur. The tonic will be the note A (la), since it is the V degree. This means that the new key will be A-dur. In the new tonality, the seventh step will be the note G, which means that one more sharp is added at the key: G#. In total, with the key we have 3 sharps: F#, C#, G#.

Figure 4. Key accidentals A-dur

And so on, until we get to the key with seven sharps. It will be the ultimate, all its sounds will be derived steps. Please note that the clef accidentals are written in the order they appear in the circle of fifths.

So, if we go through the whole circle and get all the keys, we get the following order of keys:

Now let's figure out what the "circle" has to do with it. We settled on C#-dur. If we are talking about the circle, then the next key should be our original key: C-dur. Those. we have to go back to the beginning. The circle is closed. Actually, this doesn't happen, because we can continue to build fifths further: C# - G# - D# - A# - E# - #... But if you think about it, what is the enharmonic sound of H# (imagine a piano keyboard)? Sound Do! So the circle of fifths is closed, but if we look at the signs at the key in the key of G #-dur, we will find that we will have to add F-double-sharp, and in subsequent keys these double-sharp will appear more and more .. So so, in order to feel sorry for the performer, it was decided that all the keys, where a double sharp should be used in the key, are declared uncommon and replaced by keys enharmonically equal to them, but not with numerous sharps in the key, but with flats. For example, C#-dur is enharmonically equal to the key of Des-dur (D-flat major) - it has fewer signs at the key); G#-dur is enharmonically equal to the key of As-dur (A-flat major) - it also has fewer signs at the key - and this is convenient both for reading and for performing, and meanwhile, the circle of fifths, thanks to the enharmonic change of keys, really closed!

Flat fifth circle of major keys

Everything here is by analogy with the sharp circle of fifths. C-dur is taken as a starting point, since it has no accidentals. The tonic of the next key is also at a distance of a fifth, but only down (in the sharp circle, we took the fifth up). From the note to the fifth down is the note F. She will be the tonic. We put the flat sign in front of the IV degree of the scale (in the sharp circle there was the VII degree). Those. for Fa, we will have a flat before the note C (IV degree). Etc. for each new tone.

Having gone through the entire flat fifth circle, we get the following order of major flat keys:

Enharmonic equal keys

You have already understood that keys of the same height, but different in name (the second loop of the circle, or rather, already spirals), are called enharmonic equal. On the first loop of circles, there are also enharmonic equal keys, these are the following:

• H-dur (in the key of a sharp) = Ces-dur (in the key of a flat)
• Fis-dur (in the key of a sharp) = Ges-dur (in the key of a flat)
• Cis-dur (in the key of a sharp) = Des-dur (in the key of a flat)

fifth circle

The order of arrangement of major keys described above is called the circle of fifths. Sharp - up fifths, flat - down fifths. The order of the keys can be seen below (your browser must support flash): move the mouse in a circle over the names of the keys, you will see the accidentals of the selected key (we have arranged the minor keys in the inner circle, and the major ones in the outer circle; related keys are combined). By clicking on the name of the key, you will see how it was calculated. The "Example" button will show a detailed recalculation.

Results

Now you know the algorithm for calculating major keys, called circle of fifths.

The circle of fifths of keys, or, as it is also called, the circle of fourths and fifths - in music theory, this is a schematic representation of sequentially arranged keys. The principle of aligning all keys in a circle is based on their uniform distance from each other in intervals of a perfect fifth, a pure fourth and a minor third.

There are two main modes used in music - major and minor. Today we will take a closer look at the circle of fifths of major keys. The circle of fifths of major keys was created in order to make it easier to understand the existing 30 keys, of which 15 are major. These 15 major keys, in turn, are divided into seven sharp and seven flat keys, one key is neutral, it does not have any key signs.

Each major key has its own parallel minor key. To determine such a parallel, it is necessary from a given note of the selected major scale build down the interval "small third". That is, count three steps (one and a half tones) from a given starting point in the direction of decreasing sounds.

How to use the circle of fifths of major keys?

This schematic drawing gives an idea of ​​the sequence of scales. The principle of its operation is based on the gradual addition of signs at the key as this circle passes. Should be remembered keyword"quint". Constructions in the circle of fifths of major keys are based on this interval.

If we move in a circle from left to right, in the direction of increasing sounds, then we get sharp. Following, on the contrary, from right to left along the circle, that is, in the direction of decreasing sounds (that is, if we build fifths down), we get flat tonalities.

We take the note to as the starting point. And further from the note to the upward direction of the sound, we line up the notes in fifths. To build a “pure fifth” interval from the starting point, we calculate five steps or 3.5 tones. First fifth: do-sol. This means that G major is the first key in which the key sign should appear, naturally a sharp and naturally it will be one.

Then we build a fifth from sol - sol-re. It turns out that D major is the second key from the starting point in our circle and there are already two key sharps in it. Similarly, we calculate the number of sharps in all subsequent keys.

By the way, in order to find out exactly which sharps appear with the key, it is enough to remember the so-called order of sharps once: 1st - fa, 2nd - do, 3rd - sol, then - re, la, mi and si - also everything is in fifths, only from the note F. Therefore, if there is one sharp in the key, then it will be necessarily F-sharp, if there are two sharps, then F-sharp and C-sharp.

To obtain flat tonalities, we build a fifth in a similar way, but following the circle counterclockwise - from right to left, that is, in the direction of decreasing sounds. Let us take the note C as the initial tonic, because there are no signs in C major. So, from to down or, as it were, counterclockwise, we build the first fifth, we get - do-fa. This means that the first major key with a flat key is F major. Then we build a fifth from F - we get the following key: it will be B-flat major, in which there are already two flats.

The order of flats, interestingly, is the same order of sharps, but only read in a mirror, that is, vice versa. The first flat will be - si, and the last - fa.

In general, the circle of fifths of major keys does not close, its structure is more like a spiral. With each new quint there is a transition to new round as in a spring and the transformation continues. With every transition to new level spirals are added to the next keys. Their number is growing both in the flat and sharp directions. It's just that instead of the usual flats and sharps, double signs appear: double sharps and double flats.

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

According to the presence of key signs, tonality can be divided into three groups: without signs, with sharps in the key, with flats in the key. It does not happen in music that sharps and flats at the same time will be signs in the same key.

And now I give you a list of keys and their corresponding key signs.

Tonality table

So, having carefully considered this list, it is necessary to note several important points.
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, sol, do, fa. Note that it is the reverse of the sharp sequence.

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

Definition of signs of tonality

Now follows important point. We need to learn how to determine by the name of the tonality what key signs it has and how many of them. First of all, you need to remember that the 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 signs at all, or only 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 with 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 keys of A major. We list the sharp notes: F, C, G. G is one 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, we have the key of A-flat major. We begin to list the flats: si, mi, la, re. Re is the next note after the name of the tonic (la). Therefore, there are four flats in the key of A-flat major.

fifth circle

Quint circle of keys- This graphic image connections of different keys and their corresponding signs. It can be said that everything that I explained to you before is clearly present in this diagram.

In the circle of fifths table of keys, the original note or reference point is C major. Clockwise, sharp major keys depart from it, and counterclockwise, flat major keys. The interval between the nearest keys is the fifth. The diagram also shows parallel minor keys and signs. With each subsequent fifth, signs are added to us.

A quarto-fifth circle of keys or simply a circle of fifths is a scheme for convenient and quick memorization of all keys and key signs in them.

At the top of the circle of fifths is the key of C major; clockwise - sharp keys, the tonics of which are located in perfect fifths up from the tonic of the original C major; counterclockwise - a circle of flat keys, also located in pure fifths, but only down.

At the same time, when moving around the circle of fifths clockwise with each new key, the number of sharps gradually increases (from one to seven), while moving counterclockwise, respectively, from one key to another, the number of flats increases (also from one to seven).

How many keys are there in music?

In music, mainly 30 keys are used, of which one half is major and the other half is minor. form pairs according to the principle of coincidence in them of the key signs of alteration - sharps and flats. Keys with the same signs are called parallel. In total, therefore, there are 15 pairs.

Of the 30 keys, two do not have signs - these are C major and A minor. 14 keys have sharps (from one to seven in the order of sharps FA DO SOL RELA MI SI), of these 14 keys, seven will be major, and seven, respectively, minor. Another 14 keys have flats (similarly, from one to seven, but only in the order of flats C MI LA RE SOL DO FA), of which there are also seven major and seven minor.

A table of all keys used by musicians in practice, along with their signs, can be downloaded, printed and used as a cheat sheet.

Explanation: How is a circle of fifths formed?

The fifth in this scheme is the most important. Why a pure fifth? Because the fifth is physically (acoustically) the most natural way to move from one sound to another, and this one was born by nature itself.

So, sharp keys are arranged in pure fifths up. The first fifth is built from the note “to”, that is, from the tonic of C major, a pure key without signs. The fifth from “do” is “do-sol”. This means that the note "G" becomes the tonic of the next key in the circle of fifths, it will be the key of G major and it will have one sign - F-sharp.

We build the next fifth already from the sound “sol” - “sol-re”, the resulting sound “re” is the tonic of the next tonality of the fifth circle - the tonic of the D major scale, in which there are two signs - two sharps (fa and do). With each built fifth, we will receive new sharp keys, and the number of sharps will increase more and more until it reaches seven (until all steps are raised).

Thus, if we build fifths, starting from “to”, then we get the following series of keys: G major (1 sharp), D major (2 sharps), A major (3 sharps), E major (4 sharps), B major (5 sharps), F sharp major (6 sharps), C sharp major (7 sharps). The number of recorded tonics turned out to be so wide in scope that one has to start writing it down in bass clef, and finish in violin.

The order in which the sharps are added is: FA, DO, SOL, RE, LA, MI, SI. The sharps are also separated from each other by the interval of a perfect fifth. It is related to this. Each new sharp appears on the seventh degree of the scale, we talked about this in the article. Correspondingly, if the tonics of new keys are constantly moving away by a perfect fifth, then their seventh steps are also moving away from each other by exactly a perfect fifth.

Flat major keys are arranged in pure fifths down from to". Similarly, with each new key there is an increase in the number of flats in the scale. The range of flat keys is as follows: F major (one flat), B flat major (2 flats), E flat major (3 flats), A flat major (4 flats), D flat major (5 flats), G flat major (6 flats ) and C-flat major (7 flats).

The order of appearance of flats: SI, MI, LA, RE, SALT, DO, FA. Flats, like sharps, are added in fifths, only down. Moreover, the order of flats is the same as the order of keys of the flat branch of the circle of fourths, starting from B-flat major.

Well, now, finally, we will present the whole circle of keys, to which, for the sake of completeness, we will also add parallel minors for all majors.

By the way, the circle of fifths cannot be strictly called a circle, it is rather a kind of spiral, since at a certain stage some tonalities intersect due to coincidence in pitch. In addition, the circle of fifths is not closed, it can be continued with new, more complex keys with double ones - double sharps and double flats (such keys are rarely used in music). We will talk about matching tonalities separately, but a little later.

Where did the name "quarto-quint circle" come from?

So far, we have considered movement in a circle only in fifths and have never mentioned fourths. So why are they here? Why does the full name of the scheme sound exactly like " circle of fifths»?

The fact is that a quart is a fifth. And the same range of tonalities of the circle can be obtained if you move not in fifths, but in fourths.

For example, sharp keys can be arranged not by perfect fifths up, but by pure fourths down. You get the same row:

Flat keys can be arranged not by pure fifths down, but by pure fourths up. And again the result will be the same:

Enharmonic equal keys

Enharmonism in music is the coincidence of elements in sound, but their difference in name, spelling or designation. Enharmonic equals can be simple notes: for example, C-sharp and D-flat. Anharmonicity is also characteristic of intervals or chords. In this case, we will be dealing with enharmonic equal keys , respectively, the scale scales of these keys will also coincide in sound.

As we have already noted, such tonality coinciding in sound appears at the intersection of the sharp and flat branches of the circle of fifths. These are the tones a large number signs - with five, six or seven sharps or flats.

The following keys are enharmonic equal:

• B major (5 sharps) and C flat major (7 flats)
• Parallel to the named G-sharp minor (5 sharps) and A-flat minor (7 flats);
• F-sharp major (6 sharps) and G-flat major (6 flats);
• Parallel to them, D-sharp minor and E-flat minor with the same number of signs;
• C-sharp major (7 sharps) and D-flat major (5 flats);
• Parallel to these structures are A-sharp minor (also 7 sharps) and B-flat minor (5 flats).

How to use the fifth circle of keys?

Firstly, the circle of fifths can be used as a convenient cheat sheet for learning all the keys and their signs.

Secondly, by the circle of fifths, one can easily determine the difference in signs between the two keys. To do this, simply count the sectors from the original key to the one with which we are comparing.

For example, between G major and E major, the difference is three sectors, and, therefore, three decimal places. Between C major and A-flat major there is a difference of 4 flats.

The difference in signs is most clearly shown by the circle of fifths, divided into sectors. In order for the image of a circle to be compact, the keys in it can be written using:

Finally, Thirdly, in a circle of fifths, you can instantly establish the “closest relatives” of one or another key, that is determine the tonalities of the first degree of kinship. They are in the same sector as the original key (parallel) and adjacent on each side.

For example, for G major, E minor (in the same sector), as well as C major and A minor (neighboring sector on the left), D major and B minor (neighboring sector on the right) will be considered such related keys.

We will return to a more detailed study of related keys in the future, and then we will learn all the ways and secrets of their search.

A little about the history of the circle of fifths

No one knows exactly when and by whom the circle of fifths was invented. But early descriptions a similar system is contained in the manuscript of the distant 1679 - in the work "Music Grammar" by Nikolai Diletsky. His book was intended to teach church singers. He calls the circle of major scales the "wheel of cheerful music", and the circle of minor scales - the wheel of "sad music". Musikia - this word is translated as "music" from Slavic.

Now, of course, this work is of interest mainly as a historical and cultural monument, the theoretical treatise itself no longer meets the requirements of modernity. However, it can be said that since then, the circle of fifths has become entrenched in teaching practice and has entered almost all well-known Russian textbooks on music theory.

Dear friends! If questions on the topic of the circle of fifths have not yet exhausted themselves, then be sure to write them in the comments to this article. In parting, we invite you to listen to some good music. Let it be today the famous romance by Mikhail Ivanovich Glinka "The Lark" (verses by the poet Nikolai Kukolnik). Singer - Victoria Ivanova.

The circle of fifths helps to remember easily musical harmony and study It allows you to effectively learn modes and key signs, so understanding how it works is extremely important for all students mastering music theory.

The concept of a quarto-quint circle

The quarto-quint circle is a special arrangement system according to the degree of kinship, that is, differences in the number of signs of one from the other of various keys. In graphical form, it is visually depicted as a diagram of a closed circle, in which, on the one hand, the sides are located along the ascending fifth row of tonality with sharps, and on the left, along the descending row, with flats.

If you move clockwise around the circle of fifths, the first step (tonic) of the subsequent major keys will be separated upwards from the previous ones by an interval equal to five steps, that is, by a pure fifth. In this case, one sign will always be added in the key - sharp. In the counterclockwise direction, the descending interval will also be 3.5 tones. At the same time, the number of flats will increase in each subsequent key.

What is this system used for?

The quarto-quint circle of keys is used to determine the number of characters (sharps, flats) in the key. It is also used to search for related keys and determine the degree of their proximity. Related tonalities of the first degree include majors and minors, which differ from the original one by one accidental sign. They also include those in the circle in the neighborhood, parallel to them and to the original one. How closer friend to each other in the circle are keys, 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 closeness. 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 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 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 degree of the next key, let's count five notes up. The tonic of a related key will be on the fifth step of the original, that is, on its dominant. Thus, the fifth is the interval for calculations. It is because of the use of five steps for defining keys that the circle of fifths got its name. Now consider the Rule as follows: they are transferred from the original key to the next, plus one sign is added to them (to the sixth step) - a sharp.

Let's consider the key of C major, in which there are no accidentals (sharps and flats). Its tonic is the note do, and the dominant is salt. Therefore, according to the principle of the circle of fifths, the next tonality will be G-major (otherwise G-dur). Now let's define the accidental sign. In the resulting related key, step No. 6 is fa. It is on it that there will be a sharp. To determine the next tonality from G, set aside an interval equal to five steps. Its dominant is re. This means that the next key will be D-major (D-dur). It will already have two accidentals: from the previous key (F-sharp) and C-sharp joining at the sixth step. By analogy, you can find all the other keys. When determining the one that has seven signs with the key, the circle will close enharmonically.

Major circle of fifths with flats

Flat major keys are, unlike sharp ones, on the contrary, down in pure fourths. The tonic of C major is taken as the starting point, since C-dur has no accidentals. Counting down five steps, 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 step of the mode, that is, on the subdominant. In F major, it's B flat. Having passed the entire circle of fifths, we obtain the following major flat keys: In this case, the latter has as many as seven flat keys. Further, the circle is anharmonically closed. Of course, after that, other keys appear in a spiral - with double flats, but they are used quite rarely due to their complexity.

in a circle of quints. What is their construction principle?

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

The interval between the tonic and the third is the major third. At the first step in the note A, the sounds la, do and mi form a stable triad. The interval between the first and third steps 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 the same number of accidentals. For example, G minor and B flat major contain two flats in the key, and E minor and G major contain one sharp. In parallel keys, the same scale is used, so a melody that sounds 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 lower the tonics of all major keys by a minor third, we get a minor fifth circle. The figure shows accidental signs that are available in each sharp and flat minor key.

Instead of a conclusion

So, in this article, we examined the circle of fifths and found out that it is a system of arrangement of all keys, taking into account the degree of their relationship. Thanks to anharmonicity 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 accidentals in harmony.