Music lessons - theory - fourth-fifth circle. Circle of Fifths: about music in simple words

fifth circle Keys (or circle of fifths) is a graphical scheme used by musicians to visualize relationships between keys. In other words, this convenient way organization of the twelve notes of the chromatic scale.

For the first time, the circle of fourths and fifths was described in the book "The Idea of ​​Musician Grammar" from 1679 by the Russian-Ukrainian composer Nikolai Diletsky.

Page from the book "Idea of ​​Musikian Grammar" showing the circle of fifths

You can start building a circle from any note, for example, to. Further, moving in the direction of increasing the pitch, we set aside one fifth (five steps or 3.5 tones). The first fifth is C-G, so the key of C major is followed by the key of G major. Then we add another fifth and get a sol-re. D major is the third key. After repeating this process 12 times, we will eventually return back to the key of C major.

The circle of fifths is called the circle of fifths because it can also be built with the help of fourths. If we take the note C and lower it by 2.5 tones, then we will also get the note G.

Notes are connected by lines, the distance between which is equal to half a tone.

Gayle Grace notes that the circle of fifths allows you to count the number of characters in the key of a particular key. Each time, counting 5 steps and moving clockwise around the circle of fifths, we get a key, the number of sharp signs in which is one more than in the previous one. The key in C major does not contain accidentals. In the key of G major there is one sharp, and in the key of C sharp major there are seven.

To count the number of flat signs at the key, you must move in the opposite direction, that is, counterclockwise. For example, starting with a do and counting down a fifth, you will come to the key of F major, in which there is one flat sign. The next key will be B-flat major, in which there are two flat signs at the key, and so on.

As for the minor, the minor scales, identical to the major scales in the number of signs at the key, are parallel to the (major) keys. Determining them is quite simple, you just need to build from each tonic minor third(1.5 tones) down. For example, the parallel minor key for C major would be A minor.

Very often, major keys are depicted on the outer part of the circle of fifths, and minor keys on the inner part.

Ethan Hein, professor of music at State University of Montclair, says that the circle helps to understand the structure of Western music different styles: Classic rock, folk rock, pop rock and jazz.

Keys and chords that are close together on the circle of fifths will be considered consonant by most Western listeners. The keys of A major and D major have six identical notes in their composition, so the transition from one to the other occurs smoothly and does not cause a feeling of dissonance. A major and E-flat major have only one note in common, so the transition from one key to another will sound strange or even unpleasant, ”explains Ethan.

It turns out that with each step along the circle of fifths in the initial scale of C major, one of the tones is replaced by another. For example, moving from C major to the neighboring G major leads to the replacement of only one tone, and moving five steps from C major to B major leads to the replacement of five tones in the initial scale.

So than closer friend two given keys are located to each other, the closer the degree of their relationship. According to the Rimsky-Korsakov system, if a distance of one step between keys is the first degree of relationship, two steps is the second, three steps is the third. Keys of the first degree of kinship (or simply related) include those majors and minors that differ from the original key by one sign.

The second degree of kinship includes keys that are related to related keys. Similarly, the keys of the third degree of kinship are the keys of the first degree of kinship to the keys of the second degree of kinship.

It is with this degree of relationship that these two chord progressions are often used in pop and jazz:

• E7, A7, D7, G7, C

“In jazz, the main keys most often change in a clockwise direction, and in rock, folk and country, they change counterclockwise,” says Ethan.

The appearance of the circle of fifths was due to the fact that musicians needed a universal scheme that would allow them to quickly identify the relationship between keys and chords. “If you understand how the circle of fifths works, you can easily play in the chosen key - you do not have to painfully select the right notes,” concludes Gail Grace.

Hello, dear readers of the site site. We continue to study musical art, as well as interesting moments associated with it. Today we will look at another pattern that helps to quickly calculate all possible scales with their key signs. Let's start from afar, one might say, from the origins of this knowledge... In one of the articles we wrote about ancient Greek philosopher, who devoted a lot of time to the study of music and gave it one of the most important values In human life. Among other things, he was, as you remember, a mathematician and tried to explain many phenomena using algebra. Also known is his doctrine of intervals, which he brought to music. Moreover - the whole universe, according to the scientist, carries something like musical harmony. Harmony is unthinkable without intervals, so even between planets solar system, Pythagoras was sure to exist.

So, do we need to constantly apply the formulas for constructing major or minor scales in order to build the scale we need? You can use it, or you can just remember how many characters (sharp or flat) each key has. In determining how many characters are in the key of a particular key, the fifth circle of keys will help us. What is its meaning?

As we said above, Pythagoras was looking for ways to apply the mathematical approach to music and the circle of fifths - there is confirmation that music is really somewhat similar to mathematics ... Take, for example, the key of C major - the simplest key and build up from the tonic.

Get the note G and the key of G major, with one key sign.

Further from salt, a pure fifth (hereinafter part 5) up - get the next key already with two "sharp" signs at the key. By the way, in order to find out what exactly the note will be at which the sign will stand, you need to build part 5 up, but not from the tonic, but from the first key sign (the F-sharp note, which was at the key in G major).

Thus, you will no longer have doubts about the next key with the tonic "D" and two signs in the key of F-sharp and C-sharp - everything corresponds to the key of D major.

And so we move until we reach the key, in which as many as seven sharps in the key - this is the key of C-sharp major.

With flats at the key, everything is the same, only we move ch.5 down from desired note. For example, again from "to" in C-major - we get the note "fa"

and the tonality of F with one flat sign at the key, so this is F major.

And if we want to determine the second key sign in the next one, then from the note next to which the flat stands at the key, we build h.5 down and get a new key sign.

In our case, we get the note E-flat and it turns out in the third key from C-major (if we move to the flat side) there will already be signs of B-flat and E-flat at the key, which is true for the scale of B-flat major.

Thus, you can get absolutely all possible keys up to seven flat signs with a key. We just build sequentially part 5 from the tonics of all keys (starting with C major) and each time there will be one more sharps. Also with flats, only h.5 we build down.

As for the minor, the minor scales are identical to the major scales in terms of the number of characters in the key, these are just keys parallel to them. It’s easy to find them, for the same C major - we take it from the tonic (note “to”) and build down the interval of a minor third (1.5 tones) the resulting note is the tonic of the parallel minor key (A minor).

But for guitarists, it is probably more convenient to simply remember the fingerings of all the necessary scales in all their positions and then it will not be necessary to count the formulas of major or minor scales each time, and also use the circle of fifths described in this article. With the experience of playing, you will memorize all over the fretboard and will not even think much about it.

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How to play the same music in minor from different sounds?

If you remember the circle of fifths of major keys (see the article ""), then it will not be difficult for you to deal with the circle of fifths of minor keys.

Recall the following:

• related keys are those that have 6 common sounds.
• parallel keys are those that have the same set of accidentals at the key, but one key is major and the other is minor.
• for parallel keys, the minor key tonic will be lower by a minor third of the major key tonic.

Circle of fifths in minor keys

The related keys of the minor, as well as the major, are located at a distance of a pure fifth from each other. In this regard, the keys of the minor form their own circle of fifths.

Knowing the circle of fifths of sharp major keys, we recalculate the tonics (lower by a minor third) and get the circle of fifths of sharp minor keys:

Table of minor sharp keys

Designation Name Accidentals with key A minor La Minor No accidentals E-moll E minor F# H minor B minor F#, C# F# minor F-sharp minor F#, C#, G# C# minor C-sharp minor F#, C#, G#, D# G# minor G sharp minor F#, C#, G#, D#, A# D# minor D sharp minor F#, C#, G#, D#, A#, E# A# minor A sharp minor F#, C#, G#, D#, A#, E#, H#

And similarly, the fifth circle of flat minor keys:

Table of minor flat keys

Designation Name Accidentals with key A minor La Minor No accidentals D minor D minor Hb G minor G minor Hb, Eb C minor C minor Hb, Eb, Ab F minor F minor Hb, Eb, Ab, Db B minor B flat minor Hb, Eb, Ab, Db, Gb eb-moll E flat minor Hb, Eb, Ab, Db, Gb, Cb Ab minor A flat minor Hb, Eb, Ab, Db, Gb, Cb, Fb

Just like major, minor has three pairs of enharmonic equal keys:

1. G-sharp minor = A-flat minor
2. D-sharp minor = E-flat minor
3. A sharp minor = B flat minor

Like the major circle, the minor circle is “happy” to close, and in this it is helped by enharmonic equal sharp keys. Exactly the same as in the article "".

You can visually get acquainted with the circle of fifths of minor keys (we arranged minor keys in the inner circle, and major ones in the outer circle; related keys are combined). Your browser must support flash:

Additionally

There are other ways to calculate the circle of fifths of minor keys. Let's take a look at them.

1. If you remember well the circle of fifths of major keys, but the method described above for finding the tonic of a parallel minor key is inconvenient for some reason, then you can take the VI degree for the tonic. Example: looking for a parallel minor key for G-dur (G, A, H, C, D, E, F#). We take the sixth step as the tonic of the minor, this is the note E. That's it, the calculation is finished! Since we found the tonic precisely parallel minor key, then the accidentals of both keys coincide (in the found E-moll, as in G-dur, there is a sharp before the note F).

2. We do not start from the major circle, but calculate from scratch. All by analogy. We take a minor key without accidentals, this is A-moll. The fifth degree will be the tonic of the next (sharp) minor key. This is the note E. We put the accidental sign in front of the second step (note F) of the new key (E-moll). That's it, the calculation is over.

Results

you met with circle of fifths in minor keys and learned how to count the number of signs in various minor keys.

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How to play 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 in 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 degree).

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

Example 3. Let's go completely to letter designation 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 key, the VII 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:

Table of sharp major keys

Designation Name Accidentals with key C major C major No accidentals G-dur G major F# D major D major F#, C# A major A major F#, C#, G# E major E major F#, C#, G#, D# H major B major F#, C#, G#, D#, A# Fis-dur F sharp major F#, C#, G#, D#, A#, E# cis-dur C-sharp major F#, C#, G#, D#, A#, E#, H#

Now let's figure out what the "circle" has to do with it. We settled on C#-dur. If we are talking about a 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. In fact, it doesn’t happen like that, because we can continue building 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 Des-dur (D-flat major) - it has fewer clef signs); 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 replacement of keys, really closed!

Flat fifth circle of major keys

Everything here is by analogy with a sharp fifth circle. 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:

Table of flat major keys

Designation Name Accidentals with key C major C major No accidentals F major F major Hb B major B flat major Hb, Eb Es major E flat major Hb, Eb, Ab As major A flat major Hb, Eb, Ab, Db Des-dur D flat major Hb, Eb, Ab, Db, Gb Ges-dur G flat major Hb, Eb, Ab, Db, Gb, Cb Ces-dur C flat major Hb, Eb, Ab, Db, Gb, Cb, Fb

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 on the inner circle, and the major keys on the outer; 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 helps to remember easily musical harmony and learn It allows you to effectively learn modes and key signs, so understanding how it works is extremely important for all students of 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. 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 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"). AT 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: 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 accidental signs. For example, G minor and B flat major contain two flats in the key, and E minor and G major contain one sharp. AT parallel keys the same scale is used, 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 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.