Hello, dear readers of the site site. We continue to study musical art, and 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 really is 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 down to h.5 down from the desired note. For example, again from "do" 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, minor scales are identical to major ones 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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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. 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). It makes a-moll 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.
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 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.
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How from different sounds to play the same music in minor key?
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.
- at parallel keys, the minor tonic will be lower by a minor third of the major 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 | |||||||||||||||||||||||||||
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And similarly, the fifth circle of flat minor keys:
| Table of minor flat keys | |||||||||||||||||||||||||||
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Just like major, minor has three pairs of enharmonic equal keys:
- G-sharp minor = A-flat minor
- D-sharp minor = E-flat minor
- 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 one; 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. Don't push yourself away major circle and 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.
The Circle of Fifths (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.
Quint circle of keys(or fourth-quint circle) - is a graphical scheme used by musicians to visualize relationships between keys. In other words, it is a convenient way of organizing 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 along 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 a small third (1.5 tones) down from each tonic. 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 device 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.
Thus, the closer two given keys are 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 kinship, 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 the 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 selected key - you do not have to painfully select the right notes,” concludes Gale Grace. published
