Quarto fifth circle table. Circle of fifths

December 26th, 2014 , 05:24 pm

Fourth-fifth circle

The circle of fifths of tonalities, or, as it is also called, the circle of fourths-fifths, is in music theory a schematic representation of sequential tonalities.

This schematic drawing gives an idea of ​​the order of scales. The principle of its operation is based on the gradual addition of signs to the key as this circle passes. Something to remember keyword"fifth". Constructions in the circle of fifths of major keys are based on this interval.

Take the note C (C) as the starting point. C major is at the top of the circle and has no key signs.

Next, from the note to in the direction of increasing the sound, we line up the notes in fifths.
To construct the “perfect fifth” interval from starting point We calculate five steps or 3.5 tones. First fifth: C-sol. This means that G major is the first key in which the key sign should appear, naturally sharp and naturally it will be alone.

Next we build the fifth from G - G - D. It turns out that D major is the second key from the starting point in our circle and it already has two key sharps. Similarly, we calculate the number of sharps in all subsequent keys.

By the way, in order to find out which sharps appear in the key, it is enough to remember the so-called order of sharps once: 1st - F, 2nd - C, 3rd - G, then D, A, E and B - also everything is in fifths, only from the note F. Consequently, if there is one sharp in the key, then it will necessarily be F-sharp, if there are two sharps, then F-sharp and C-sharp.

Moving down the diagram and moving further around the circle, sharps are replaced by flats.
F sharp and G flat occupy the same position in the diagram, they are also identical in sound and are one key - both in musical texts and in the musical stave. IN musical terminology they are enharmonic.

To obtain flat tones, we build a fifth in a similar way, but following the circle counterclockwise - from right to left, that is, in the direction of lowering the sounds.

Let's take the note C as the initial tonic, because there are no signs in C major. So, from C downwards 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, which already has two flats.

The order of flats, interestingly, is the same order of sharps, but only read in a mirror way, that is, in reverse. The first flat will be B, and the last flat will be F.

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

Circle of fifths(or circle of quarts and fifths) – is a graphical diagram used by musicians to visualize the relationships between keys. In other words, it is a convenient way of organizing the twelve notes of the chromatic scale.

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

A page from the book “The Idea of ​​a Musician Grammar”, which depicts the circle of fifths

You can start building a circle from any note, for example C. Next, moving towards increasing the pitch of the sound, 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 G-D. D major is the third key. By 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 constructed using quarts. If we take the note C and lower it by 2.5 tones, we 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 signs in the key of a particular key. Each time, counting 5 steps and moving clockwise around the circle of fifths, we get a tonality in which the number of sharps is one more than in the previous one. The key of 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 in the key, you need to move in the opposite direction, that is, counterclockwise. For example, starting with C and counting down the fifth, you will arrive at the key of F major, which has one flat sign. The next key will be B-flat major, in which two flat signs are on the key, and so on.

As for the minor, then minor scales, identical to major ones in the number of signs in the key, are parallel (major) keys. Determining them is quite simple; you just need to build a minor 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 city ​​of Montclair, says the circle helps understand the structure western music different styles: classic rock, folk rock, pop rock and jazz.

“Keys and chords that are close to each other on the circle of fifths will be considered consonant by most Western listeners. The tonalities of A major and D major contain six identical notes, so the transition from one to another occurs smoothly and does not cause a feeling of dissonance. A major and E flat major have only one general note, so changing 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 adjacent G major results in the substitution of just one tone, while moving five steps from C major to B major results in the substitution of five tones in the initial scale.

Thus, the closer two given tones are located to each other, the closer the degree of their relationship. According to the Rimsky-Korsakov system, if there is a distance of one step between tonalities, this is the first degree of relationship, two steps is the second, three is the third. The 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 relationship includes tonalities that are related to related tonalities. Likewise, tonalities of the third degree of kinship are tonalities of the first degree of kinship to tonalities of the second degree of kinship.

The degree of relationship is why these two chord progressions are often used in pop and jazz:

E7, A7, D7, G7, C

“In jazz, the keys tend to change clockwise, while in rock, folk and country they tend to move 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 will be able to play in your chosen key with ease—you won't have to struggle to find the right notes,” concludes Gail Grace. published

Dmitry Nizyaev

Let's try to make some observations, having at hand such a visual system as quarto-fifth circle. The patterns themselves may not be new to you, but even your old knowledge can be systematized and become easier for you to use. Or maybe you will discover something unexpected for yourself.

For example, many students have significant difficulty remembering which key signs have different tones. Most people have to remember this by simple rote learning. Others, when the name of a key is mentioned, remember the notes of the pieces they have played. Here's another way for you: remember the position of the key on a circle, like on a watch dial. The position itself will tell you the number of characters.

By the way, did you notice that when constructing a circle (in the last lesson), new key signs also appeared in fifths? In G major there is an “F” sign, and in the next D major a “C” is added. Between "fa" and "do" there is a fifth. But this is just an interesting observation, nothing more.

But here is another useful discovery from looking at the circle: the new, last sign in the right half of the circle always ends up on the VII degree of tonality ("F" in G major, "G" in A major, etc.) So, that's enough for you remember the order of the signs, there are only seven of them, and in two seconds you will be able to calculate their number in any key. Let's say E major. The signs appear in the order "fa-do-sol-re-la-mi-si". Which one will be the 7th degree in E major? "Re", fourth in order. Answer: There are four sharps in E major. Why not a way?

Now look at the left, flat half of the circle. There the opposite pattern is revealed (again symmetry is omnipresent!). Namely: if in sharps the last sign was the penultimate degree of tonality, then in flats, on the contrary, the penultimate sign is the last degree, that is, simply, the tonic. For example, in the key of E-flat major there are three signs: “B”, “E” and “A”. The penultimate one is tonic. Consequently, here too you just need to remember the order of the signs - and their number will be calculated instantly and easily.

Another symmetry. Compare the order of appearance for sharps and flats:

What's it like? Looks like reverse poetry, doesn't it? "And the rose fell on Azor's paw." It reads the same in any direction.

We'll keep watching. For example, how do the positions of the same keys correlate in a circle? C major is at the very top, and C minor is at "nine o'clock" - and therefore has three flats in the key. Did you see? (it would be great if you learned to make all these observations in your head, without referring to the picture (see figure). But this is possible with time). Now take (or imagine) a paper circle so that you can put it in the circle and turn it. Draw a two-tailed arrow on it, covering a quarter of the circle. Put it in a circle - and no matter what position it finds itself, it will always point to the tones of the same name. Doesn't it look like a cunning toy? And the conclusion to make your life easier is ready: the same keys always have a difference of three key signs, and the major is located on the sharp side relative to the minor. Hmm, the picture looks like the cover of a science fiction novel about time travel...

Another trick. Not very useful, but beautiful. If you “move your finger” along the diagram, moving along the chromatic scale, you get a rather interesting trajectory, right? (see picture)

Another observation that lies on the surface: the famous quarto-fifth sequence, called “golden”, is simply a uniform step-by-step movement in this circle. Remember, when we got to know her, I said that this sequence could continue indefinitely - now it’s clear why. After all, it moves not in a straight line, but in a circle! And after twelve links it will be forced to close on its own beginning.

Now try to come up with many different sequences - or at least trace along this circle those that we examined in that lesson - and you will find that the most beautiful and natural combinations of chords in them correspond to movement along the adjacent cells of the circle, like on a ladder. And the most dramatic and unexpected combinations are jumps in the same circle between far-distant cells. Oh how!

Meanwhile, clockwise and counterclockwise motions do not sound the same. See how the triads of any two adjacent positions of the circle relate to each other. For example, G major and C major. "Salt" is the dominant of "do", but "do" of "sol" is the subdominant, right? And psychologically, the movement from the dominant to the tonic sounds more natural than vice versa, because in the first case it means resolving tension, and in the second it means escalating it. Now play the same “golden” quarto-fifth sequence of triads, going in a circle in one direction and the other (examples 2 ). Agree that the first example does not sound as forced and artificial as the second - because in each of its links a movement from the dominant to the tonic or counterclockwise in our circle is realized. Thus, you can take into account that such a “rotation” of chords in your music counterclockwise will psychologically lead your listener to resolution, to calm, to “home”. A reverse movement It is appropriate to use, on the contrary, when building tension and preparing for the climax.

Let us now, as we planned in the previous lesson, trace on a circle how the tonalities of the first degree of relationship (or simply related ones) are located. Cut out a paper circle with one arrow from the center. We put it in our circle, pointing to C major. Last time we already found all related keys for it, now let's turn the arrow:

D minor: step left of center
E minor: step right of center
F major: step left of center
G major: step right of center
La Minor: return to center

The first time I did this, I was shocked! Not only does the arrow never move more than one step away from the “house,” but it also dances a square dance around it! And again comes to the center in the end. The apotheosis of symmetry, right?

The picture is no worse for the original minor key. We take A minor and “dance” related tonalities from it:

C major: the arrow is stationary
D minor: step left of center
E minor: step right of center
F major: step left of center
G major: step right of center

Almost the same thing, right? This is not surprising: after all, for both original tonalities the “relatives” are the same, since they have a common number of signs and, therefore, a diatonic scale.

The only violation of this harmonious picture is associated with the sixth related key, which - remember? - was included in the list later and with a certain degree of convention, namely, using the steps of the harmonic mode. Let's break this down. As you know, the harmonic mode (both major and minor) is distinguished by the presence of an augmented second between the VI and VII degrees. In C major, these are the notes “A” and “B”. How can you expand this interval? There is only one way: by lowering the "A". Because there is nowhere to raise the "si". Now try to construct all the triads in which the resulting “A-flat” can participate. These will be the triads “D-F-A” (and as “A” decreases, it becomes diminished); “fa-la-do” (here the major is replaced by a minor); and “la-do-mi” (a major triad will turn into an augmented one). As you yourself understand, neither increased nor decreased triads can serve as tonics for the desired keys. So it turns out that if we accept the note “A flat” into the legal composition of C major, then we have at our disposal only one new related key - F minor. On a circle it will be "120 degrees counterclockwise". Follow the thought? This will be the sixth and final related key for major.

Let's briefly repeat this path for A minor. In a harmonic mode, an increased second is needed between degrees VI and VII, i.e. between "fa" and "sol". There is nowhere to lower “F”, so we get “G-sharp”. Triads involving “G-sharp” will be as follows: “C-E-G” (major will become augmented); "mi-sol-si" (minor will become major); and “G-B-D” (major will become diminished). Only one again new key- E major. Let's find it on a circle - 120 degrees clockwise from A minor. That is, the picture is absolutely the same, exactly the opposite! Mirror situation. It turns out that even the forced introduction of an additional related tonality does not break the symmetry. Oh how!

The circle of fifths of tonalities, or, as it is also called, the circle of fourths-fifths, is in music theory a schematic representation of sequential tonalities. The principle of arranging all tonalities in a circle is based on their uniform distance from each other along the intervals of a perfect fifth, a perfect 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 in major keys. The circle of fifths of major keys was created 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, one key is neutral, it does not have any key signs.

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

How to use the circle of fifths in major keys?

This schematic drawing gives an idea of ​​the order of scales. The principle of its operation is based on the gradual addition of signs to the key as this circle passes. The key word to remember is “fifth”. Constructions in the circle of fifths of major keys are based on this interval.

If we move around the circle from left to right, in the direction of increasing sounds, we will get sharp ones. By following, on the contrary, from right to left along the circle, that is, in the direction of lowering the sounds (that is, if we build fifths down), we get flat tones.

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

Next we build the fifth from G - G-D. It turns out that D major is the second key from the starting point in our circle and it already has two key sharps. Similarly, we calculate the number of sharps in all subsequent keys.

By the way, in order to find out which sharps appear in the key, it is enough to remember the so-called order of sharps once: 1st - F, 2nd - C, 3rd - G, then D, A, E and B – also everything is in fifths, only from the note F. Therefore, if there is one sharp in the key, then it will necessarily be F-sharp, if there are two sharps, then F-sharp and C-sharp.

To obtain flat tones, we build a fifth in a similar way, but following the circle counterclockwise - from right to left, that is, in the direction of lowering the sounds. Let's take the note C as the initial tonic, because there are no signs in C major. So, from C downwards 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, which already has two flats.

The order of flats, interestingly, is the same order of sharps, but only read in a mirror way, that is, in reverse. The first flat will be B, and the last flat will be F.

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

Key. Circle of fifths tonalities.

Key– this is the height of the fret. The concept of tonality consists of two elements: the name of the tonic and the type of mode.
The major modes of the tempered scale form together a certain system tonalities connected by common tetrachords. If the upper tetrachord of a given major mode is taken as the lower tetrachord of another mode and a similar tetrachord is constructed at a tone distance from its upper sound, a scale of a new major key will be obtained. This key differs from the previous one by one key sign, and its tonic lies a fifth higher. If we continue to equate tetrachords, a series of tonalities will be built, which is called fifths. A similar series of keys can be built by increasing the number of flats.

Circle of fifths is the arrangement of major keys in the order of adding key signs: sharps - up in perfect fifths, and flats - down in perfect fifths.

In major, the last sharp appears on the 7th degree, and the last flat appears on the 4th degree. The order of appearance of sharps is: F-do-sol-re-la-mi-si, and flats - in reverse side: si-mi-la-re-sol-do-fa. Minor keys, like major keys, can be arranged in order depending on the number of key signs. In this case, a new sharp appears on the 2nd degree, and a new flat - on the 6th degree.

Parallel keys- These are major and minor keys with the same key signs. The tonics of these keys are located at a distance of a minor third, in which the upper sound is the tonic of a major key. For example, C major and A minor.

Keys of the same name- These are major and minor keys with a common tonic. For example, C major and C minor.

One-note keys- These are major and minor tonalities with a common tertian tone, that is, the third degree. The minor key in such a pair is always a semitone higher than the major key. For example, C major and C sharp minor.

Enharmonically equal tonalities– these are two major or two minor keys having a common scale that is written differently. The sum of the signs in such keys is 12. Any key can be replaced enharmonically, but in practice six pairs of such keys (with five, six and seven key signs) are used.