Quanto fifth circle of keys. Why fifths and why circle? Sharp circle of fifths in major keys

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, minor scales, identical to major scales in the number of signs in the key, are parallel (major) tonalities. 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

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

We know that major keys use both root degrees and derivatives. In this regard, the necessary alteration signs are placed at the key. In previous articles, we compared C major and G major (C major and G major) as an example. In G major we have an F sharp so that the correct intervals between degrees are maintained. It is this (F-sharp) in the key of G-dur that is indicated in the key:

Figure 1. Key signs of the tonality G-dur

So how can we determine which tonality which accidental signs correspond to? It is this question that the circle of fifths 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 sharp circle of fifths the tonality will become the V step of our tonality (an example will be below). In the alteration signs of that next key, all the signs of our previous key will remain, plus the sharp of the 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 alteration signs in this key. The note G is a V degree (the V degree is a fifth, hence the name of the circle). It will be the tonic of a new key. Now we are looking for a sign of alteration: in the new key, the VII step is the note F. For this we set the sharp sign.

Figure 2. Found the key sign of the sharp key of 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 D (D), since it is the V degree (a fifth of the note G). In D-dur there should be another sharp. It is placed for the VII level of D-dur. This is the note C ©. This means that D-dur has two sharps in 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 switch completely to letter designation steps. Let's determine the next key after D-dur. The root note will be A (A), since it is the V degree. Means, new key will be A major. In the new key, the VII step will be the note G, which means that at the key another sharp is added: G#. In total, the key has 3 sharps: F#, C#, G#.

Figure 4. Key accidental signs A-dur

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

So, if we go through the entire 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're talking about about the circle, then the next key should be our original key: C-dur. Those. we must go back to the beginning. The circle is closed. In fact, this does not happen, because we can continue to build fifths further: C# - G# - D# - A# - E# - #... But if you think about it, what is enharmonic equal to sound H# (imagine a piano keyboard)? Sound Do! This is how 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-sharps will appear more and more.. So So, in order to feel sorry for the performer, it was decided that all keys where a double-sharp must be placed in the key are declared unusable and replaced with enharmonically equal keys, but no longer 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 in the key); G#-dur is enharmonically equal to the tonality of As-dur (A-flat major) - it also has fewer signs in the key - and this is convenient both for reading and for performance, and the circle of fifths, meanwhile, thanks to the enharmonic replacement of tonalities, is truly closed!

Flat circle of fifths in major keys

Everything here is analogous to the sharp circle of fifths. Behind starting point take the key of C-dur, since it does not have accidental signs. The tonic of the next key is also at a distance of a fifth, but only downwards (in the sharp circle we took the fifth up). From the note C, a fifth down, is the note F. This will be the tonic. We place a flat sign in front of the IV degree of the scale (in the sharp circle there was a VII degree). Those. for F we will have a flat before the note B (IV degree). Etc. for each new key.

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

Enharmonically equal keys

You have already understood that tonalities of the same pitch, but different in name (the second loop of the circle, or rather, already a spiral), are called enharmonically equal. On the first loop of circles there are also enharmonically equal tonalities, these are the following:

• H-dur (in the key of sharps) = Ces-dur (in the key of flats)
• Fis-dur (in the key of sharps) = Ges-dur (in the key of flats)
• Cis-dur (in the key of sharps) = Des-dur (in the key of flats)

Circle of fifths

The order of arrangement of major keys described above is called the circle of fifths. Sharps go up in fifths, flats go down in fifths. The order of the keys can be seen below (your browser must support Flash): move your mouse in a circle over the names of the keys, you will see alternation marks of the selected key (we have placed minor keys in the inner circle, and major keys 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.

Hello, dear readers of the site site. We continue to study musical art, and interesting points associated with him. 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 the ancient Greek philosopher, who devoted a lot of time to the study of music and gave it one of the most important meanings 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 teaching on intervals, which he introduced into music. Moreover, the entire universe, according to the scientist, carries within itself something like musical harmony. Harmony is unthinkable without intervals, therefore even between planets solar system, Pythagoras was sure there were .

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 simply remember how many signs (sharps or flats) each key has. The circle of fifths of keys will help us in determining how many signs are in the key of a particular key. What is its meaning?

As we said above, Pythagoras was looking for ways to apply a mathematical approach to music and the circle of fifths - there is confirmation that music is indeed 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.

Then from G a perfect fifth (further part 5) upward - you get the next key 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 appear, you need to build part 5 upward, but not from the tonic, but from the first key sign (the note F-sharp, which was at the key in G major).

Thus, you will no longer have any doubts about the following key with the tonic “D” and two signs at the key F-sharp and C-sharp - everything corresponds to the key of D major.

So we move until we reach a key in which there are as many as seven sharps in the key - this is the key of C-sharp major.

With flats in the key, everything is the same, only we move down part 5 from the desired note. For example, again from “to” in C major - we get the note “F”

and the key is F with one flat sign at the key, which means it 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 is at the key we build part 5 down and get a new key sign.

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

Thus, you can get absolutely all possible keys up to seven flat signs in the key. We simply build sequentially part 5 from the tonic of all keys (starting with C major) and each time there will be one more sharp. The same with flats, only part 5 we build downwards.

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

But for guitarists it’s probably more convenient to simply remember the fingerings of all the necessary scales in all their positions and then you won’t need to count out the formulas for major or minor scales, and also use the circle of fifths described in this article. With playing experience, you will memorize the entire fretboard and won't even think much about it.

Subscribe to not to miss new articles. Good luck to you.

Dmitry Nizyaev

Let's try to make some observations, having at hand such a visual system as the circle of fourths. 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). Again there is only one 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!

minor keys. Alteration in major and minor.

Alteration means change.

Alteration marks are signs that change a note.

A sharp is a sign of raising a note by a semitone.

A flat is a sign of lowering a note by a semitone.

Bekar is a sign that cancels the effect of a sharp or flat.

The signs are random, which are placed near the note and last one measure, and

key signs that are displayed at the key and remain throughout

the whole melody.

The order in which sharps appear is F, C, G, D, A, E, B.

The flats appear in reverse order.

Circle of fifths is a system in which all keys are of the same scale

arranged in perfect fifths.

Major keys are located from the note C: up to ch5 - sharp keys,

down ch5 – flat keys.

C major – G major – D major – A major – E major – B major

C major – F major – B major – E major – A major – D major

To determine the key signs in a minor key, you need to go to

parallel major key and use the circle of fifths or

build the circle of fifths using the same principle minor keys from the note A.

Alteration of degrees in major: II # b, IY #, YI b

in minor: II b, IY b#, YII#

TICKET No. 7.

1. The main triads of the mode, their circulation and connection.

Main triads modes are triads built from the main degrees of the mode.

At stage I - tonic triad (T 5/3)

At the IY stage – subdominant triad (S 5/3)

At the Y step – dominant triad (D 5/3)

The main triads in major are major, and in natural minor are minor. Besides, in harmonic major a minor subdominant appears, and in a harmonic minor a major dominant appears.

The main triads have inversions.

major minor resolution

T5/3 I b3 + m3 m3 + b3

T6 III m3 + h4 b3 + h4

Т6|4 Y h4 + b3 h4 + m3

D5/3 Y T, T6/4

connection chords is the connection between chords through smooth voicing. Each voice in the chords should move smoothly, without jumps.

Connecting the main triads in C major:

Т5|3 S6|4 Т5|3 D6 Т5|3 Т6 S5|3 Т6 D6|4 Т6 Т6|4 S6 Т6|4 D5|3 Т6|4

Alternating different chords in a scale form chord sequences.