Quantum circle. Quarto-fifth circle of 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 keys(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

Tonality is the pitch of the fret. 12 major and 12 minor tonalities form a system quarto-fifth circle. Keys located a fifth above and a fifth below are interconnected by common tetrachords

In tempered tuning, any sharp key can be replaced by an enharmonically equal flat key and vice versa.

Minor keys, like major keys, are also arranged in a circle at a distance of fifths from each other.

Parallel are called major and minor keys that have the same scale ( identical signs). The tonics of parallel keys are at a distance of a minor third: A – fis, Es – c.

Same names are called major and minor keys, the tonics of which are at the same height: D – d, B – b.

Odnotertsovs are called major and minor keys, in the tonic triads of which the third tone coincides. These keys are half a tone apart and have a difference of four decimal places: C – cis, Des – d.

According to musicians, every key is suitable for conveying certain images and emotions. Thus, in the Baroque era, the tonality of D major expressed “noisy” emotions, bravura, heroism, and victorious jubilation. The key of B minor was considered associated with images of suffering and crucifixion. The saddest were the “soft” keys of C minor, F minor, B flat minor. C minor was used to express sadness and mourning. Associated with the concept of “trinity” (Trinity) was E-flat major with its three flats. One of the pure, “solid” keys used by Bach to express joyful feelings is G major. The keys of A major and E major are light, often associated with music of a pastoral nature. C major, which has no accidental signs, was considered the purest tonality. This tonality was chosen for works dedicated to the purest and brightest images.

Composers different eras I was attracted by the idea of ​​creating a cycle of works written in all 24 keys. The first in this row was Johann Sebastian Bach - This two volumes of The Well-Tempered Clavier. In each volume, the keys are followed by semitones, starting with C major and C minor. After Bach, cycles of works in all keys were created by F. Chopin(24 Preludes), C. Debussy(24 Preludes), A. Scriabin(24 Preludes), D. Shostakovich(24 preludes and fugues), R. Shchedrin ( 24 preludes and fugues), S. Slonimsky (24 preludes and fugues), K Karaev(24 Preludes), P. Hindemith(Ludustonalis). The order of tonalities is different for each composer: by semitones, by the circle of quarto-fifths. Paul Hindemith creates his own system of following tonalities

For many musicians, keys evoke color associations. Connection absolute altitude musical sounds and tonalities with certain colors or images are called color hearing. They had such hearing Scriabin, Rimsky-Korsakov, Asafiev and other composers. This table reflects the color-tonal associations of A. Scriabin. Please note that the order of the colors is sharp keys close to the rainbow: red, orange, yellow, green, blue, indigo, violet!

Task 3.4

1. Write the upper tetrachords of natural, harmonic, melodic major and minor in keys Es – dur, H – dur, f – moll, g – moll.

2. Write a complete functional formula for harmonic major and minor As – dur, E – dur, fis – moll, d – moll. Execution sample

3.What keys do these tetrachords belong to?

4. What keys do these turns belong to?

5. Pe rewrite melodies from Bach's HTK in the indicated keys

A ) f – moll, c – moll

b ) d – moll, f – moll

This article is mainly dedicated to beginning guitarists, but it may also be useful to people learning another instrument.

We decided to briefly tell you why, when playing, some combinations of notes sound beautiful, while others, to put it mildly, cause pain in the ears, as well as where the ill-fated sharps and flats in keys come from. In our opinion, this is the minimum that every self-respecting musician should know.

You may have seen this picture:

It depicts the circle of fifths. Don’t be afraid of this scary phrase, because in fact there is nothing complicated about it. It just shows signs at the key in minor and major keys. IN in this case There is no point in explaining what a major and minor key is, but we will be happy to try to explain what the key signs are and where they come from.

Let's look at the following picture, which shows the cleats of a piano:

Notes are signed on each key:

C=do, D=re, E=mi, F=fa, G=sol, A=la, B=si

You may ask why they didn’t sign the black keys? It's very simple, they have the same names as the notes surrounding them. A simple example: a black key between the notes C and D. We can call it either C# (sharp) or Db (flat), which is equivalent. Those. if we name it after the note before it, we add a sharp, if after it we add a flat. Let's move on. Two adjacent notes are separated by a semitone, and don’t forget about the black keys, these are also notes (on a guitar, a semitone corresponds to 1 fret, and a tone corresponds to 2 frets).

It's time to move directly to tonalities.

Each major key has its own parallel minor key, and vice versa, and they are called that because they have the same set of accidentals (sharps or flats) in scales. To put it simply, a scale is a scale, those notes that are “acceptable” in given keys (of course, this is not always the case, but we will not go deeper into more severe cases). Where do they come from? Everything is very, very simple. In the picture with the piano you can see the formulas for minor and major. What do they mean? It is generally accepted that there are seven notes, so we will have 7 notes in the scale. As you know, with an example everything is better understood

Let's say we want to build major scale from the note C and find out what chords are in this key, and find a minor key parallel to it. Easily!

We take the formula for the major key M=t+t+pt+t+t+t+pt:

1. C+t=D
2. D+t=E
3. E+f=F
4. F+t=G
5. A+t=B
6. B+f=C

As a result, we got the C major scale: C D E F G A B. As it turned out, we have no signs in it. We will do the same for the minor key, only according to the formula for the minor m=t+pt+t+t+pt+t+t (do this yourself with any key to consolidate), and if you make up minor scales for different notes, then it turns out that the minor scale from the note A also has no signs. As you probably already guessed, A minor will be parallel tonality for C major. Also in this example, you can notice an interesting property: in order to find out the parallel minor key for a major, you need to subtract 1.5 tones from the tonic (the main note after which the key is named, in our case C), and vice versa, add 1.5 to the tonic of the minor key tones.

To reinforce this, let's look at a quick example.

Let's build a major scale from the note G (G):

1. G+t=A
2. A+t=B
3. B+f=C
4. C+t=D
5. D+t=E
6. E+t= !attention! F# (we hope you understand why)

We got the scale: G A B C D E F#. We subtracted 1.5 tones from the note G and got the parallel minor key em. Now look at the circle of fifths. Did everything come together?) You see how simple it is, and there is no magic.

By analogy, it is also done for all other keys.

In conclusion, it remains to tell how to understand the chords from which notes in the scale will be major and which will be minor.

Each note in the scale has its own degree. From 1 to 7. So, if we write them down in steps (for example, let’s take C-major, A-minor) we get:

degrees: 1 2 3 4 5 6 7 or for minor 1 2 3 4 5 6 7

notes: C D E F A B C A B C D E F G

The first note is always the main note and is called the tonic. Next in order of precedence are the notes on the 4th and 5th steps - the subdominant and dominant, respectively. Chords built from these degrees will always be the same as a chord built from the tonic, i.e. C major, F major, G major, or: a minor, d minor, e minor. Chords built from other steps will always be opposite.

And finally, for those who didn’t give up and made it through everything to the end, an example for the key of G major.

steps: 1 2 3 4 5 6 7

notes: G A B C D E F#

1. level - G major
2. level - A-minor
3. level - b-minor
4. level - C major
5. level - D major
6. level - e-minor
7. level - F#-major

That's all! Good luck in your studies!

The circle of fifths is a fairly well-known concept. music theory, but, unfortunately, not everyone knows what it is for and how it can be used in their musical practice.

Usually the circle of fifths is described as a spiral of tonalities located clockwise in fifths up from the note C, and counterclockwise in fifths down or in fourths up (hence another name for the circle of fifths).

Although the circle of fifths is indeed a circle of keys, its use is much broader than just finding the number of signs in a particular key.

Since my goal is to give you the most rich information, which is not in most textbooks, then I need to tell you everything about the circle of fifths that I know or could find in additional sources.

So, the first thing you should know is that the circle of fifths reflects the interaction of all 12 sounds of the chromatic scale.

As is known, the chromatic scale is an artificially created modal structure that is practically never found in pure form, since it has no tonal or modal center.

Displaying notes in the circle of fifths is closer to musical reality.

Chromatics displays the smallest possible division in our music system coordinates (tempered tuning) and is a mathematical structure, and the circle of fifths reflects the mathematical ratio of 3:2 and is based on physical laws.

Look at the circle representing the interaction of chromatics and the circle of fifths

The fifth is the most perfect interval after the octave, which is the 3rd in the overtone series.

As you know, the fifth movement in the bass and melody sounds most complete and is the basis of cadences, and the movement from the 5th degree to the first (fourth - inversion of the fifth) is the basis of hymnic intonation.

Another interesting fact for those who didn't know. Pianos are most often tuned in fifths.

We can say that this is the most important interval in music :). Well, guitarists also love to play fifths, since they sound perfectly clear when played through distortion.

AND last fact– the circle of fifths was first described by our compatriot Nikolai Pavlovich Diletsky, which cannot but rejoice. Russians invented the circle of fifths :)

If we move from the note C through fifths, then we will inevitably encounter the phenomenon of tonal anharmonicity. When keys consist of the same sounds, but different notes. I recorded a special video lesson about this.

A little about the most obvious things for those who are hearing about the circle of fifths for the first time.

Moving in a circle, we find ourselves in new key, in which the number of characters is always one more than in the previous one. The names of keys and signs are written on the circle itself. But in order to remember the signs themselves, you can also use the fifth scheme.

Sharps start from F# and go up in fifths.

And flats start from Bb and go down fifths.

For example, you considered that the note B is a 5th step in fifths from the note C - this means that the number of sharps in the key is 5 and you need to build 5 fifths from the note F# - F#-C#-G#-D#-A# these will be the sharps we need.

Now let's talk about more interesting features circle.

Let's take a look at the circle itself and see what notes surround the C note:

Right is G

Left is F

And these are S and D keys.

That is, the circle can be used as a hint to find the main functions in any key!

This is its first hidden property.

Tonality and modulations

Another important property of the circle of fifths is that it clearly shows the harmonic gravity of chords. We can see it if we move in a circle counterclockwise. You may notice that the IV or F chord for C major is located after the tonic, that is, directed beyond the key to the Bb major chord.

For this reason, most classic revolutions are based on movement from stage II to stage V, rather than from stage IV. The IV stage, as a rule, is introduced at the beginning of formations, for example, I-IV-viio-III-VI-II-V. Many theorists even propose to consider stage IV as stage II without tonic.

Because this interpretation is more logical from the point of view of physics and musical perception.

Using the circle of fifths, you can build modulations in progressions, since the next 7 keys are the most used for modulations (including minor ones).

Moving around the circle of fifths and replacing chords with corresponding keys allows you to get the well-known harmonic swing.

For example, Em-Am-D7-G-C-F#7b5-B7

progression from the song Shadows in your smile and hundreds of others. The movement is characteristic of jazz. Reverse movement also possible.

Also more complex species The fourth-fifth movement can be used to create modern sequences, but I will write about this in a separate article.

Also, if you move from any note 5 times clockwise, you get all the notes of the pentatonic scale.

As you can see, the circle of quarto-fifths is an excellent cheat sheet for theory, modulation and memorizing keys.

minor keys. Alteration in major and minor.

Alteration means change.

Alteration signs are signs that change a note.

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

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