minor tones. Alteration in major and minor.
Alteration means change.
Accidentals are signs that change the note.
A sharp is a sign of raising a note by a semitone.
A flat is a sign for lowering a note by a semitone.
Becar is a sign that cancels the action of a sharp or flat.
Signs are random, which are placed near the note and act for one measure, and
key signs that are set at the key and remain throughout
the whole melody.
The order of occurrence of sharps: fa, do, salt, re, la, mi, si.
Flats appear in reverse order.
Circle of fifths called a system in which all keys are of the same fret
arranged in perfect fifths.
Major tonalities are located from the note To: up ch5 - sharp keys,
down on h5 - flat keys.
C Major – G Major – D Major – A Major – E Major – B Major
C Major – F Major – B Major – E B Major – A B Major – D B 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 in the same way circle of fifths minor keys from the note la.
Alteration steps in major: II # b, IY #, YI b
in minor: II b, IY b #, YII #
TICKET #7.
1. The main triads of the mode, their circulation and connection.
Main triads fret are triads built from the main steps of the fret.
On the I degree - tonic triad (Т 5/3)
On the IY step - subdominant triad (S 5/3)
On the Y degree - dominant triad (D 5/3)
The main triads in major are major, in natural minor they are minor. In addition, a minor subdominant appears in the harmonic major, and a major dominant appears in the harmonic minor.
The main triads have inversions.
major minor resolution
Т5/3 I b3 + m3 m3 + b3
Т6 III m3 + ch4 b3 + ch4
Т6|4 Y ch4 + b3 ch4 + m3
D5/3 Y T, T6/4
connection chords is called the connection between chords through smooth voicing. Each voice in the chords should move smoothly, without jumps.
Connection of the main triads in C major:
T5|3 S6|4 T5|3 D6 T5|3 T6 S5|3 T6 D6|4 T6 T6|4 S6 T6|4 D5|3 T6|4
The alternations of different chords in a fret form chord progressions.
Tonality is the pitch of the fret. 12 major and 12 minor keys form a system quarto-quint circle. Keys located a fifth above and a fifth below are interconnected by common tetrachords
In a tempered tuning, any sharp key can be replaced by an enharmonic equal flat key and vice versa.
Minor keys, like major ones, are also arranged in a circle at a fifth's distance from each other.
Parallel are called major and minor keys, having the same scale (the same signs). Tonics parallel keys are at a distance of a minor third: A - fis, Es - c.
eponymous major and minor keys are called, the tonics of which are at the same height: D - d, B - b.
single-ended major and minor keys are called, in the tonic triads of which the tertian tone coincides. These keys are at a semitone distance and have a difference of four signs: C - cis, Des - d.
According to the musicians, each key is suitable for conveying certain images and emotions. So, in the Baroque era, the key in D major expressed "noisy" emotions, bravura, heroism, victorious jubilation. The key in B minor was considered associated with images of suffering, crucifixion. The saddest were the "soft" keys in C minor, F minor, B-flat minor. To express sadness, mourning was used in C minor. With the concept of "trinity" (Trinity) was associated E-flat major with its three flats. One of the pure, "solid" keys used by Bach to express a joyful feeling is G major. The keys of A major and E major are light, often associated with music of a pastoral nature. The purest tonality was considered to be C major, which has no signs of alteration. This tonality was chosen for works dedicated to the purest and brightest images.
Composers different eras attracted the idea to create a cycle of works written in all 24 keys. The first in this series was Johann Sebastian Bach - this is two volumes of the Well-Tempered Clavier. In each volume, the keys follow semitones, starting from C major to C minor. After Bach, cycles of works in all keys are 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 sequence of keys in each composer is different: by semitones, by the circle of fourths and fifths. Paul Hindemith creates his own system of following tonalities
For many musicians, keys evoke color associations. Altitude relationship musical sounds and keys with certain colors or images is called color hearing. They had such a hearing Scriabin, Rimsky-Korsakov, Asafiev and other composers. This table reflects the color-tonal associations of A. Scriabin. Please note that the order of colors of sharp keys is 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. Sample execution
3.What keys do these tetrachords belong to?
4. What tonalities do these turns belong to?
5. Pe rewrite melodies from HTC Bach in the indicated keys
a ) f-moll, c-moll
b ) d-moll, f-moll
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 we have to start writing it down in bass clef, and finish in violin.
The order in which the 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 arranged in perfect 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 the “quarto-quint circle”?
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, third, 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 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.
Dmitry Nizyaev
Let's try to make some observations, having at hand such a visual system as a circle of fifths. By themselves, the manifested patterns 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 find it difficult to remember which key signs have different keys. Most people have to memorize this by simple memorization. Others, at the mention of the name of the key, recall the notes of those pieces that they had a chance to play. Here's another way for you: remember the position of the key on the circle, as on the clock face. The position itself will tell you the number of characters.
And by the way, did you notice that when building a circle (at the last lesson), new key signs also appeared in fifths? In G major - the sign "fa", and in the next D major, "do" is added. Between "fa" and "do" - fifth. But it's just interesting observation, no more.
And here is another useful discovery from looking at the circle: the new, last sign in the right half of the circle always turns out to be on the 7th degree of tonality ("F" in G major, "G" in A major, etc.) So, you have enough remember the order of the signs, only seven pieces, and in two seconds you can 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 of them will be the 7th degree in E major? "Re", fourth in order. Answer: There are four sharps in E major. Why not a way?
Look now at the left, flat half of the circle. There, the reverse pattern is found (again, symmetry is ubiquitous!). 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: "si", "mi" and "la". The penultimate one is the tonic. Therefore, here you just need to remember the order of the characters - and their number will be calculated instantly and easily.
Another symmetry. Compare the order of appearance for sharps and for flats:
What is it? Sounds like a turnaround poem, doesn't it? "And the rose fell on Azor's paw." It reads the same in every direction.
Let's watch again. For example, how the positions of the same keys are related 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 could learn to make all these observations in your mind, without consulting the picture (see fig.). But this can be done with time). Now take (or imagine) a paper circle so that you can put it inside the circle and rotate 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 is in, it will always show on eponymous keys. Doesn't it look like a tricky toy? And the conclusion is ready to make your life easier: the keys of the same name always have a difference of three key mark, and the major is on the sharp side of the minor. Hmm, the picture looks like a cover to fantasy novel about time travel...
Another focus. Useless, but beautiful. If you "wiggle your finger" according to the scheme, moving along chromatic scale, then it turns out to be a rather entertaining trajectory, right? (see pic.) 
Another observation that lies on the surface: the famous fourth-quint sequence, called "golden" is just a uniform step-by-step movement around this circle. Remember, when we got to know her, I said that this sequence can continue indefinitely - now it’s clear why. After all, it does not move in a straight line, but in a circle! And after twelve links it will be forced to lock itself into its own beginning.
Now try to come up with a lot of different sequences - or at least follow those that we analyzed in that lesson along this circle - and you will find that the most beautiful and natural combinations of chords in them correspond to movement along the neighboring cells of the circle, like stairs. And the most abrupt and unexpected combinations are jumps along the same circle between far-flung cells. Oh how!
Meanwhile, clockwise and counterclockwise movement sounds different. 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 for "do", but "do" for "sol" is a 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 the resolution of tension, and in the second - its forcing. Now play the same "golden" quarto-fifth sequence of triads, going in a circle in one direction and in the other (examples 2 ). Agree that the first example does not sound as strained and artificial as the second - because in each of its links a movement is realized from the dominant to the tonic or counterclockwise around our circle. 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, "home". And it is appropriate to use the reverse movement, on the contrary, when escalating tension, preparing a climax.
Let's now, as we gathered in the previous lesson, trace on the circle how the tonalities of the first degree of kinship (or simply related ones) are located. Cut out a paper circle with one arrow from the center. We put it in our circle, point to C major. Last time we already found all related keys for it, now let's turn the arrow:
D minor: step left from center
E minor: step right from center
F major: step left from center
G major: step right from center
La Minor: return to center
The first time I did this, I was shocked! Not only has the shooter never gone more than one step away from "home", but she is also dancing a quadrille around him! 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 keys from it:
C major: the arrow is stationary
D minor: step left from center
E minor: step right from center
F major: step left from center
G major: step right from center
Pretty much the same, right? This is not surprising: after all, for both initial keys, the "relatives" are the same, since the number of signs and, consequently, the diatonic scale they have in common.
The only violation of this harmonious picture is related to the sixth kindred key, which - remember? - was included in the list later and with a certain degree of conventionality, namely, using the steps of the harmonic mode. Let's chew it up. As you know, the harmonic mode (both major and minor) is distinguished by the presence of an augmented second between the VI and VII steps. In C major, these are the notes "la" and "si". How can you expand this interval? Only one way: lowering "la". Since there is nowhere to raise "si". Now try to build all the triads in which the resulting "A-flat" can participate. These will be triads "d-fa-la" (and with the decrease in "la" it becomes reduced); "fa-la-do" (here the major is replaced by a minor); and "la-do-mi" (the major triad will turn into an enlarged one). As you yourself understand, neither augmented nor diminished triads can serve as tonics for the desired keys. So it turns out that if we take the note "A-flat" into the legal composition of C major, then we get at our disposal only one new related key - F minor. On a circle it would be "120 degrees counterclockwise". Are you following a thought? This will be the sixth and last related key for the major.
Let's briefly repeat this path for A minor. In a harmonic mode, an augmented second is needed between steps VI and VII, i.e. between "fa" and "sol". "F" nowhere to lower, so we get "sol-sharp". Triads with the participation of "sol-sharp" will be as follows: "do-mi-sol" (major will become increased); "mi-sol-si" (minor will become major); and "sol-si-re" (major will become diminished). Again, only one new key - E-major. Let's find it on the 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 violate the symmetry. Oh how!
This lesson is rather intended for those who are already studying in music school or even school. From many years of practice, I can say that the fifth circle of tonalities is a topic that is not assimilated by students in any way, which causes problems with mastering the material and performing any work. Yes, yes, without knowing what key we are playing in, it is extremely difficult to navigate, and for some reason it is difficult to play it. Therefore, before performing any piece, it is necessary to determine in what key it is written. Believe me - then you will sort it out much faster.
So, what is tonality, we talked in detail in, and now I will explain to you the system by which they are located. If to speak plain language- then in each key there are some signs, that is, when playing a scale or a piece, we also use black keys. And here are some - a harmonious and logical system will help - a fifth circle of keys.
In the study of music theory, there are moments that need to be understood, but there is information that you just need to memorize like a rhyme. Here is the rule below in the picture you need to memorize.
The order of attaching key characters is always the same:
Signs in any key are joined only in this order. If you notice, then this is the same sequence that is read from two sides - in one direction - sharps, in the opposite direction - flats. Here it must be memorized in both directions. On the musical staff it looks like this
Order of Key Signs in KeysNow let's answer the first question - why fifth?
Here next rule which should be easy to understand.
With each fifth built up, one sharp is added.
In the picture it looks like this:
We start from C major (or A minor, more on that below) and go clockwise.
We know that there are no signs in C major and A minor. This is an axiom that must be remembered. However, all beginners already know C major, because it is played only on white keys, which is very convenient. So, in C major. If we build a fifth from “to” upwards, we get the note sol. So, in G major there will already be one sharp. Which? We look above at the order of joining sharps - the first sharp is fa. So, in G major - F sharp. And when we play the G major scale, we raise the F note in it and instead of the white key we will play the black one.
Now we are building a fifth from G up (we stopped in the key of G major). It turns out the note D. Here in D major there are already two sharps - which ones? We look at the order of sharps - the first two are F and C.
From re we build another fifth, we get the note la. Here in A major there are already three sharps - F, C, G. They are the first three.
From la - the next fifth - it turns out the note mi. In E major, the first four sharps are already - F, C, G, D.
From mi - fifth up and you get the note si - in B major there are 5 sharps - fa, do, sol, re, la.
Quint from si - and a new key F sharp (why not fa - read here) - F sharp major - 6 sharps - fa, do, sol, re, la, mi.
And the last fifth from F sharp to sharp. So it turned out the key to sharp major - 7 sharps - fa, do, sol, re, la, mi, si. Oh how. In fairness, I want to say that keys with 7 sharps are rare in practice, but they do happen.
The same thing will happen if we build fifths in minor keys, taking the note la as the starting point - that's where 0 signs are.
We build a fifth from la - it turns out the tonality of e minor. There is one sharp in E minor. Which? We look at the order - F - the first sharp.
From mi one more fifth and we get B minor, in which there will already be two sharps - F and C.
From si, after 5 steps, the note F sharp is formed (be careful - not F, namely F sharp). In F sharp minor, there are 3 sharps - F, C, G.
From F # Quint - C # minor, in which there are already 4 sharps.
From up to # 5 steps we skip - and we get a new key with 5 sharps - G # minor.
From G # fifth - D # minor - 6 sharps.
From re#quint - la#. And in A sharp # - 7 sharps.
Keys with flats in key
In this picture, we go counterclockwise.
With each fifth built down, one flat is added.
From to down the fifth - we get the note F. In the key of F major, one flat. Which? Let's look at the order of the flats. We see that this is B flat.
We build one more fifth down from fa and get the note si flat. In the key of B major, there are already two flats - si and mi.
From si b we build another fifth and get to the note mi b. And in E b major there are already 3 flats - si, mi, la. And so on.
If you understand this principle, then it will not be difficult to determine the number of characters in any key. Now it’s clear why “quint”? Because it is built in fifths. Why a circle? Look carefully at the pictures above - we start with the keys of C major, and end with C # major or C major - not quite, of course, a circle, but still. Same thing with minor keys- starts from la, and ends with la# or lab in minor.
For ease of perception, I divided the keys and separately showed sharp and flat. In theory textbooks, the circle of fifths of keys is presented in the form of such a picture.
All keys - with both sharps and flats And finally, I suggest you listen to Frederic Chopin's waltz in C minor. Highly famous work, beautiful, flying and in a magnificent performance by Alexander Malkus.
