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 a certain system of tonalities interconnected 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 keys 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 that have a common scale, which 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.
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 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. 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 stave. In musical terminology they are enharmonic.
To obtain flat keys, 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, 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 to understand the structure of 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 keys 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 only have one note in common, so moving 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, than closer friend two given tones are located close 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. “Once you understand how the circle of fifths works, you'll be able to play in your chosen key with ease—you won't have to struggle to find the right notes,” concludes Gail Grace.
As a rule, representatives of the musical sphere simply call this entire system the circle of fifths, so as not to complicate the pronunciation. There is another name - the diquint system.
Operating principle and device
For many years, this system of the musical sphere has been commonly depicted as a ball or circle, which has a spiral inside. The topmost point symbolizes the notes, and moving in a clockwise direction, the remaining notes are already placed in accordance with the sequence. Considering the system in the opposite direction, one can already observe F, B-flat, and so on. Moreover, this established order is considered generally accepted and standard, and all because in “C” major there simply cannot be a single sign in the treble clef.
Quarters and fifths
Again, it is worth referring to the generally accepted design of this system. Namely, the highest point represents a marked note, which cannot always be denoted by syllables; marking with a single letter is acceptable. This tradition of the circular system has taken root due to the fact that the major key is devoid of any symbols, that is, it is simple.
The note indicated on the circle fully symbolizes the major key. For greater convenience, as a rule, another note can be added to it, which will already symbolize the opposite key - minor. As for the distance between them within a circle, the interval will be equal to either a fifth or a quart.
A little theory
In fact, the entire system of a circular quarto-fifth device is a spiral. Moreover, it does not connect in any place, but increases to infinity. But in practice, this tendency is considered inappropriate, because the entire tonality is distributed over eight or nine steps. It starts with “C” major, which is then no longer used. Moreover, if you take a tonality with a lower indicator, then the gamma will still completely coincide.
No one will develop the spiral to a larger number, because a tonality, for example, with thirteen symbols, is even difficult to pronounce. Such concepts as “g-double-sharp” and so on appear.
The main purpose of the circle of fifths
As a rule, this system is used to solve several problems at once. There are three main ones:
- search for identical keys;
- recognition of the number of characters in an existing or specified key;
- determining the maximum similarity of tones.
Considering the first problem and its solution, it can be noted that there are several degrees of relationship or similarity of tonality. In simple words, similar tones are those that differ from each other by one sign. And what is most characteristic is that in this system the differences are visible, as they say, to the naked eye, since the entire system is built as clearly as possible.
Related tonalities are also those that are located close to each other from the starting point. That is, the so-called neighbors.
The second solution to the problem involves determining the number of characters relative to the key. As a rule, their number can be from zero to seven, but in practice keys with a large number of signs are rarely used.
As for determining the degree of kinship, it is very simple to recognize it: the closer they are located relative to each other, the closer the degree of kinship itself will be. For example, a distance equal to one step implies the first degree and so on. But if there are already more than three steps, then there can be no talk of any relationship at all.
A little history
It is worth noting that musicians over the years have strived to find a special and universal system. It was she who ultimately became this circle, which represents simple diagram. This system allows you to quickly recognize the relationship of keys, chords and other necessary points. Each musician, using this circle, can independently determine the features of a given key, because directly on musical instrument this is inconvenient to do.
The emergence of the diquintic system
The first publications about her appeared in 1678. The author of the publication was a Russian composer with Ukrainian roots named Nikolai Diletsky. By the way, he is also the author of many other techniques related to musical direction.
Almost a century later, this system was recognized abroad. As for the implementation of the system in the work of musicians, it can be observed in many single compositions. The system was initially used in classic version, but our contemporaries were able to introduce it into jazz and even rock.
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How to perform the same music in a minor key using different sounds?
If you remember the circle of fifths in major keys (see the article “”), then it will not be difficult for you to understand the circle of fifths in minor keys.
Let's remember the following:
- Related tonalities are those that have 6 common sounds.
- parallel keys are those that have the same set of accidentals at the key, but one key is major and the other is minor.
- in parallel keys, the tonic of the minor key will be lower by a minor third than the tonic of the major key.
Circle of fifths in minor keys
Related keys of minor, as well as major, are located at a distance of a perfect fifth from each other. In this regard, the minor keys form their own circle of fifths.
Knowing the circle of fifths of sharp major keys, we recalculate the tonics (lowering them by a minor third) and get the circle of fifths of sharp minor keys:
| Table of minor sharp keys | |||||||||||||||||||||||||||
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And similarly, the circle of fifths for flat minor keys:
| Table of minor flat keys | |||||||||||||||||||||||||||
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Just like major, minor has three pairs of enharmonically equal tonalities:
- G sharp minor = A flat minor
- D sharp minor = E flat minor
- A sharp minor = B flat minor
Like the major circle, the minor one is “glad” to close, and in this it is helped by enharmonically equal sharp keys. Exactly the same as in the article "".
You can visually familiarize yourself with the circle of fifths of minor keys (we have arranged minor keys in the inner circle, and major keys in the outer circle; related keys are combined). Your browser must support flash:
Additionally
There are also ways to calculate the circle of fifths for minor keys. Let's look at them.
1. If you remember well the circle of fifths of major keys, but the above method of finding the tonic of a parallel minor key is inconvenient for some reason, then you can take the VI degree as the tonic. Example: looking for a parallel minor key for G-major (G, A, H, C, D, E, F#). We take the sixth degree as the tonic of the minor, this is the note E. That’s it, the calculation is complete! Since we found the tonic precisely parallel minor key, then the alteration signs of both keys coincide (in the found E-minor, like in G-dur, there is a sharp before the note F).
2. We do not start from the major circle, but calculate from scratch. Everything is by analogy. Let's take a minor key without accidental signs, this is A-minor. The V degree will be the tonic of the next (sharp) minor key. This is the note E. We place the alteration sign in front of the second degree (note F) of the new key (E-minor). That's it, the calculation is finished.
Results
Have you met circle of fifths in minor keys and learned how to count the number of signs in different minor keys.
