Today we will do some interesting work - we will learn to look for distant related tonality, and to do it as quickly as we find “relatives” in the first degree.
To begin with, we will clarify one important detail. The fact is that someone prefers to use the Rimsky-Korsakov system, according to which between tonalities there can be three degrees of kinship, and someone adheres to another system, according to which there are not three, but four degrees. So, we will take Rimsky-Korsakov’s system of kinship as a basis, since it is simpler, but we also don’t refuse the second system and we will separately discuss this topic at the end.
The difference between the 3rd and 4th-level systems of kinship is that one of the groups of keys, namely the second, is simply divided into two, or, if you will, it absorbs two, which constitute the 2nd and 3rd degree in 4-degree system. Let's try to visualize what was said:
How to look for related second degree tonalities?
Here we just have to find 12 keys. The principle itself, from where they come from, is thoroughly analyzed in the article “Degrees of Kinship of Tonalities,” and now we will simply learn to find them in major and minor.
Key of the second degree of kinship for major
In the major of 12 keys the major must be 8 pieces, the other 4 must be minor. Without unnecessary problems, we will turn to the steps of the original tonality. Perhaps, it would be more correct to search by building intervals from the tonic, but it is easier to associate new tonalities with the steps of the original one.
So, for starters, the minor tonalities are 4, so we simply memorize the steps: I (the minor minor of the same name), V (minor dominant), VII (just remember - the seventh), VIIb (the seventh reduced).
For example, for the C-dur tonality (letter of the keys) this will be c-moll, g-moll, h-moll and b-moll.
Now major keys - there are 8 of them and they are paired, now you will understand what is meant by the word "paired". They are tied to the following steps: II, III, VI and VII. And everywhere it will be like this: natural level and lowered, that is, two major keys for each level (one without bemolik, the other with a bemolik).
For example, for the same C major, it will be: D-dur and Des-dur, E-dur and Es-dur, A-dur and As-dur, H-dur and B-dur. Everything is very simple, the main thing to remember magic code - 2367 (composed of step numbers).
Key of the second degree of kinship for minor
If our initial tone is minor (for example, in C minor), then for her 12 related to the second degree tonalities for her will be divided like this: on the contrary, only 4 major and the remaining 8 minor.
Tonics of major keys will coincide with such steps (remember): I (like major), II (simple second), IIb (second low), IV (major subdominant). For example, for C minor, these will be such "cousins": C-dur, D-dur, Des-dur and F-dur.
There are eight minor keys and, attention, everything is very interesting here: their tonics occupy the same degrees as the 8 major major tonics: II, III, VI and VII in natural and reduced form. That is, such tonalities as d-moll and des-moll (nonexistent tonality, but everything is as it is), e-moll and es-moll, a-moll and as-moll, h- moll and b-moll.
Interesting observation (you can skip)
If we talk in general about cousins for major and minor, then a number of interesting moments are pegged:
- out of 24 (12 + 12) tonic for each case there are 9 + 9 (18) pieces that coincide tonally and differ only in the mood mood (including 8 + 8, which are associated with "code 2367" and 1 + 1 of the same name);
- the keys of the same name are related to the second degree in this system, and in the 4-degree system they generally turn out to be “second cousins”;
- the largest number of second-degree tonalities is associated with introductory steps (VII - 4 tones for major, II - 4 tonalities for minor), with steps on which reduced triads were created in the original tone in its natural form, due to which these tonics they did not enter the circle of first-degree relatives (a kind of compensation happens, as it were - multiplication by two in the next degree);
- The second degree kinship tonalities are: for major - the minor dominant tonality, and for minor - the major subdominant's tonality (do we remember special cases in the circle of first degree tonal minor harmonic major and major major dominant?).
Well, enough, it's time to move on and move on to the next, third degree of kinship, which characterizes the relationship between the most distant tonalities (there is not a single common triad in them).
Third degree relationship
Here, in contrast to the problem of the previous degree, it is not necessary to invent an elephant, to reinvent the calculator or the bicycle. Everything is known for a long time, everyone successfully uses it. I'll tell you too!
Total five tonalities. In the same way, we first consider the case if the initial key is major, and then the case if we are looking for missing relatives for the minor key.
Well, by the way, there is something in common between these cases, there are even general tonalities (two whole pieces). The total is the tonic of the two mentioned common keys are at a triton distance from the original tonic. And we use this tonic twice - for major and minor tonality.
So, if we have the original key of the major (the same in C major, for example), then at the distance of the triton from its tonic there is a note in F-sharp. With F sharp, we do both major and minor. That is, two out of five tones are Fis-dur and fis-moll.
And then just miracles! From the received minor tritonic tonality walking through the clean quints up. All you need to do three steps - we get the three remaining tones: cis-moll, gis-moll and dis-moll.
If the initial key is minor (in C minor for example), then we do almost the same thing: we build a newt, and we immediately get two keys (Fis-dur and fis-moll). And now, attention, from the major tritonic tonality (that is, from Fis-dur) walking three quints down! We get: H-dur, E-dur and A-dur.
For those who adhere to the 4-degree system
It remains to make out how to find related keys to those who prefer to allocate four degrees instead of three. At once I will say that the fourth degree is the same third one without changes. There are no problems with this.
But, as has already been said, the second “by three” incorporates the second and third “by four”. And the second degree includes only 4 keys, and the third - 8. For yourself, you can find 12 tonalities at once, and then exclude 4 tones of the second degree of kinship from them, so that you have 8 tonalities of the third degree.
How to find the tonality of the second degree "in four"?
This is the main feature of the Moscow system of kinship of keys. And, of course, everything here is logical and simple. It will be necessary to find double dominants and double subdominants (as if they were not called correctly).
In major, we look for the tonality of the double dominant (II step with a major triad on it) and its parallel, as well as the tonality of the double subdominant (VII low with a major triad on it) and its parallel. Examples for C major - D-dur || h-moll and B-dur || g-moll. Everything!
In the minor, we do the same, only everything that we find is left minor (that is, the double dominant is not that - DD, and this dd is natural, about the subdominant - similarly). We add the parallels to the found and we get the tonalities of the second degree of relationship for up to the minor: d-moll || F-dur and b-moll || Des-dur. All ingenious is simple!
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