The theory of harmony knows the most important phenomenon of music, the brilliant period of whose dominance has already ended, and a comprehensive scientific and theoretical justification with which all scientists would agree still does not exist. This phenomenon is major and minor.
The quality that characterizes the opposite direction specific to the relationship between major and minor is usually denoted as mood. Major as “hard” (dur), “more” (maggiore), minor as “soft” (moll), “lesser” (minore) in their contrasting combination serve as a powerful means musical expressiveness, a means of a wide and varied range of action. Major and minor are the basis of two tonal modes common during the peak period of European music beginning in the 18th century. (Bach, Handel, Haydn, Mozart, Beethoven, Schubert, Schumann, Chopin, Liszt, Wagner, Glinka, Balakirev, Borodin, Mussorgsky, Tchaikovsky, Rimsky-Korsakov, Rachmaninov, Glazunov, Scriabin), modes that largely retain their significance and for 20th century music (Stravinsky, Messiaen, especially Prokofiev, Myaskovsky, Shostakovich, Shchedrin, etc.). Major and minor can play significant role and for the expression of other modes, outside the major-minor system. For example, Dorian and Phrygian and some others are modes of a minor basis, Mixolydian, Lydian are of a major basis (discovery of Zarlino).
For all these oppositions, the basic type of opposition is the same: major and minor, dur and minor, “hard” and “soft.”
The opposites themselves - “hard” and “soft” - have a history much older than major and minor as modes or even as chords. Back in ancient Greece there was a contrast between “hard” (or “syntonic”, that is, with a “sharp” tension of the middle strings in a tetrachord) and “soft” (with a “weak” tension) chromia (in Claudius Ptolemy). And Boethius considered diaton to be a “hard and natural” species (durius et naturalis), and chromium to be a “softened” species (mollius). Following this and whole tone(characteristic of the diatone) was contrasted by medieval theorists with the semitone (characteristic of the chromium), as the interval “hard”, “perfect”, simple - “soft”, “imperfect”, complicated. Later (in the 16th century) this opposition was transferred to thirds - major (tertia dura) and minor (tertia mollis; by J. Cocleus).
The first “hard” and “soft” scales were historically not our major and minor scales, and medieval solmization hexachords with the structure:
(Their syllables originate from the initial syllables of the lines of the hymn “Ut queant laxis”, adapted by Guido Aretinsky for the practical development of tones and semitones of the scale.)
In the hexachord system there are three provisions hexachord depending on whether it falls into soft b(that is B-flat), or hard(“square”) (that is si-bekar), or neither one nor the other hits. Accordingly, the three hexachords were called “soft” (molle), “hard” (durum) or “natural” (naturale) (example 135).
(Even N.P. Diletsky in 1679-1681 called music in the corresponding scales “dural” - without signs and “flat” - with flats.)
In the 17th century, the concepts dur and moll began to denote the modal inclination depending on the third, major and minor (in Kepler’s genus durum = g-e-d-c-H-G, a genus molle = g-es-d-c-B-G; at the end of the 17th century, A. Werkmeister used designations in the modern sense - a-moll, e-moll).
The modern formulation of the question of major and minor includes primarily three main problems:
1) the essence of major and minor triads;
2) the essence of the classical major and minor modes (tonal-functional system);
3) major and minor inclinations of the mode in the music of the 20th century.
The third problem is not related to the content of this work. The second is dealt with mainly in the chapter on tonal functions. Here we will talk about the first problem, which, naturally, is connected with the other two.
The first scientific theory of the essence of major and minor, the connection and opposition of the two moods was proposed by the famous Italian music theorist Josephfo Zarlino in the book “Fundamentals
harmony" (or "The Doctrine of Harmony", lit. "Harmonic Instructions"; Venice, 1558). In Chapter 31 of Part 3, he gives an extremely concisely presented, but completely fully expressed idea of interpreting major and minor as aesthetic opposites based on the ancient (even Pythagorean) aesthetic theory of proportions (according to the edition: Zarlino G. Le Institutioni Harmoniche. Venetia, 1573. P. 211). Main three types "average"(arithmetic, harmonic and geometric) or three types of “division” (the same) Zarlino sets out in the first part (Chapter 35 and following). Let us explain the three types of “averages” with a diagram (cf.: Zarlino G. Le Institutioni Harmoniche. Venetia, 1573. P. 54; "super-third" proportion - a ratio when the larger number exceeds the smaller one by one third):
Table 13
Arithmetic the average is obtained with three numbers, where the difference between the first and second is equal to the difference between the second and third. For example: 4, 3, 2 or 3, 2, 1, or 6, 4, 2, or 7, 4, 1, etc.
Geometric the average is obtained with three numbers, where the ratio of the first and second is equal to the ratio of the second and third. For example: 4, 2, 1 or 9, 3, 1, or 16, 4, 1, etc.
Harmonic the average is obtained with three numbers, where the ratio of the differences of the first and second, second and third is equal to the ratio of the first and third. For example:
Other examples: 6, 3, 2 or 15, 12, 10, or 20, 15, 12, or 28, 7, 4.
Harmonic mean - inversion of arithmetic:
Arithmetic = 1, 2/1, 3/1, 4/1, 5/1, 6/1;
Harmonic = 1, l/2, 1/3, 1/4, 1/5, 1/6;
(for clarification: 1, 1/2, 1/3 = 6, 3, 2).
Zarlino associates “all the diversity and perfection of harmony” with the action of two intervals - fifths and thirds or their “replicates” (that is, intervals derived from them, for example sixths). The sounds of the fifth are unchanged, but the third (that is, the major third) can take its position inside the fifth, being placed either below,
either at the top, thereby dividing number of fifths (3:2) in various ways. Since one of the sounds of the third coincides with either the lower or the upper, another one is added to the fifth one sound corresponding to the “average” value. Hence the justification of major and minor by the theory of “averages”. Zarlino writes that the major third (“la Terza maggiore”), placed in the lower part of the fifth, makes the harmony “cheerful” (allegra), and placed in the upper part - “sad” (mesta). Keeping in mind that Zarlino's way of noting times in string lengths rather than in vibration numbers, we get harmonic proportion as an explanation of the major (major triad) and arithmetic- to explain the minor (if we express the same thing in a way typical of our time - in numbers of vibrations, then the data will be reversed: harmonic proportion- for minor, arithmetic proportion - for major). Thus, the sounds of fifths are extreme members:
The third is placed in the middle in two ways:
At the end of chapter 31, Zarlino makes a remarkable statement: arithmetical proportionality is a little removed from the perfection of harmony, since its parts are not in their natural position; on the contrary, the harmonic consonates completely. In these words, Zarlino anticipates an orientation toward the “natural,” that is, the natural order of sounds (a natural scale that he did not know). According to Tsarlino, major and minor are equal and logical (since they materialize in sounds the two most important aesthetic laws of proportions, which in principle equal rights), and at the same time the major is close to nature, and the minor is more distant from it. Hence the difference in expression, the nature of expressiveness.
Zarlino also noted that these two moods - major and minor - underlie all modes (although Zarlino’s theoretical taxonomy of modes is still completely alien to the idea of a two-mode system), and divided all modes accordingly into two groups:
1) with a major third and a major sixth (above the finalis WITH, F, G);
2) with minor third and minor sixth (D, E, A).
The interpretation of Nikolai Diletsky (1679, 1681) is not deep scientific theory, but it is very colorful in its wording and original in its rationale for the relationship between major and minor triads. Formally considering music “triple in meaning” (threefold, that is, three frets) - “cheerful, pitiful and mixed”, Diletsky is in fact based on the idea of only two opposite modes, which he understands depending on the underlying triads - ut-mi-sol And re-fa-la. The dependence is interpreted unambiguously, which indicates full awareness of the two-mode nature of the modern Diletsky si-
stems: “if the tone is given to singing ut, mi, salt, there will be a merry music if the tone re, fa, la- will be pitiful." Diletsky receives the rationale for both triads from Guidon’s hexachord (the very names of the “six signs of Musik” speak about this - ut, re, mi, fa, sol, la), which coincides with the two main consents- “dark” and “light”. The hexachord is divided “in two”:
If Tsarlino divided the fifth in different ways, then Diletsky divides the six sounds of the hexachord, thereby representing a unique “modal” approach.
The German theorist Moritz Hauptmann, in his book “The Nature of Harmonics and Metrics” (1853), to explain the major and minor triads, leans towards the so-called "dualistic" interpretation according to which major and minor mirror opposite to each other. Hauptmann assumes that there are only three directly understandable intervals - the octave, the fifth and the (major) third. Merging into a monolithic unity, they provide only two chords - major and minor triads. The sounds from which these intervals are built and which thereby unite the intervals into a monolithic chord are located differently in both chords: in major it is the lower sound of the fifth, from which the intervals are directed up (C-G, C-e), in minor it is the top sound of the fifth, from which the intervals are directed downwards. Therefore, the sound that combines the major consonance (Klang) has have their own fifth and third, and the sound that unites the minor consonance, available(have) fifths and thirds. Hence the logical opposition between the states: the real (active) “to have” (das Haben) and the passive (passive) “to be” (das Sein). As a result, the major triad is tending (upward) strength, and minor - descending (down) heaviness.
Hugo Riemann (together with other German theorists - A. Oettingen, G. Helmholtz, Z. Karg-Ehlert) further developed the theory of dualism of major and minor, according to which minor is understood as mirror image(inversion) major. Riemann tried to find a natural, objective justification for major and minor. For a major (major triad) this is, naturally, a natural scale. For the minor, such a natural justification is obviously not found. Riemann turned to theory undertons, a series of which is mirror-symmetrical to the series of overtones, differing from it only in the direction of the same intervals (numbers), example 136.
Some confirmation of the Untertonian theory can be found. Because natural series(which is the overtone series and which Riemann also wants to represent the undertones) is realized in the phenomena of resonance, then in the spirit of Hauptmann’s theory the initial tone of the overtone series has all others, and the initial tone of the undertone available for all others (example 137).
However, such confirmation cannot refute the main objection to the theory of untertons as natural phenomena: the overtone series is really given by the nature of the sounding body, since overtones are produced by dividing the sounding body into parts. Undertones, in order to be equal natural phenomena with overtones, should be obtained multiplication(?!) mass of the sounding body, which is absurd (multiplication means that to extract the sound of the lower octave, for example, on a string, the length of the string must be doubled during vibration, which is physically impossible).
Despite the existence of a number of other theories of major and minor (among which we should mention the theories of A. S. Ogolevets and P. N. Meshchaninov, see p. 255), it is difficult to name one that could be considered answering all questions. Probably Zarlino's theory (including the problem of major and minor in general theory aesthetic proportions) and Hauptmann's theory ( in the best possible way substantiating the semantic content of the concepts of major and minor) in their complementarity provide the most reliable basis for a correct understanding of this most important phenomenon music.
Musical mode - another concept from music theory, with whom we will meet. Mode in music is a system of relations between stable and unstable sounds and consonances, which works for a certain sound effect.
There are quite a lot of modes in music, now we will consider only the two most common (in European music) - major and minor. You have already heard these names, and you have also heard their banal decodings such as major - a cheerful, life-affirming and joyful mode, and minor - sad, elegiac, soft.
These are only approximate characteristics, but in no case are labels - music in each of the musical modes can express any feelings: for example, tragedy in a major key or some bright feelings in a minor key (you see, it’s the other way around).
Major and minor - the main modes in music
So let's analyze the major and minor modes. The concept of mode is closely related to scales. The major and minor scales consist of seven musical steps (that is, notes) plus the last, eighth step repeats the first.
The difference between major and minor lies precisely in the relationship between the degrees of their scales. These steps are spaced from one another by a distance of either a whole tone or a semitone. In major, these relationships will be as follows: tone-tone semitone tone-tone-tone semitone(easy to remember - 2 tones semitone 3 tones semitone), in minor – tone semitone tone-tone semitone tone-tone(tone semitone 2 tones semitone 2 tones). Let’s look at the picture again and remember:
Now let's look at both musical modes specific example. For clarity, let’s build a major and minor scale from the note to.
You can see that there is a significant difference in the notation of major and minor. Play these examples on instruments - you will find a difference in the sound itself. Let me make one small digression: if you do not know how tones and halftones are calculated, then refer to the materials of these articles: and.
Properties of musical modes
Mode in music exists for a reason, it performs certain functions, and one of these functions is regulating the relationship between stable and unstable steps. For major and minor, stable degrees are the first, third and fifth (I, III and V), unstable - the second, fourth, sixth and seventh (II, IV, VI and VII). The melody begins and ends with steady steps if it is written in a major or minor mode. Unstable sounds always tend towards stable sounds.
The first step is of particular importance - it has a name tonic. Stable steps together form tonic triad, this triad is an identifier of a musical mode.
Other musical modes
The major and minor scales in music are not the only options for scales. In addition to them, there are also many other modes characteristic of one or another musical cultures or artificially created by composers. For example, pentatonic scale- a five-step mode in which the role of tonic can be played by any of its steps. The pentatonic scale is extremely widespread in China and Japan.
Let's summarize. We defined the concept, learned the structure of the scales of major and minor modes, and divided the steps of the scales into stable and unstable.
Did you remember that tonic is the main stage of the musical scale, basic sustained sound? Great! You've done a good job, now you can have a little fun. Look at this cartoon joke.
To know how to determine the tonality of a work, you first need to understand the concept of “tonality.” You are already familiar with this term, so I will just remind you without delving into the theory.
Tonality is generally the pitch of the sound. in this case– the pitch of a particular mode, for example major or minor. A mode is the construction of a scale according to a certain scheme and, in addition, a mode is a specific sound coloring of a scale (major mode is associated with light tones, minor mode is associated with sad notes, shadow).
The height of each particular note depends on its tonic (the main sustained note). That is, the tonic is the note to which the fret is attached. The mode, in interaction with the tonic, gives tonality - that is, a set of sounds arranged in a certain order, located at a specific height.
How to determine the tonality of a piece by ear?
It is important to understand here that not at any moment of the sound you can say with certainty what tone it sounds in this part works. Need to select individual moments and analyze them. What are these moments? This can be the very beginning or the very end of a work, as well as the end of a section of a work or even a separate phrase. Why? Because the beginnings and ends sound stable, they assert, and in the middle there is usually a movement away from the main key.
So, having chosen a fragment for yourself, pay attention to two things:
- What is the general mood in the work, what mood is it - major or minor?
- What sound is the most stable, what sound is suitable to complete the work?
When you determine this, you should have clarity. It depends on the type of inclination whether it is a major key or a minor one, that is, what mode the key has. Well, the tonic, that is, the stable sound that you heard, can simply be selected on the instrument. So, you know the tonic and you know the modal inclination. What else do you need? Nothing, just connect them together. For example, if you heard a minor mood and the root of F, then the key will be F minor.
How to determine the tonality of a piece of music in sheet music?
But how can you determine the tonality of a piece if you have sheet music in your hands? You probably already guessed that you should pay attention to the signs on the key. In most cases, using these signs and tonic, you can accurately determine the tonality, because key signs present you with a fait accompli by offering only two specific keys: one major and one parallel minor. What exactly is the tonality in this work depends on the tonic. You can read more about key signs.
Finding tonic can be challenging. Often this is the last note of a piece of music or its logically completed phrase, a little less often it is also the first. If, for example, a piece begins with a beat (an incomplete measure preceding the first), then often the stable note is not the first, but the one that falls on the strong beat of the first normal full measure.
Take the time to look at the accompaniment part; from it you can guess which note is the tonic. Very often the accompaniment plays on the tonic triad, which, as the name implies, contains the tonic, and, by the way, the mode too. The final accompaniment chord almost always contains it.
To summarize the above, here are a few steps you should take if you want to determine the tonality of a piece:
- By ear - find out the general mood of the work (major or minor).
- Having notes in hand, look for signs of alteration (at the key or random in places where the key changes).
- Determine the tonic - conventionally this is the first or last sound of the melody, if it does not fit - determine the stable, “reference” note by ear.
It is hearing that is your main tool in solving the issue that this article is devoted to. By following these simple rules, you will be able to determine the tonality of a piece of music quickly and correctly, and later you will learn to determine the tonality at first sight. Good luck!
By the way, a good hint for you on initial stage may become a cheat sheet known to all musicians - . Try using it - it’s very convenient.
Let's take a closer look at the piano keyboard. It has white and black keys. The distance between adjacent keys is called a semitone. Two semitones make up a tone.
For example, between the keys “C” and “C sharp” there is a semitone, between the keys “C sharp” and “D” there is also a semitone. And between the “do” and “re” keys there is a tone. There is a semitone between the “E” and “F” keys, because they are the closest keys, there is no black key between them.
Major and minor
A certain structure of semitones and tones makes up a musical mode. There are many modes in music. The most common of them are major and minor. You've probably heard these names.
Major mode is built according to the following system:
Tone-tone-semitone-tone-tone-tone-semitone
For example, we need to build a major scale from sound C. This is what we get:
We built "C major". If you build a major scale using the same scheme from the sound “D”, you get “D major”. And by analogy, you can build a major scale from any sound.
Minor scale is built according to a different scheme:
Tone-semitone-tone-tone-semitone-tone-tone
For example, let's build a minor scale from the sound A, as you probably already guessed, A minor. Here's what it looks like:
Using the same principle, you can build minor scales from any other sounds.
It turns out that tonality is the pitch position of a major or minor scale. That is, building a scale from a specific sound (tonic). The sounds of a scale are called scale degrees. They are designated by Roman numerals.
One of the functions of the fret is the ratio of stable and unstable steps. I, III and V are stable stages. II, IV, VI, VII – unstable. Unstable sounds gravitate towards stable ones. Usually piece of music begins and ends in steady steps. Stage I (tonic) has special meaning, it is the most important and the most stable.
The tonic triad consists of stable degrees (I, III and IV). In C major these will be sounds (do-e-sol). This is the basis of the mode, the most stable chord to which all other chords of the mode gravitate. In addition to the tonic, the main triads include the triad of the fourth degree (or subdominant), the triad of the fourth degree (dominant). The dominant (denoted by the Latin letter D) is unstable, always gravitating towards the tonic (denoted by the letter T). Subdominant (denoted by the letter S) – expresses mild instability, gravitates towards the tonic much less actively than the dominant.
The main triads (T, S, D) form the basis of mode tonality. When they say about a song that it is built on three chords, they usually mean these chords.
In addition to the main triads, there are also side triads. These include II, III, VI, VII stages. They do not have special names, except for the VII step, they are called by the number of the step, for example, the triad of the 2nd step. The triad of the 7th degree is called the diminished triad.
Exercise
To consolidate the material, I suggest completing this task.
Construct the following scales yourself according to the scheme for constructing major and minor: F major, G major, B minor, D minor. The task must be completed in writing in pencil on a sheet of music.
If anything is unclear, write your questions in the comments.