What is a major? Musical mode What is C major theory.

In music, there are two musical modes that are basic - these are major and minor. Let's talk in more detail about what a major is, what a major mode is and how the major mode differs from the minor mode, as well as how this word is used in modern slang.

What is major: definition

Major is a set of sounds of a musical instrument, implying a peppy and cheerful tone. This wording is due to the fact that all music is inherently created to convey the feelings and emotions of a person. A composer who composes a certain musical composition or symphony is based on his feelings and puts them into music.

The process of developing a musical composition is quite complex and often intertwined with the experimental method of selecting the necessary sounds. Each recorded note is followed by a heavy selection of subsequent notes and an attempt to harmonize them with each other so that the music sounds pleasing to the human ear.

major scale

Due to the fact that the set of sounds is unlimited, and the human ear is able to perceive sounds in the range from 20 to 20,000 Hz, it became necessary to classify certain simple sets of keys. The main ones that can be played on any musical instrument are the major and minor modes. It turns out that the major scale is the sequence of any composition, which, on a psychological level, evokes in a person associations with a cheerful and cheerful mood. Also, any composition can be recorded in a minor key to get the opposite effect of sound and perception on a psychological level. A minor mode is a mode whose sounds form a small and minor triad.

Differences between major and minor

Any set of notes can be written as a major or minor scale. That is, any musical composition consisting of a certain set of notes can be played both in a minor sound and in a major one.

The difference between the major and the minor is that between the second tone and the first in the minor there is a small third, and in the major - a large one. In simple terms, major-minor is a harmonic expression of the states of the soul joy-sadness.

Music term in everyday life

In youth slang, the word major is used in a context indicating wealthy people living in abundance and abundance. It is believed that people with great material wealth get almost everything they want. And the person who gets what he wants is in joy and euphoria. And vice versa: people who do not have a large amount of material wealth do not always get what they want and therefore are not always in a state of joy and pleasure.

Musical mode- Another concept from musical theory, which we will get acquainted with. Lad in music- this is a system of relations of stable and unstable sounds and consonances, which works for a certain sound effect.

There are quite a few frets in music, now we will consider only the two most common (in European music) - major and minor. You have already heard these names, you have also heard their banal interpretations such as major - a cheerful, life-affirming and joyful way, and minor - sad, elegiac, soft.

These are only approximate characteristics, but by no means labels - music in each of the musical modes can express any feelings: for example, tragedy in major or some kind of bright feelings in minor (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 steps of their scales. These steps are separated 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). Look at the picture again and remember:

Now let's look at both the one and the other musical mode using a specific example. For clarity, let's build the major and minor scales from the note before.

You can see that there is a significant difference in the notation of major and minor. Play these examples on the instruments and you will find the difference in the sound itself. I will allow myself one small digression: if you do not know how tones and semitones are considered, then refer to the materials of these articles: and.

Properties of musical modes

Lad in music exists for a reason, it performs certain functions, and one of these functions is the regulation of the relationship between stable and unstable steps. For major and minor, the stable steps are the first, third and fifth (I, III and V), the unstable ones are the second, fourth, sixth and seventh (II, IV, VI and VII). A melody begins and ends with steady steps, if it is written in a major or minor scale. Unstable sounds always strive for stable sounds.

The first stage is of particular importance - this, it has a name tonic. Stable steps together form tonic triad, this triad is the identifier of the musical mode.

Other musical modes

Major and minor scales in music are not the only variants of scales. In addition to them, there are many other modes that are characteristic of certain musical cultures or artificially created by composers. For example, pentatonic scale- a five-step mode, in which any of its steps can play the role of tonic. The pentatonic scale is extremely widespread in China and Japan.

Let's summarize. We gave a definition of the concept, learned the structure of the scales of major and minor modes, divided the steps of the scales into stable and unstable.

Did you remember that tonic is main stage of the musical mode, the main sustained sound? Great! Well done, now you can have some fun. Check out this cartoon joke.

Dedicated to L. G. and A. G., muses and fairies, who disenchanted my sense of beauty ...

Soft music played softly. Her unhurried minor chords flowed smoothly around, taking us somewhere into the deep distance. For some reason, there was a hint of sadness ... then the tempo began to increase, high notes gave way to low ones, the tension gradually increased, and finally a bright, solemnly joyful, major denouement sounded. What happened to us? Mystery of nature...

To avoid ambiguity, here are a few introductory phrases that clarify the terminology.

As is known, any sound signal of limited duration can be represented as an equivalent Fourier series (spectrum) as a sum of "pure" tones (sinusoidal oscillations) with different amplitude, frequency and initial phase. In this work, we will consider mainly stationary sound signals that do not change in time.

According to the fundamental tone (first harmonic) of sound, the lowest frequency of sound is called. All other frequencies above the fundamental are called overtones. That. the first overtone is the 2nd highest tone of the sound spectrum. An overtone with a frequency N times the fundamental frequency (where N is an integer greater than 1) is called the Nth harmonic.

Musical (or harmonic) is a sound that consists only of a set of harmonics. In practice, this is a sound, all overtones of which approximately fit into the harmonic frequencies, and some arbitrary harmonics may be absent, including the first one. In this case, the main tone is called "virtual" and its height will be determined by the psyche of the subject-listener from the frequency ratios between real overtones.

One musical sound can differ from another in its fundamental frequency (pitch), spectrum (timbre) and loudness. In this work, these differences will not be used, but all our attention will be focused on the mutual ratio of the pitches of the sounds.

We will consider the effects of listening to one or more musical sounds taken together, taken outside of any other musical context.

As you know, the simultaneous sounding of two musical sounds of different heights (two-voice chord, dyad, consonance) can give the subject the impression of a pleasant (euphonious, continuous) or unpleasant (irritating, rough) combination. In music, this impression of consonance is called consonance and dissonance, respectively.

It is also known that the simultaneous sounding of three (or more) musical sounds of different heights (three-voice chord, triad, triad) is capable of producing an emotional impression of various colors in the subject. Different - according to the sign (positive or negative) and strength (depth, brightness, contrast) of the corresponding emotions.

Emotions evoked in people by listening to music, according to their type, among all known emotions, belong to aesthetic (intellectual) and utilitarian emotions. On the classification of emotions, incl. musical see more.

For example, the triad of the notes “do, mi, sol” (major) and the triad of the notes “do, mi-flat, sol” (minor) have, respectively, a pronounced “positive” and “negative” emotional coloring, usually referred to as “joy” and "sadness" (or grief, sadness, suffering, regret, grief, longing, despondency - according to).

The emotional coloring of chords practically does not depend on changes in the overall pitch, volume or timbre of the sounds that make them up. In particular, we will hear an almost unchanged emotional coloring in chords from fairly quiet pure tones.

Looking ahead, we note that if some arbitrary chord can be defined as minor or major, then for the vast majority of subjects, the emotions caused by its sound will be utilitarian, i.e. refers to the category of "sadness or joy" (having a negative or positive sign of emotion). The emotional strength (brightness of emotion) of this chord in the general case will depend on the specifics of the situation (the state of the subject-listener and the structure of the chord). Essentially (in a statistical sense) one can put a one-to-one correspondence between major/minor and the emotions they cause. And most likely it is the emotional coloring of these chords that allows "ordinary people" to recognize the major or minor key of individual chords.

That. Let us summarize that the aesthetic component of the “pleasant-unpleasant” sound (consonance and dissonance) arises in us when listening to two-part chords, and the emotional component of the “joy-sadness” sound (major and minor) arises in us only when a third voice is added. Note that other types of chords (non-major or non-minor) may not have the utilitarian component of the "contained" emotions.

CHORD PROPORTIONS

It is logical to make the assumption that when a different number of simultaneous musical sounds is perceived, the rule of transition from quantity (1, 2, 3 ...) to quality is triggered. Let's see what new qualities can appear in this case.

Even in ancient times, it was discovered that a chord of two (individually pleasant) sounds can be pleasant or unpleasant (consonant or dissonant) to the ear.

It has been found that such a chord sounds consonant if the ratio of the pitches of its sounds (with an error of say 1% or less) is a proportion of relatively small whole (natural) numbers, in particular from numbers from 1 to 6 and 8.

If this proportion consists of relatively large coprime numbers (15/16, etc.), then such a chord sounds dissonant.

I note that the accuracy with which the whole proportions of musical sounds should be determined, as well as the choice of a specific proportion from a number of alternatives, may depend on the context of the situation. A brief historical excursion into musical intervals is given in.

The list of pitch ratios of two musical sounds (musical intervals) in descending order of consonance according to looks like this: 1/1, 2/1, 3/2, 4/3, 5/4, 8/5, 6/5, 5/3, and further dissonances 9/5, 9/8, 7/5, 15/8, 16/15.

This list may not be complete (at least in terms of dissonances), because is based on possible musical intervals within the equal temperament system of 12 notes per octave (RTS12).

It is also known that the perception of consonance and dissonance occurs at an intermediate level of the human nervous system, at the stage of preliminary processing of individual signals from each ear. If, with the help of headphones, two sounds are separated into different ears, then the effects of their “interaction” (consonance peaks, virtual pitch) disappear.

Slightly digressing to the side, I note that although today there are more than a dozen theories of consonance and dissonance, it is very difficult to give a clear explanation why the interval 7/5 is dissonance, and 8/5 is consonance (moreover, more perfect than, for example, 5/3) is very difficult .

However, for the most part, we don't need it here. A good topic for a separate study?

So, we note the following new fact. When switching from listening to one musical sound to two simultaneous sounds, the subject has the opportunity to extract information from the ratio of the pitches of these sounds. Moreover, the subject's psyche highlights the ratios of heights in the form of proportions of relatively small natural numbers, which are ranked in one category - consonance / dissonance.

Now let's move on to the consideration of chords from three sounds. In triads, in comparison with consonances, the number of (pairwise) intervals increases to three, and in addition, a new entity appears - the “monolithic” triad itself (like a “triple” interval) - the general ratio between the pitches of all three sounds considered together.

This monolithic ratio can be written as the "direct" proportion A:B:C or in another form as the "inverse" proportion (1/D):(1/E):(1/F) of coprime natural triples A, B,C or D,E,F. Purely mathematically, all such proportions can be divided into three main groups:

A direct proportion is "simpler" than an inverse one, i.e. A*B*C< D*E*F

The inverse proportion is "simpler" than the direct one, i.e. A*B*C > D*E*F

Both proportions are the same ("symmetrical"), i.e. A*B*C = D*E*F (and thus A=D, B=E, C=F).

That. the new quality of the triad - information of a new type - can only be contained in these triple proportions, falling into one of the three categories described above.

Depending on the degree of consonance of all pairwise intervals, triads can be either consonant or dissonant. In some cases (when using various integer approximations), the choice of a specific composition of both proportions can be ambiguous. However, for consonant chords, this ambiguity does not appear.

According to musical practice, there are four main types of triads - major and minor (consonances), increased and decreased (dissonances). Almost all consonant chords can be categorized as major and minor.

The pitch ratios of the aforementioned major triad are, with great accuracy, a direct proportion of 4:5:6. The pitch ratios of the aforementioned minor triad are, with great accuracy, the inverse proportion /6:/5:/4. The direct and inverse proportions of the augmented and diminished triads are the same, because they consist of equal intervals (4-4 and 3-3 RTS12 semitones), and these equal proportions look like /25:/20:/16 = 16:20:25 and /36:/30:/25 = 25, respectively: 30:36.

The ratio of the pitches of major triads is always more simply (using smaller integers) expressed in direct proportions, and minor triads - in inverse proportions, and this is a well-known fact. Already Josephfo Zarlino (1517-1590) knew the opposite meaning of major and minor chords (Istituzione harmoniche 1558). However, even 450 years later, it is not so easy to find a serious work in which this fact is widely used for harmonic analysis or chord synthesis. The reason for this may have been persistent, but erroneous attempts by various authors to explain the phenomenon of major and minor (see below). Maybe the connection of chords with the proportions of heights has become something like the forbidden topic of "perpetual motion"?

On the basis of simple mathematics and experimental data, we will postulate: any major chord (it is simpler in direct proportion) can be turned into a minor chord (it is easier in inverse proportion) if instead of direct proportion we write the inverse of the same numbers. Those. if the proportion A:B:C is major, then the inverse (different!) proportion /C:/B:/A is minor. Of course, any direct proportion can (without changes!) be represented as an inverse, and vice versa. In particular, 4:5:6 = /15:/12:/10 and /4:/5:/6 = 15:12:10.

Summarizing all this, we can conclude that the three groups into which all the proportions of triad pitches are divided really play an important role in musical practice, and correspond to the division of chords into major, minor and "symmetrical" (consisting of the same intervals).

One may wonder: what is the "internal" representation of musical triads in the subject's psyche? How does he use the information about the aforementioned “new quality” of the triad?

Taking into account the highly developed apparatus of the human auditory system, it can be assumed that although the higher nervous system of a person is quite capable of representing a minor triad in the form of a direct proportion (15:12:10), it is also (if not easier) capable of presenting the same triad in in the form of an inverse proportion (/4:/5:/6), and “at the first comparison” of these proportions (to determine the category), “discard” the straight line because of its 15 times greater complexity (the product of three numbers of direct and inverse proportions is equal to 1800 vs 120).

We will further call the main proportion of the chord one of the two proportions of the pitches of its sounds (direct or reverse), which consists of smaller numbers (in the sense of their product), while the other proportion will be called secondary. That. The main proportion of a major chord will always be a direct proportion, and a minor one will always be an inverse proportion.

And finally, we note that although the aforementioned minor and major triads consist in pairs of the same intervals (4:5, 4:6, 5:6), they have the opposite emotional coloring, which is absent from any separate pair of their sounds. The only difference between monolithic triads (minor and major) is the fact of mutual inversion of their main proportions.

It is logical to conclude that the corresponding new "emotional" information of the chord is contained precisely in this last property (the type of main proportion), which can only manifest itself when three or more sounds are combined, but cannot be detected when two are combined (because, let's say A:B is exactly the same as /A:/B). There is simply no other source of (emotional) information contained in a triad and cannot be (do not forget that we are considering stationary sounds with an unchanged spectrum). An additional confirmation of this conclusion is that the sound of "symmetrical" chords lacks a utilitarian component of emotions.

Example 1. Sounding Proportions

2:3:4 = /6:/4:/3 gives a soft major. 2:3:6 = /3:/2:/1 gives a soft minor.

3:4:5 = /20:/15:/12 gives a brighter (contrasting) major, and 20:15:12 = /3:/4:/5 gives a deeper (contrasting) minor.

4:5:6 = /15:/12:/10 gives the brightest major, and 10:12:15 = /6:/5:/4 gives the deepest minor.

To listen to chords, it is better to use pure tones with exact frequency ratios, using for example. .

MAJOR AND MINOR THEORIES

Chords have been sounding in music for many hundreds of years, and almost as many people have been thinking about the reasons for their harmony.

For two-part chords, the first explanation of this property was made a very long time ago (and captivatingly simple and clear, if you close your eyes to some dissonances - see above). For three-part major and minor chords, the above facts about direct and inverse proportions were also established quite a long time ago.

However, it turned out to be much more difficult to find an answer to the question why different chords have a different sign (and strength) emotional coloring. And to the second question - why does a minor chord, for all its complexity (when presented in direct proportions - so to speak, in "major notation") sound harmonious, but let's say "almost the same" in terms of complexity of the numerical proportion "dischord" (such as 9:11 :14) sounds unpleasant - it was difficult to answer.

Generally speaking, it was not entirely clear how to justify both major and minor "equally well"?

This mystery of the nature of major and minor has been tried by many authoritative researchers. And if the major was still explained “quite simply” (as it seemed to many authors, for example, “purely acoustically”), then the problem of substantiating the minor, similar in clarity, is apparently still on the agenda, although there are a great many very different theoretical and phenomenological constructions, trying to give its solution.

The interested reader may refer to .

Historically, theories of the minor were based either on non-physical "undertones" (overtones with a frequency an integer number of times less than the frequency of the fundamental tone of the sound - not existing in reality), or on the "metaphysical" facts of the triple coincidence of overtones in chord sounds, which, although it can, but does not have to always be the case - for example, in the case of a chord of pure tones.

Some authors, when "substantiating" chords, also referred to the non-linear properties of hearing, described for example. V . However, this indisputably occurring fact very rarely works in practice, because even a chord that is not too weak in volume will not generate distinguishable combination tones due to non-linearity.

Other authors used very complex musical-theoretic constructions (or purely mathematical schemes, closed as “things in themselves”), the exact meaning of which was often impossible to understand without a detailed study of the specific terminology of these theories themselves (and sometimes this explanation was based on a paraphrase of some abstract terms through others).

Some authors are still trying to approach this issue from the point of view of cognitive psychology, neurodynamics, linguistics, and so on. And they almost succeed ... Almost - because the chain of explanations is sometimes too long and far from indisputable, and besides, there is no algorithmic formalization of theories, and so on. basis for their quantitative experimental verification.

For example, in one of the most interesting, detailed and versatile studies of the phenomenon of major and minor, a hypothesis is presented that the basis of the emotional content of sounds was laid down by nature in the instinct of higher animals, which was further developed in humans. It has been experimentally established that the dominance of a particular individual of the pack in the animal world is accompanied by the use of low or falling sounds of "speech", and subordination - by the use of high or rising ones. Further, it is assumed that dominance is equal to "joy", and subordination - "sadness". Then a table is built of dissonant symmetrical triad chords (with two identical intervals from 1 to 12 semitones PTC12) with a list of changes of these chords to minor when increasing or to major when decreasing the pitch of any sound of the original chord by one semitone.

Even apart from the fact that some of the changed chords cannot be unambiguously attributed to major or minor, it is not clear why, when listening to a chord, a human subject must necessarily (and instantly) “think” that one of the sounds of this (consonant) chord is shifted from the sound of another (uniquely defined and, moreover, dissonant) chord for some fixed interval - a semitone? And how can this rather abstract thought turn into "innate" emotions? And why should the mind be limited only by the capabilities of the RTS12? RTS12 what, also came up with Nature and invested in instinct?

However, I agree that the emotional content of major and minor is based on the emotions available to many higher animals ... it's not clear if they can experience these emotions by listening to chords? I don't think so. Because determining the mutual proportions of the pitches of three or more sounds of a chord is a process of a higher order of complexity than determining the pitch of one sound (or the direction of change in this pitch).

The human hearing apparatus has received special development in connection with the advent of verbal communication, which has given rise to the ability to analyze the spectrum of complex sounds in detail and quickly, the by-product of which is most likely our ability to enjoy music.

Utilitarian emotions in higher animals (as well as in humans), however, may well be evoked through the perception of information from other sense organs - and above all - through the visual perception of events and their further interpretation.

A few words about the emotionality of human speech and monophonic music. Yes, they can "contain" utilitarian emotions. But the reason for this is the essential non-stationarity of the spectrum - changes in the pitch and/or timbre of these sounds.

And yet - about the individual differences of the subjects. Yes, with the help of special education (training) it is possible to accustom people (as well as some animals) to the fact that even one sound (or any chord) will evoke utilitarian emotions in them (grief from a reflexively expected whip or joy from a carrot ). But this will not be in accordance with the natural nature of things which we seek to establish.

Here is a phrase from a 2008 doctoral dissertation in musicology that seems to put an end to the issue of known theories of major and minor: “despite the fact that many authors have described the perception of major / minor chords and scales, it still remains a mystery why major chords feel happy and minor chords feel sad.”

I think that the development of a correct theory of major and minor is only possible if two important conditions are met:

Attracting additional areas of knowledge (except music and acoustics), -using the mathematical apparatus of additional areas of knowledge.

We need to remember history. The idea that the "meaning" of a chord must be sought outside the "old" space of music theory was first heard at least a hundred plus years ago.

Here are a couple of quotes.

Hugo Riemann (1849-1919) by the end of his career abandoned the justification of major and consonance through the phenomenon of overtones and stood on the psychological point of view of Karl

Stumpf, considering the overtones only as an "example and confirmation", but not proof.

Karl Stumpf (1848-1936) transferred the scientific foundation of music theory from the field of physiology to the field of psychology. Stumpf refused to explain consonance as an acoustic phenomenon, but proceeded from the psychological fact of "tonal fusion" (Stumpf C.Tonpsychologie. 1883-1890).

So, concluding the section, I will note that, most likely, Stumpf and Riemann were already absolutely right that it is impossible to substantiate a chord either acoustically, or metaphysically, or purely musically, and what is necessary for this is the involvement of psychology.

Now let's approach the question "from the other end" and ask the question: what is emotion?

THEORIES OF EMOTION

Let us briefly consider two theories of emotions that, in my opinion, are closest to the level at which the possibility of applying their laws opens up in such a complex issue as the psychological structure of the phenomena of music perception.

For other theories and details, I refer the reader to a rather extensive review in.

Frustration Theory of Emotions

In the 1960s the theory of cognitive dissonance by L. Festinger arose and was thoroughly developed.

According to this theory, when there is a discrepancy between the expected and actual results of an activity (cognitive dissonance), negative emotions arise, while the coincidence of expectation and result (cognitive consonance) leads to the appearance of positive emotions. The emotions arising from dissonance and consonance are considered in this theory as the main motives for the corresponding human behavior.

Despite many studies confirming the correctness of this theory, there are other data showing that in some cases, cognitive dissonance can also cause positive emotions.

According to J. Hunt, for the emergence of positive emotions, a certain degree of discrepancy between attitudes and signals is necessary, some “optimum discrepancy” (novelty, unusualness, inconsistency, etc.). If the signal does not differ from the previous ones, then it is evaluated as uninteresting; if it differs too much, then it seems dangerous, unpleasant, annoying, etc.

Information theory of emotions

Somewhat later, an original hypothesis about the causes of the phenomenon of emotions was put forward by P.V. Simonov.

According to her, emotions appear due to a lack or excess of information necessary to satisfy the needs of the subject. The degree of emotional stress is determined by the strength of the need and the magnitude of the deficit of pragmatic information necessary to achieve the goal.

P.V. Simonov considered the advantage of his theory and the “formula of emotions” based on it that it contradicts the view of positive emotions as a satisfied need. From his point of view, a positive emotion will arise only if the information received exceeds the previously available forecast regarding the probability of satisfying the need.

Simonov's theory was further developed in the works of O.V. Leontiev, in particular, by 2008 a very interesting article was published with a number of generalized emotion formulas, one of which I will describe in detail below. I quote next.

By emotions, we will mean a mental mechanism for controlling the subject's behavior, assessing the situation according to a certain set of parameters ... and launching the corresponding program of his behavior. In addition, each emotion has a specific subjective coloring.

The above definition assumes that the type of emotion is determined by the corresponding set of parameters. Two different emotions must differ in a different set of parameters or their range of values.

In addition, various characteristics of emotions are described in psychology: sign and strength, time of occurrence relative to the situation - previous (before the situation) or ascertaining (after the situation), etc. Any theory of emotion must allow for an objective determination of these characteristics.

The dependence of an emotion on its objective parameters is called the formula of emotions.

One-Parameter Emotion Formula

If a person has a certain need with the value P, and if he manages to get a certain resource Ud (for Ud > 0) that satisfies the need, then emotion E will be positive (and in case of loss of Ud< 0 и эмоция будет отрицательной):

E \u003d F (P, Ud) (1)

The resource Ud is defined in the work as the "Level of achievements", and the emotion E - as ascertaining.

For concreteness, you can imagine a person playing a new game for himself and not knowing what to expect from it.

Joy.

If the player has won a certain amount of UD > 0, then a positive emotion of joy arises with the power

E \u003d F (P, Ud).

Woe.

If the player "won" the amount of Oud< 0 (т.е. проиграл), то возникает отрицательная эмоция горя

force E \u003d F (P, Ud).

Another method for formalizing emotions is proposed in the work.

According to him, emotions are considered as a means of optimal behavior control, directing the subject to achieve the maximum of his “target function” L.

An increase in the objective function L is accompanied by positive emotions, a decrease - by negative emotions.

Since L depends in the simplest case on some variable x, then emotions E are caused by a change in this variable with time:

E = dL/dt = (dL/dх)*(dх/dt) (2)

It is also noted that along with the above-described (utilitarian) emotions, there are also so-called. “intellectual” emotions (surprise, conjecture, doubt, confidence, etc.) that arise not in connection with a need or goal, but in connection with the intellectual process of information processing itself. For example, they may accompany the process of observing abstract mathematical objects. A feature of intellectual emotions is the absence of a specific sign in them.

At this stage, we will stop quoting and move on mainly to the presentation of the original ideas of the author.

MODIFICATION FORMULA OF EMOTIONS

First of all, we note that formulas (1, 2) are very similar, given that the resource parameter Yd is actually the difference between the current and previous value of a certain integral resource R. For example, in the case of our gambler, it is logical to choose his total capital as R , Then:

UD = R1 - R0 = dR = dL

However, both formulas (1, 2) are "not entirely" physical - they equate quantities that have different dimensions. It is impossible to measure, say, time in kilometers or joy in liters.

Therefore, firstly, the formulas of emotions should be modified by writing them in relative terms.

It is also desirable to clarify the dependence of the strength of emotions on their parameters. to increase the credibility of the results for a wide range of changes in these parameters.

To do this, we use the analogy with the well-known Weber-Fechner law, which says that the differential perception threshold for a variety of human sensory systems is proportional to the intensity of the corresponding stimulus, and the magnitude of the sensation is proportional to its logarithm.

Indeed, the joy of that very player should be proportional to the relative size of the winnings, and not absolute. After all, a billionaire who loses one million will not grieve as much as the owner of a million with a small ponytail. And the heights of the “most similar” musical sounds are connected by an octave ratio, i.e. also logarithmic (an increase in the frequency of the fundamental tone of the sound by 2 times).

I propose to write the modified emotion formula (1) as follows:

E = F(P) * k * log(R1/R0), (3)

where F(P) is a separate dependence of emotions on the need parameter P;

k - some constant (or almost constant) positive value, depending on the subject area of ​​the resource R, on the base of the logarithm, on the time interval between the measurements of R1 and R0, and also possibly on the details of the nature of a particular subject;

R1 is the value of the objective function (total useful resource) at the current time, R0 is the value of the objective function at the previous time.

It is also possible to express the new emotion formula (3) in terms of the dimensionless value L = R1/R0, which can be logically called the relative differential objective function (the current value of the integral objective function relative to some previous moment of time, which is always at a fixed distance from the current moment).

E = F(P) * Pwe, where Pwe = k * log(L), (4)

where, in turn, L = R1/R0, and the parameters k, R0, and R1 are described in formula (3).

Here, the value of the power of emotions Pwe is introduced, which is proportional to the “flow of emotional energy” per unit of time (i.e., the everyday meaning of the expression “intensity of emotions”, “strength of emotions”). The expression of the strength of emotions in units of power allocated by the subject's body to emotional behavior is known from the works of other authors, so we should not be surprised at the appearance of such a (somewhat unusual) term as "emotion power".

It is easy to see that formulas (3 and 4) automatically give the correct sign of emotions, positive when R increases (when R1 > R0 and thus L > 1) and negative when R falls (when R1< R0 и т.о. L < 1).

Now let's try to apply new emotion formulas to the perception of musical chords.

INFORMATIONAL THEORY OF CHORDS

But first, some "lyrics". How can the informational theory of emotions described above be expressed in simple human language? I will try to give a few rather simple examples that clarify the situation.

Suppose today life has given us a “double portion” of certain “life blessings” (against the average daily volume of “happiness”). For example - twice the best lunch. Or we had two hours of free time in the evening against one. Or we went on a mountain hike twice as much as usual. Or we were told twice as many compliments as yesterday. Or we got double bonuses. And we rejoice, because the function L has become equal to 2 today (L=2/1, E>0). And tomorrow we got it all fivefold. And we rejoice even more (we experience more powerful positive emotions, because L=5/1, E>>0). And then it all went on as usual (L=1/1, E=0), and we no longer experience any utilitarian emotions - we have nothing to rejoice at, and nothing to be sad about (if we have not had time to get used to happy days). And then suddenly a crisis broke out and our benefits were cut in half (L = 1/2, E<0) - и нам стало грустно.

And although for each subject the objective function L depends on a large set of individual sub-goals (sometimes diametrically opposed - for sports opponents or fans, for example), everyone's personal opinion is common to everyone - whether this event brings them closer to some of their goals, or away from them.

Now back to our music.

Based on the proven facts of science, it is logical to assume that when listening to several sounds at the same time, the subject's psyche tries to extract all kinds of information that these sounds can contain, including information that is at the highest level of the hierarchy, i.e. from the ratios of the pitches of all sounds.

At the stage of analyzing the parameters of triads (unlike consonances, see above), individual information flows from different ears are already used together (which is easy to check by giving any two sounds to one ear, and the third to the other - the emotions are the same).

In the process of interpreting this combined information, the subject's psyche tries to use, among other things, its "utilitarian" emotional subsystem.

And in a number of cases she successfully succeeds - for example, when listening to isolated minor and major chords (but chords of other types can apparently generate other types of emotions - aesthetic / intellectual).

It is possible that some rather simple analogies (on a higher/lower level) with the meaning of "similar" information from other sensory channels of perception (visual, etc.) allow the subject's psyche to classify major chords as carrying information "about benefit", accompanied by positive emotions, and minor - “about the loss”, accompanied by negative ones.

Those. in the language of the formula of emotions (4), the major chord should contain information about the value of the objective function L > 1, and the minor chord should contain information about the value L< 1.

My main hypothesis is the following. When perceiving a separate musical chord in the psyche of the subject, the value of the objective function L is generated, which is directly related to the main proportion of the pitches of its sounds. At the same time, major chords correspond to the idea of ​​the growth of the objective function (L>1), accompanied by positive utilitarian emotions, and minor chords correspond to the idea of ​​the fall of the objective function (L<1), сопровождаемое отрицательными утилитарными эмоциями.

As a first approximation, we can assume that the value of L is equal to some simple function of the numbers included in the main proportion of the chord. In the simplest case, this function can be some kind of "average" of all the numbers of the main proportion of the chord, for example, the geometric mean.

For any major chords, all of these numbers will be greater than 1, and for any minor chords, they will be less than 1.

For example:

L \u003d N \u003d "average" of the numbers (4, 5, 6) from the major proportion 4: 5: 6,

L \u003d 1 / N \u003d "average" of numbers (1/4, 1/5, 1/6) from the minor proportion / 4: / 5: / 6.

With such a representation of L, the amplitude of the strength of emotions (i.e., the absolute value of Pwe) generated by the major and (reverse) minor triads will be exactly the same, and these emotions will have the opposite sign (major is positive, minor is negative). A very encouraging result!

Let us now try to clarify and generalize formula (4) for an arbitrary number of voices of the chord M. To do this, we define L as the geometric mean of the numbers from the main proportion of the chord, resulting in the final form of the “formula of musical emotions”:

Pwe = k * log(L) = k * (1/M) * log(n1 * n2 * n3 * ... * nM), (5)

where k is still some positive constant - see (3),

Let's call the value Pwe (from formula 5) the "emotional power" of the chord (or simply power), positive for major and negative for minor (an analogy: the flow of vitality, for major - inflow, for minor - outflow).

For uniformity with the logarithmic frequency scale (recall about the octave), we will use the base 2 logarithm in formula (5). In this case, we can put k = 1, because in this case, the numerical value of Pwe will be in a quite acceptable range near the region of the “single” amplitude of emotions.

For further analysis, along with the “main” one, we may also need the “side” power of the chord, corresponding to the substitution into formula (5) of its side proportion (see above). If not specified, the "main" Pwe is used everywhere below.

The appendix to the article gives the values ​​of the main and side powers of some chords.

THE DISCUSSION OF THE RESULTS

So, having put forward a number of fairly simple and logical assumptions, we have obtained new formulas (3, 4, 5), which connect the generalized parameters of the situation (or the specific parameters of chords for formula 5) with the sign and strength of the utilitarian emotions they evoke (in the context of the situation).

How can this result be assessed?

Quoting work:

“There were probably no attempts to objectively determine the strength of emotion. However, it can be assumed that such a definition should be based on energy concepts. If an emotion causes some behavior, then this behavior requires a certain expenditure of energy. The stronger the emotion, the more intense the behavior, the more energy is required per unit of time.

Those. one can try to identify the strength of emotion with the amount of power that the body allocates for the corresponding behavior.

Let's try to approach the new result as critically as possible, since there is nothing to compare it with yet.

First, the power of emotions Pwe from formulas (4, 5), although proportional to the “subjective power” of emotions, their connection may not be linear. And this connection is only a certain average dependence along the entire continuum of subjects, i.e. may be subject to significant (?) individual deviations. For example, the "constant" k can still change, although not too much. It is also possible that some other function should be used instead of the geometric mean in formula (5).

Secondly, if we keep in mind the specific form of the formula of musical emotions (5), then it should be noted that although formally M can be equal to 1 or 2 in it, we can talk about the emergence of utilitarian emotions only when M >= 3. However, already with M = 2, aesthetic / intellectual emotions are possible, and with M > 3, there is a possibility of additional factors (?) that somehow affect the result.

Thirdly, apparently the area of ​​valid values ​​of the Pwe amplitude for the category of major and minor has an upper limit of 2.7 ... 3.0, but somewhere already from the value of 2.4 the area of ​​saturation of the utilitarian-emotional perception of chords begins, and the lower limit of the range passes approximately in the same place. possible "invasion" of dissonances.

But this latter is rather a general problem of "not monotony" of a number of dissonant intervals, not directly related to the emotional perception of chords. And the limited dynamic range of the power of emotions is a common property of any human sensory system, easily explained by the lack of analogies with events in “real life” that correspond to too rapid changes in the objective function (by 7-8 times or more).

Fourthly, "symmetrical" (or almost symmetrical) chords, in which direct and inverse proportions consist of the same numbers (even if there are no obvious dissonances in them) apparently fall out of our classification - their utilitarian-emotional coloring is practically absent, corresponding to the case pwe = 0.

However, the formal result of applying formula (5) can be supplemented with a simple semi-empirical rule: if the main and side powers of some chord (almost) coincide in amplitude, then the result of formula (5) will not be the main power, but a half-sum of powers, i.e. (approximately) 0.

And this rule begins to work already when the difference between the amplitudes of the main and secondary Pwe is less than 0.50.

Most likely, a very simple phenomenon takes place here: since it is impossible to distinguish between the direct and inverse proportions of a chord by complexity, then the classification of this chord in the categories of utilitarian emotions (“sadness and joy”) is simply not made. However, these chords (as well as intervals) can generate aesthetic/intellectual emotions, eg. “surprise”, “question”, “irritation” (if there are dissonances), etc.

With all its imaginary or real shortcomings, formula (5) (and, apparently, formulas 3 and 4) still gives us very good theoretical material for numerical estimates of the strength of emotions.

In at least one particular area - the area of ​​emotional perception of major and minor chords.

Let's try to test this formula (5) in practice by comparing a couple of different major and minor chords. A very good example is the chords 3:4:5 and 4:5:6 and their minor variants.

For the purity of the experiment, one should compare pairs of chords composed of pure tones with approximately the same average volume level, and for both chords it is better to use such pitches so that the “weighted average” frequency of these chords (in Hertz) is the same.

A pair of major triads can consist of tones with a frequency of eg. 300, 400, 500 Hz and 320, 400, 480 Hz.

To my ear, it seems quite noticeable that the emotional “brightness” of the 3:4:5 major (with Pwe = 1.97) is indeed somewhat less than that of the 4:5:6 major (with Pwe = 2.30). Approximately the same, in my opinion, happens with the minor /3:/4:/5 and /4:/5:/6.

This impression of the correct transfer of the power of emotions by formula (5) is also preserved when listening to the same chords composed of sounds with a rich harmonic spectrum.

TOTAL

In total, in accordance with the information theory of emotions, the paper proposes modified formulas that express the sign and amplitude of utilitarian emotions through the parameters of the situation.

A hypothesis has been put forward that when a musical chord is perceived in the subject's psyche, the value of some objective function L is generated, which is directly related to the proportion of the pitches of the sounds of the chord. At the same time, major chords correspond to direct proportions, giving rise to the idea of ​​the growth of the objective function (L>1), causing positive utilitarian emotions, and minor chords correspond to inverse proportions, giving rise to the idea of ​​a decrease in the objective function (L<1), вызывающее отрицательные утилитарные эмоции.

A formula for musical emotions has been put forward: Pwe = log(L) = (1/M)*log(n1*n2*n3* ... *nM), where M is the number of chord voices, ni is an integer (or reciprocal) of the general proportion of pitches corresponding to the i-th voice of the chord.

A limited experimental check has been made, the limits of applicability of the formula of musical emotions, in which it correctly conveys the sign and (in my opinion) their amplitude, have been investigated.

CODA

The fanfares sound joyful!

Then everyone stands up - and holding hands - a cappella sing the Hymn to Reason!

The centuries-old mystery of major and minor has finally been solved! We won...

LITERATURE AND LINKS

1. Sound system Audiere, Download archive Use wxPlayer.exe from the bin folder.
2. Trusov V.N. Site materials mushar.ru 2004 http://web.archive.org/http://mushar.ru/
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6. Ilyin E.P. Emotions and feelings. 2001
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8. Leontiev V.O. Formulas of emotions. 2008
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12. Altman Ya.A. (ed.) Auditory system. 1990
13. Lefevre V.A. Human formula. 1991
14. Shiffman H.R. Feeling and perception. 2003
15. Teplov B.M. Psychology of musical abilities. 2003
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18. Garbuzov N.A. (ed.) Musical acoustics. 1954
19. Rimsky-Korsakov N. Practical textbook of harmony. 1937
20. Leontiev V.O. What is emotion. 2004
21. Klaus R. Scherer, 2005. What are emotions? And how can they be measured? Social Science Information, Vol 44, no 4, pp. 695-729
22. BEHAVIORAL AND BRAIN SCIENCES (2008) 31, 559-621 Emotional responses to music: The need to consider underlying mechanisms
23. Music Cognition at the Ohio State University http://csml.som.ohio-state.edu/home.html Music and Emotion http://dactyl.som.ohio-state.edu/Music839E/index.html
24. Norman D. Cook, Kansai University, 2002. Tone of Voice and Mind: The connections between intonation, emotion, cognition and consciousness.
25. Bjorn Vickhoff. A Perspective Theory of Music Perception and Emotion. Doctoral dissertation in musicology at the Department of Culture, Aesthetics and Media, University of Gothenburg, Sweden, 2008
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28. Levelt W., Plomp R. The appreciation of musical intervals. 1964

ACKNOWLEDGMENTS

I express my gratitude to Ernst Terhardt and Yury Savitski for the literature, kindly provided to me for writing this work. Thank you very much!

AUTHOR'S INFORMATION

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Version.

APPLICATION

Emotional power Pwe of the main proportions of some chords, calculated by formula (5).

The bulk of the proportions are direct proportions corresponding to major chords.

Minor chords can be generated from proportions that are the inverse of major proportions by simply changing the Pwe sign of the major proportion (as in a couple of examples).

The secondary power of some chords is given in brackets, if it approaches the main one in amplitude.

For symmetrical chords, both these powers differ only in sign.

Main Side Pwe Main (Side) Note Proportion Proportion Proportion

Some symmetrical [pseudo]chords

1:1:1 1:1:1 0 (0)

1:2:4 /4:/2:1 1 (-1)

4:6:9 /9:/6:/4 2.58 (-2.58) fifth triad

16:20:25 /25:/20:/16 4.32 (-4.32) increased triad

1:2:3 /6:/3:/2 0.86 (-1.72)

2:3:4 /6:/4:/3 1.53 (-2.06)

2:3:5 /15:/10:/6 1.64

2:3:8 /12:/8:/3 1.86

2:4:5 /10:/5:/4 1.77

2:5:6 /15:/6:/5 1.97

2:5:8 /20:/8:/5 2.11

3:4:5 /20:/15:/12 1.97 /3:/4:/5 20:15:12 -1.97

3:4:6 /4:/3:/2 -1.53 (2.06)

3:4:8 /8:/6:/3 2.19 (-2.39) almost symmetrical

3:5:6 /10:/6:/5 2.16 (-2.74)

3:5:8 /40:/24:/15 2.30

3:6:8 /8:/4:/3 2.39 (-2.19) almost symmetrical

4:5:6 /15:/12:/10 2.30 major triad

/4:/5:/6 15:12:10 -2.30 minor triad

4:5:8 /10:/8:/5 2.44 (-2.88)

5:6:8 /24:/20:/15 2.64

Some dissonant triads

4:5:7 /35:/28:/20 2.38

5:6:7 /42:/35:/30 2.57

1:2:3:4 /12:/6:/4:/3 1.15

2:3:4:5 /30:/20:/15:/12 1.73

3:4:5:6 /20:/15:/12:/10 2.12

Three types of major scale

Most often, music is recorded in the major and minor scales. Both of these modes have three types: natural, harmonic and melodic. All types have the same base. In harmonic and melodic major or minor, certain steps (VI and VII) change. They go up in minor and go down in major.

Natural Major.

natural major- this is an ordinary major scale with its key signs, if they exist, of course, and without any accidental accidental signs. Of the three types of major, natural in musical works are more common than others.

The major scale is based on the well-known formula from the sequence in the scale of whole tones and semitones: 1t-1t-0.5t-1t-1t-1t-0.5t.

Here are examples of several simple major scales in their natural form: the natural C (C major), the G (G major) scale in its natural form, and the natural F (F major) key scale:

Harmonic Major.

Harmonic Major- this is a major with a reduced sixth step(VIb) . This sixth step is lowered in order to be closer to the fifth. And the fret takes on an oriental hue.

Here is how the harmonic major scales of the previously shown keys look like: C (C major), G (G major) and F (F major).

In C (C major), ab (A-flat) appeared - a sign of a change in the natural sixth step, which has become harmonic. In G (G major), the sign eb (E-flat) appeared, and in F (F-major) - db (D-flat).

Melodic Major.

As in the melodic minor, in major two steps change at the same time VI and VII , only everything here is exactly the opposite. Firstly, these two sounds do not rise, as in a minor, but go down. Secondly, they alter they are not in an upward movement, but when descending.

It is curious that due to the lowering of the sixth step, all sorts of interesting intervals can form between this step and other sounds - increased and decreased. These can be tritones or characteristic intervals - I recommend that you figure this out.

melodic major- this is a major scale in which a natural scale is played during an ascending movement, and two steps are lowered during a descending movement - the sixth and seventh (VIb and VIIb).

Note examples of melodic major are C (C major), G (G major) and F (F major):

In melodic C (C major), two "random" flats appear in the downward movement - bb (b-flat) and ab (a-flat). In G (G major), F # (F-sharp) is first canceled - the seventh step is lowered, and then a flat appears before the note e (mi) - the sixth step is lowered. In the melodic F (F major), two flats appear: еb (E-flat) and dь (D-flat).

So, there are three types of major. These are natural (simple), harmonic (with a reduced sixth step) and melodic (in which, when moving upwards, you need to play / sing a natural scale, and when moving down, lower the seventh and sixth steps).

There is a wide variety in music frets. By ear, it is easy to distinguish Russian ditties from Georgian songs, oriental music from western, etc. Such a difference in melodies, their moods, is due to the mode used. The major and minor modes are the most widely used. In this chapter, we will look at the major scale.

major scale

Lad, whose stable sounds form a major triad, is called major. Let's explain right away. A triad is already a chord, we will talk about it a little later, but for now, by a triad we mean 3 sounds, taken either simultaneously or sequentially. A major triad is formed by sounds, the intervals between which are thirds. Between the lower sound and the middle one is a major third (2 tones); between the middle and upper sounds - a small third (1.5 tones). Major triad example:

Figure 1. Major triad

A major triad with a tonic at its base is called a tonic triad.

The major scale consists of seven sounds, which represent a certain sequence major and minor seconds. Let us designate the major second as “b.2”, and the minor second as “m.2”. Then the major scale can be represented as follows: b.2, b.2, m.2, b.2, b.2, b.2, m.2. A sequence of sounds with such an arrangement of steps is called a natural major scale, and a mode is called a natural major. Generally speaking, the scale is called the ordered arrangement of the sounds of the mode in height (from tonic to tonic). The sounds that make up the scale are called steps. Scale steps are indicated by Roman numerals. Do not confuse with scale steps - they have no designations. The figure below shows the numbered steps of the major scale.

Figure 2. Major scale steps

The steps have not only a digital designation, but also an independent naming:

Stage I: tonic (T);

Stage II: descending introductory sound;

Stage III: mediant (middle);

Stage IV: subdominant (S);

Stage V: dominant (D);

Stage VI: submediant (lower mediant);

Stage VII: rising introductory sound.

Stages I, IV and V are called the main stages. The rest of the steps are secondary. Introductory sounds gravitate towards the tonic (strive for resolution).

Steps I, III and V are stable, they form a tonic triad.

Briefly about the main

So, the major mode is the mode, in which the sequence of sounds forms the following sequence: b.2, b.2, m.2, b.2, b.2, b.2, m.2. Let us recall once again: b.2 - a major second, represents a whole tone: m.2 - a minor second, represents a semitone. The sequence of sounds of a major scale is shown in the figure:

Figure 3. Natural major scale intervals

The figure indicates:

• b.2 - major second (whole tone);
• m.2 - small second (semitone);
• 1 indicates a whole tone. Perhaps this makes the diagram easier to read;
• 0.5 is a semitone.

Results

We got acquainted with the concept of “mode”, analyzed the major mode in detail. Of all the names of the steps, we will most often use the main ones, so their names and locations must be remembered.