Sound harmony 9. Expressive means of music: What is harmony in music

Overtone tuning, musical tuning schemes, harmony of intervals,
12 and 19 semitone scale - comparison.

"Pythagoras gave such a clear preference for stringed
tools that warned his students against
allowing the ears to listen to the sounds of the flute and
cymbals. He further argued that the soul must be
purified from irrational influences by solemn singing,
which should be accompanied on the lyre."
link below

Dear readers. We are talking about harmony. Composing poetry, like singing or reciting them in a singsong voice, is an exclusively harmonic activity. Therefore, in this article - a little about harmony in music.
What lines of verse, what sounds do we call harmonious? It is known what - those that delight our ears. And if you look closely, they have a certain symmetry. Rhythm and rhyme in versification, rhythm and harmony of overtones in music. We will talk about overtones.
Take a look at the drawing. Imagine that the upper and lower long segments are strings of the same length, and stretched in such a way that they emit a sound Up to the first octave with their normal sound. That is, when the midpoints of these strings vibrate up and down as a whole.
But they can also sound differently - making the oscillations shown in the figure. The sound of these vibrations is higher, it is the sound of overtones, the third and fourth (we count by the number of antinodes). Stretched with the same force, but more short strings with the sounds Fa and Sol can create exactly the same sounding overtones. And therefore, we perceive the simultaneous sounding of the notes Do and Sol, or Do and Fa, as harmonious.

If the harmony of the sound of the strings was noticed a very long time ago, then its detailed development is associated with the name of Pythagoras. He is believed to have created the diatonic series - a sequence of seven sounds of the octave, arranged in harmony in the ratios of the numbers 1 2 3 and 4.
You can find a colorful (though not quite correct from the point of view of a physicist) description of Pythagoras' experiments here:
Pythagorean theory of music and color.

Read and enjoy. Since we will now proceed to a rather boring lesson - tuning the piano. Let me explain why I even took up this case.
I made a piano using computer keys. With the sound of keys, a mnemonic record of the resulting sound, with the ability to edit, listen to and store the notes of this record in a regular text file. Since the notation of notes familiar to musicians is used in the recording, such as - C D E F G A B for notes of the first octave and the same letters, only lowercase, for notes in the second octave, reading notes and editing musical text may well occur in a text file. If you open it, for example, using the Notepad program. It turned out, in my opinion, convenient and interesting. I will talk about this program specifically in the next article.
I was faced with the task of setting up a computer piano. It seemed to me too easy to take the frequencies of an equal temperament series. And I began to understand the configuration schemes.
Details of the settings you can see on this link -
www.tuning-piano-kharkiv.com

We will not create an equal temperament system, but first of all we will turn to the classical tuning scheme 2/3 or "by fifths down". Usually this is the setting. I'll explain why.
Fifth - an interval of 5 tones, the upper step of which, called the dominant, is known for the sensation of resolving into the tonic - to the lower step of the fifth. From La to Re.
This is where the setup starts. The frequency of the note La of the first octave is taken as a standard, it is equal to 440 Hz.
We multiply this frequency by 2 and divide by 3 (according to the 2/3 scheme), we find Re - the "fifth down" from the sound La.
And then we continue in the same spirit. If the frequency obtained by us turns out to be lower than the frequency La / 2, then we multiply the frequency by 2, returning it closer to the original La. We do this mathematically, and the tuner does all this, focusing on his hearing.
And here is a miracle. After 12 cycles, we return to the sound of La. Almost exactly, but not quite. We get not 440 Hz, but 434.078 Hz. The frequency difference (in our case - about 6 Hz) is called the Pythagorean comma.
Approximately the same, but somewhat differently, Pythagoras acted in his calculations. About the Pythagorean system, see here - http://www.px-pict.com/7/3/2/1/8/1.html

A trifle or not a trifle - a Pythagorean comma, can it be neglected?
6 Hz from a frequency of 440 Hz is 6/440=0.002348 i.e. rounded up 0.23%. While the frequency rises from the note A to the next semitone (A sharp), increasing by 5.35% (I give a table with frequencies below).
5.35/0.23=23.3 and, it would seem, coma can be neglected.
But let's look at the intervals, looking ahead a little, to the frequency table. Calculations show that the interval between La and La# is, as already mentioned, 5.53%. But this is not the case everywhere, the table also often shows intervals between semitones of 6.79%, for example, for the same La-La# interval, but for tuning by fourths. When moving along chromatic scale the frequency goes up and down from the midline.
This "detuning" is eliminated by additionally slightly tightening each string during tuning, and getting a uniformly tempered scale. In this series, the sound rises not by 5.35% and not by 6.79% per semitone, but by 5.94%.
Why did I put the word "detuning" in quotation marks? Because it is these changing intervals, entering integral part into other intervals of different keys, give originality to the sound of these keys. I will refer to a wonderful description of the beauties of tonalities, right here -
http://www.forumklassika.ru/showthread.php?t=90809
Figurative perception of "light" and "dark" keys in the 17th-20th centuries

I will quote some descriptions relating to keys with a perfect dominant and subdominant (for example, C major) and to keys with a broken subdominant (E major), and with a broken dominant, and at the same time with many other intervals, with an ideal subdominant (A major).

C-dur “Perfectly clean. Innocence, purity, naivety, the voice of a child”
“Jolly and belligerent”
“Joyful and clean”
“The state of nature, virgin purity and chastity, the charming innocence of youth”
“Ease and nobility”
“Joyful and pure; innocence and simplicity”
“Simple, unadorned”
“Totally clean”
“Clean, confident, determined; expressing innocence, firm intention, courageous seriousness and deep religious feeling”
“Bold, energetic, commanding, suitable for repelling war or entrepreneurship”
“Clean, confident, resolute, full of innocence, seriousness, deep religious feelings”; “Simple, naive, outspoken” “White”
"Red" (Scriabin)

E-dur “Bright joyful exclamations, joyful laughter, and at the same time incomplete, incomplete pleasure sound in E-major”
"Uplifting"; "Bright"; “Emitting light, warm, joyful”
“Delight, splendor, brilliance; the brightest and most powerful tonality”
“Bright and clean, good for anything shiny”
“Expresses despair or mortal sadness with incomparable fullness; he is especially suitable in those extreme love affairs, where nothing can be helped and there is nothing to hope for, and under certain circumstances he has in himself something so piercingly-farewellly-sadly-penetratingly that can only be compared with the fatal parting of soul and body ” (I.Matteson)
“Juicy green, spring is in full bloom. Swaying branches adorned with fresh foliage” (Riemann, HTC) “Blue-whitish”
“Blue, sapphire, brilliant, night, dark azure”
“Night, very starry sky, very deep, perspective”
=== pay attention to "incomplete, incomplete" - isn't this an echo of the imperfection of the subdominant? D.M.

A-dur “This tone is an innocent declaration of love, satisfaction with the state of affairs; hope to see the beloved again after separation; youthful vivacity and faith in God”
“Joyful and pastoral”; “Golden, warm and sunny”;
“Must have a very strong impact; he is brilliant, but more prone to expressing sad and mournful feelings than to amusement”
“The most beautiful, modest, kind, soft, delicate, gentle, devoid of sharp audacity, La. Each author noticed the charm of this tonality, saving it for the most sincere feelings”
“Filled with faith and hope, radiates love and simple genuine joy, surpasses all other tones in expressing sincere feelings”
“Fresh and healthy, vital”; “Sincere, sonorous” “Green”
“Clear, spring, pink; it is the color of eternal youth, eternal youth”
“Rather a joyful, intoxicating mood than a light sensation, but as such it approaches D major”
=== end of citation D.M.

So, these "errors" of harmony and violations of intervals turn out to be unusually expressive in music as a result. Isn't it the same in poetry, where deviations from the norm create peculiar semantic and emotional accents.
Equal temperament tuning is called insipid and soulless. And isn't that the case in poetry, in which a verse that is completely smooth in rhythm sometimes turns out to be just as disgusting as a clumsy verse.

Now I want to demonstrate the computer calculation of the 2/3 setting as I received it from the computer:
1 Alja 1,440
2D re .6666666865348816 293.3333435058594
3 Gsol .8888888955116272 391.1111145019531
4 C do .5925925970077515 260.7407531738281
5 Ffa .790123462677002 347.6543273925781
6 - lja# .5267489552497864 231.7695465087891
7 - re# .7023319602012634 309.0260620117188
8-sol# .9364426136016846 412.0347595214844
9 - do# .6242950558662415 274.6898498535156
10-fa# .8323934078216553 366.2531433105469
11 B si .5549289584159851 244.1687622070312
12 E mi .7399052977561951 325.558349609375
13 Alja .9865403771400452 434.0777893066406
\ in this column are the relative heights of the frequencies, in the next - the frequencies

Exactly the same calculation can be carried out according to the 3/4 scheme - multiply by 3, divide by 4
The difference is in the order of tones - instead of ADGCF, etc. - AEB etc. only not 434.077 for La at the output, but 446.003 - that is, the same comma, but already positive. This tuning is called "down fourths", or "up fifths", which is the same:

1 Alja 1,440
2 E mi .75 330
3 Bsi .5625 247.5
4 - fa# .84375 371.25
5 - do# .6328125 278.4375
6-sol# .94921875 417.65625
7 - re# .7119140625 313.2421875
8 - lja# .533935546875 234.931640625
9 Ffa .8009033203125 352.3974609375
10 C do .600677490234375 264.298095703125
11 Gsol .9010162353515625 396.4471435546875
12D re .6757621765136719 297.3353576660156
13 Alja 1.013643264770508 446.0030517578125

It would be possible not to demonstrate this picture, but it curves very beautifully on decimal numbers. This is because we are dividing not by 3 (which is not very consistent with the 10-th counting system), but by 4.

Let's go further, 2/3, 3/4 - it is clear that these numbers mean the ratio of the number of overtones on the arching strings, and why not go further and try other overtones in the form of simple fractions and other tuning schemes? Will it suddenly fit? This is me regarding the comma))
Let's supplement the Pythagorean series with the number 5.

The calculation shows that for the ratio 4/5, nothing in the sense of convergence in a reasonable number of cycles shines. Also, as for the number 7, if you try to include the Pythagorean series. But on the other hand, for 3/5 and for 5/6, a quite decent setting of 19 semitones is obtained. And it, along with other settings, I want to discuss.
As well as my impressions of the implementation of all five settings on the computer keys.
These 5 settings are as follows - p-t (equal temperament scale) and schemes 2/3, 3/4, 3/5, 5/6.

TABLE 1
All frequencies different settings, Hz (first octave)

Equal temp. 2/3 3/4 3/5 5/6 3/5-Hg 2/3 Hg Pythagorean harmonious
difference tuning intervals for 3/5
frequencies, Hz overtones, deviation
-1- -2- -3- -4- -5- -6- -7- -8- -9-
261.63 260.74 264.29 264.00 264.42 to 2.37 -0.89 260.74 (2/3)
277.17 274.68 278.43 273.71 274.16 ==# 32/31 0.438%
277.17 274.68 278.43 283.78 284.24 ==b 274.69 (2/3) fr.
293.66 293.33 297.33 294.23 294.71 re 0.57 -0.33 293.33 (2/3) 10/9 0.31%
311.13 309.02 313.24 305.05 305.55 ==#
311.13 309.02 313.24 316.80 317.31 ==b 309.03 (2/3) fr. 6/5 0%
329.63 325.55 330.00 328.45 328.99 mi -1.18 -4.08 330 (3/4) 5/4 -0.47%
329.63 325.55 330.00 340.54 341.09 fa b
349.23 347.65 352.39 353.07 353.65 fa 3.84 -1.58 347.65 (2/3) 4/3 0.30%
369.98 366.25 371.25 366.07 366.66 ==#
369.98 366.25 371.25 380.16 380.77 ==b
392.00 391.11 396.44 394.14 394.79 salt 2.14 -0.89 391.11 (2/3) 3/2 -0.47%
415.29 412.03 417.65 408.65 409.31 ==#
415.29 412.03 417.65 423.69 424.38 ==b 412.03 (2/3) fr. 8/5 0.31%
440.00 440.00 440.00 440.00 440.00 for 0 0 440 5/3 0%
466.16 463.53 469.86 456.19 456.93 ==#
466.16 463.53 469.86 472.98 473.74 ==b 463.54 (2/3) fr. 9/5 -0.47%
493.88 488.33 495.00 490.38 491.18 si -3.5 -5.55 495 (3/4)
493.88 488.33 495.00 508.43 509.25 to b 31/16 -0.60%
fr. - Phrygian scale
=======================================

Pythagorean system - diatonic scale do - re - mi - fa - salt - la - si - do
Phrygian scale do - reb - mib - fa - sol - lab - sib - do
the frequencies of these scales were calculated based on the materials of the article
http://www.px-pict.com/7/3/2/1/8/1.html

Firstly, I want to congratulate you and myself, the tuning according to the 3/5 and 5/6 schemes converged and demonstrated not even 6 Hz, but only 0.7 Hz at the 19th step, I am quite competing with the equal temperament. And although with such a uniform tuning, no difference in the sound of keys is expected, but the subtleties of the melody are added, due to the new sounds that have appeared - 7 flats from each step of the diatonic series, in addition to the already existing 5 sharps. The enharmonism of sounds on sharps and flats dispersed. Now the F sharp sound is different from the new G flat sound.

I would like to draw your attention to the fact that the Pythagorean scale, together with the Phrygian scale, fit perfectly into the classical 2/3 tuning, with the exception of two sounds Mi and Si, which can be attributed to the 3/4 tuning.
Why did the Pythagoreans do this with these sounds?
To answer this question, let's turn to the 7th column of the table. It shows the frequency difference between the 2/3 tuning and the equal temperament tuning. We see that it is for Mi and Si that the difference in hertz is noticeable. And the 3/4 tuning of these notes is closer to equal temperament. Therefore, the Greeks took the frequencies of the 3/4 scheme for Mi and Si. They strove not only for harmony, but also for the uniformity of the sound range.

But what about the uniformity of the diatonic scale in 19-semitone tuning? We will not distinguish between settings 3/5 and 5/6, since the frequency difference for them is negligible, not the same as between 2/3 and 3/4.
*** By the way! If you tune the piano not classically - "by fifths down" but by fourths, then all that magnificent description of the imagery of musical keys that you could read above will move 2.5 tones lower - the attributed C-dur will have to be attributed to G-dur. The key of C-dur will be colored in the colors of F-dur.

The diagram shows the alternation of semitone intervals in an octave, indicated by _ 5.35% - 6.79% Hz / semitone
La
| ? ? - this is Mi
|_-_ _-_-_ -_ _-| |_-_ _-_-_-_ _-_-_ _-_-_-_ _-| 2/3 tuning from Mi in fifths
|_-_ _-_-_ _- _-| |_-_ _-_-_ _-_-| 3/4 is equivalent to A tuning in fourths
| |

It can be seen from the diagram that if we trace the alternation of intervals in the 2/3 tuning in 2 octaves, then there will be a place that matches the alternation of intervals with the 3/4 tuning octave

Let's return to the diatonic scale in 19 semitone tuning and look at column 6 of the table. Do, Sol, Si and, especially, Fa stick out.
The sound of the scale is unusual, although the resolution to the tonic is clearly felt.
You can read about scales on Wikipedia, in particular about the whole tone scale, which can be implemented as a fret in 12 semitone tuning. A setting of 19, having an odd number of semitones, does not allow this. But you can try other scales.

Diatonic scale in normal tuning, number of semitone steps shown (sum=12)
| 2 2 1 2 2 2 1 | if from Do, then this is the usual "do-re-mi-fa-sol-la-si-do"

Diatonic scales in 3/5 tuning (19). I found two acceptable scales.
| 3 3 1 4 3 3 2 | - "C-major on white keys" with the replacement of F by Fb to improve harmony, I tried it, it sounds almost familiar.
and from D flat - not all in flats, but with climbing into sharps, I tried it, it also sounds good.

| 3 3 2 3 3 3 2 | - from re#, sounds more evenly in the middle of the scale, but with worse resolution in the tonic.
the same scale from C - according to the performance of "ordinary C-major on white keys"

One important remark must be made here. The diatonic scale in classical tuning turns out to be harmonically unified. That is, the sounds included in it follow the tuning sequence. This corresponds to the fact that the major diatonic scale occupies a solid sector on the circle of fourths and fifths.
For 19 semitone settings, you can also build a similar circle, reflecting the mutual harmony of its neighbors. However, this will be harmony not in fourths and fifths, but in minor thirds and sixths. Seven close neighbors on this circle can also be distinguished, and among them are those that form the dominant and tonic (with a frequency ratio of 3/2), but the subdominant is far from this solid sector. The notes of this continuous sector in the form of a fret sound very interesting, with an oriental motif, and are successfully resolved into the tonic.
The scheme of this fret is as follows - | 1 4 1 4 1 4 4 |
In the article to which I refer a little lower, the six steps of this mode are located in consonant minima (Fig. 14a) in pairs, while the last step falls on dissonance and strongly gravitates towards the first step.
The steps are unevenly distributed along the octave - three close pairs and one note spaced from these pairs. But those uniform diatonic scales, examples of which were given above, turn out to be broken along the circle of tuning 3/5, although they contain intervals of classical tuning.
All this constitutes a very interesting object for the study of harmony.
I must say that people are engaged in such research. In the practical sphere, (you can look at the search engine) - who tunes the guitar by thirds, who discusses temperament by thirds (not as deeply as we do, but in the form of a potential attempt), who tunes the piano by thirds, tightening the strings and listening to the number of beats ( to obtain an evenly tempered series, but we are doing the opposite - so that there are no beats on thirds). A discussion of the possibilities of constructing a scale other than a scale with 12 semitones is also being discussed on the Internet - http://forum.buza.su/viewtopic.php?f=54&t=2165

Already after writing this article, I found what I advise you to read, seriously interested in this problem, there is also a 19-tone scale - http://unism.narod.ru/arc/2006gs/gs.pdf with many drawings, formulas and explanations.
But the proposed keyboard seems unsuccessful and uncomfortable to me. But the computer keyboard turned out to be very suitable for this purpose. In addition, the proposed accidental signs, which may be more correct from the point of view of musical theory, are, in my opinion, completely inconvenient in practical terms - two sharp signs (increase by 1 semitone and increase by 2 semitones) and two flat signs. Who will look at them?

Let's continue. After the experiments described, it is interesting to turn to the next topic - how are things going with the harmony of the intervals, in 12 semitone and 19 semitone settings? For comparison, take the p-temp settings. and 3/5 - both uniform, and therefore we will compare them. Due to the uniformity of the settings, it is enough to compare the intervals in one key - C major. Moreover, all intervals for comparison can be taken in relation to a single note - Do. Due to the uniformity of the settings, any interval shifted in semitones by any number of semitones will not change its harmonic quality.

We will search for harmonic intervals and evaluate their quality as follows.
We take two prime numbers, starting with small ones, and form them simple fraction, greater than one, but less than two. The first such fraction is 3/2=1.5, we multiply this number by the frequency of the lower sound Do.
For the 3/5 setting, this is 264 Hz. 264 x 1.5 = 396 Hz We are looking for the frequency closest to this value in the table. We find 394.14 Hz note Salt. This is the approximate dominant. Let's evaluate its quality.
We divide 394.14/264 = 1.49295, and it should be 1.5. What is the percentage difference?
Divide 1.49295/1.5=0.995303 subtract one and multiply by 100. Get -0.4697 round up => -0.47%
So, in the 3/5 setting, the imperfection of the dominant, expressed as a fraction of 3/2, is -0.47%

We select the following suitable prime numbers. See table.
We see that in the 5/3 attunement, the subdominant 4/3 on the Fa is not quite perfect.
Let's continue the process. Note that fractions with a number of 7 do not give harmonic intervals, while fractions 5/3 and 6/5 give intervals that are ideal in harmony. As expected in the setting with the number 5.

At 19 semitone settings, the dominant and subdominant look worse, but the harmony of other intervals improves. Let's look at this in a table:

TABLE 2 Deviations of harmonic intervals from the ideal value
for equal temperament tuning and tuning 3/5 to 19 semitones
p-temp. 3/5
do-re small whole tone 10/9 1.02% small whole tone 10/9 0.31%
do-mib minor third 6/5 0.90% minor third 6/5 0%
to-mi more. third 5/4 0.79% big third 5/4 -0.47%
do-fa q 4/3 0.11% q 4/3 0.30% subdominant
do-sol fifth 3/2 -0.11% fifth 3/2 -0.47% dominant
do-lab minor sixth 8/5 -0.79% minor sixth 8/5 0.31%
do-la sixth 5/3 0.91% sixth 5/3 0%
do-sb minor seventh 9/5 -1.01% minor seventh 9/5 -0.47%

Average in absolute value 0.705% 0.291% i.e. 2.4 times less

Yes, we have seen that despite the relatively less perfection of the dominant and subdominant, in general, the intervals in 19 semitone tuning turn out to be almost 2.5 times more perfect than the intervals of the equal temperament scale in terms of harmonic consonance. But will the existing imperfections be perceived by the subtle ear. Let's give some clarification on this.

The perception of frequency by ear depends on the duration of the sound presented to the sound.
According to the formula
cos(x)+cos(y) = 2 cos((x+y)/2) cos((x-y)/2) - the sound of two close frequencies is perceived as the sound of the middle frequency, accompanied by amplitude beats. The beat frequency is the half-difference of the frequencies, and the duration of one beat is the period during which the sound rises from zero and then falls. This period is 1/(x-y) in seconds if x and y are frequencies in Hz. Thus, the frequency difference from the ideal one at a detuning of 2 Hz is perceived only when playing quarter notes (duration of sounding 0.5 seconds) or when playing at a slower tempo.
A detuning of 0.5 Hz or less can be considered negligible, since it can only be noticed when playing notes of an integer duration.
The Pythagorean comma for classical piano tuning is 6 Hz on the note la of the first octave, this is 13.6% of the reference frequency (and it is quite audible). And even more it will be heard in the second octave, where on the note la it will be 12 Hz. Therefore, the falseness of the tuning, or its imperfection, is more audible in the upper octaves.
2 Hz in relation to 440 Hz is 0.45%. Tuning imperfections of this magnitude will be noticeable when playing notes in the first octave at a tempo of 2 notes per second (1/4th notes) and slower.
Yes, the imperfection of the dominant and subdominant sounds of 0.47% in the 3/5 tuning will be noticeable in the first octave when playing quarter notes, but let's look at the key of A major in the classical tuning. What was said about her? "Each author noticed the charm of this tonality, saving it for the most sincere feelings." And the dominant in it is broken - 1.35%

It's not about harmony. And the point is how composers will be able to extract divine sounds and give them expressiveness, using those features of harmony musical instruments that these tools have.
The same applies to poetry.

Thank you for your attention.
======================== 17.01.2015

I express my gratitude to Nikita Skiba, a 3rd year student of the Moscow Conservatory in the viola class, for the interest he showed in the sound coming from the computer, which inspired me for all this activity, including the creation of a program, the convenience and features of which we discussed together.

The article can be downloaded from here - https://yadi.sk/i/umsaM6J-e6Sbp Word format
========

P.S. Dear reader, if you do not understand why I was so enthusiastic about this work and posted a lot of numbers in the article, maybe. and boring, I'll explain. Since the time of Pythagoras, we have been using a 12-semitone scale to tune our musical instruments, either in a "pure" form, or in a form corrected by equal temperament. However, as it turned out, there is another scale, with 19 sounds.
It is quite harmonious, and an order of magnitude more uniform than the traditional one. In addition, as it turned out, other similar scales (except for 12 and 19) with a reasonable number of tones do not exist in nature.

You can object that since the time of Pythagoras, many have practiced harmonies, and if something worthwhile were contained in 19 sounds, then this harmonic series would certainly be discovered.
But I will also object. Since the time of Pythagoras, musicians have tuned their instruments not just by ear, but, thanks to Pythagoras, according to his system. And bearing in mind the sufficient scholasticism of the Middle Ages, it is difficult to imagine that anything could change, and the musical material has already been accumulated in 12 tones significant. Why did you have to leave him? At the present time, apparently, it is only theoretically known about the 19-tone sound range - http://unism.narod.ru/arc/2006gs/gs.pdf and this information has appeared relatively recently.

Dmitry Nizyaev

The classical course of harmony is based on a strictly four-voice texture, and this has a deep justification. The fact is that all music as a whole - both texture, and form, and the laws of constructing a melody, and all conceivable means of emotional coloring - comes from the laws of human speech, its intonations. Everything in music comes from the human voice. And human voices are divided - almost conditionally - into four registers in height. These are soprano, alto (or "mezzo" in vocal terminology), tenor and bass. All countless varieties of human timbres are just special cases of these four groups. There are simply male and female timbres, and there are high and low among both - these are the four groups. And, strange as it may seem, four voices - different voices- this is exactly the optimal amount necessary for voicing all the harmonies existing in the harmony. Coincidence? God knows... One way or another, let's take it for granted: Four votes is the foundation.

Any texture, no matter how complicated and cumbersome you create it, will essentially be a four-voice, all other voices will inevitably duplicate the roles of the main four. An interesting note: the timbres of the instruments also fit perfectly into the four-voice scheme. Even the ranges of notes available to them are practically the same as the ranges of human voices. Namely, in string group: the role of soprano is played by the violin, mezzo - alto, tenor - cello, bass - double bass, of course. In the woodwind group, in the same order are: flute, oboe, clarinet, bassoon. For brass: trumpet, horn, trombone, tuba. I am listing all of this for a reason. You can now safely replace the timbres of one group with another without worrying about the pitch range, without rewriting melodies. You can easily transfer the music for a string quartet to the same wind quartet, and the music will not suffer, since the roles of voices, the structures of their melodies, technical limitations, emotional coloring - correspond to each other just like human voices.

So, the first rule: we will do everything in four voices. Secondly, since we are not pursuing the goals of arrangement, but only studying the interaction of consonances (just as mathematics does not mean physical apples or boxes by numbers, but operates with numbers in general), then we do not need any tools. Or rather, anyone who can produce four notes at the same time will do, by default - the piano. In addition, for the sake of purity and transparency of our thinking, we will write examples and exercises in the so-called "harmonic" texture, that is, vertical "pillars", chords. Well, except that from time to time it will be possible to give a more developed textural example to show that the law under study is valid even in such conditions. Rule Three: Harmony exercises or illustrations are written on a piano (i.e. double) musical staff, and the voices are distributed equally among the lines: on the top - soprano and alto, on the bottom - tenor and bass. The spelling of the stems under these conditions differs from the traditional one: regardless of the position of the note head, the stem is always directed upwards for the soprano and tenor, and always downwards for the rest. So that the voices in your eyes are not confused. Fourth: if we need to name a polyphonic consonance with words, the notes are listed from bottom to top with an indication of the sign (even if it is in the key), agreed? Fifthly - this is VERY important - never substitute, say, C-sharp for D-flat in harmony, even though this is the same key. First, these notes have all the same different meanings(they belong to different keys, have different gravity, etc.), and secondly, despite the generally accepted opinion, they actually even have different heights! If we talk about tempered and natural tuning (I don’t know yet if this will happen), then you will see that C-sharp and D-flat are completely different notes, there is nothing in common. So let's agree for now: such a substitution of one sign for another can happen only "for a reason", and not at will. This is called "anharmonism" - we will have such a topic in the future. Well, let's start praying...

STEPS

All patterns studied by harmony are absolutely exactly repeated in any key, they simply do not depend on the name of the tonic. Therefore, in order to express this or that consideration, suitable for any key, we cannot use the names of notes. For convenience, the scale of any key is supplied with numbers that replace the names of notes, and these conditional numbers are called steps. That is, the very first main sound scale - no matter what note it is, and what mode it is - becomes the first step, then the score goes up to the seventh step (in C major, for example, it is "si"), after which the first follows again. Step numbers will be represented by Roman numerals "I - VII". And if we find out that, for example, between D and F (II and IV degrees of C major) there is an interval of a minor third, then you can be sure that the same interval will be between the II and IV degrees of any major, no matter how impossible the signs are neither turned out to be at the key. Convenient, isn't it?

sobriety

We already know that a triad is a combination of three notes arranged in thirds. To make you feel at ease among the triads, I advise you to practice building triads from arbitrary notes both up and down. Moreover, it would be nice to be able to do this just instantly, combining three methods: press them on the keys (even on imaginary ones), sing them in order to memorize their color, and sing them silently, in the imagination. This is how an "inner ear" is brought up, which will help you to have sounding music right in your head, continue working right on the street, and in addition, it will give you an opportunity, which is hardly available to anyone, to “lead”, “sing”, track in your mind several melodic lines at once (after all, you won’t cover more than one melody at a time with your voice!).

You have already been told that there are four types of triads: major, minor, augmented and diminished. But these are just words, names. But are these words associated in your mind with coloring? What emotions does the word "reduced" evoke in you? This is where your inner ear is at your service, and you feel a relative "minority" (due to the abundance of small thirds) and a cutting "live" dissonance (a diminished fifth). As a result - a sad, aching, full of pain, and at the same time reeking of oriental exotic coloring. You have also been told what a fret is. We already know that if you "select" for work among absolutely identical semitones several, located in a certain way on the keyboard, then the concept of tonic appears, gravity appears, in a word, unequal relationships between the selected notes. Fret - this is the whole set of gravity, stability of a certain set of sounds. Let's introduce now new term- "diatonic". This is something like a coordinate system within which all events take place. That is, we are dealing with only seven keys out of twelve in each octave, and the remaining five do not seem to exist for us. These seven keys are the diatonic scale, the diatonic scale, the current coordinate system for key and mode data, is that clear? Any sound that does not belong to this scale is no longer considered "diatonic", but "chromatic" (in a given key). And now back to our triads. From theory lessons, you know that a major triad consists of a major and minor third, right? But this is out of tune. But within the diatonic scale of the same C major, the combination of the degrees of the mode and their gravity comes to the fore, while the intervals between them lose all interest. For example, the major triad from the note "fa" really consists of a large (fa-la) and small (la-do) thirds, and this still does not say anything, this is a faceless and uncolored definition. And if we press the triad "fa - do - la", then it will turn out to be consisting of a fifth and a sixth, and will not fit this definition! But in terms of the key of C major, our triad takes on meaning: this is a subdominant triad, regardless of the location of the notes inside it. The characters and desires of each note become noticeable in it.

"Fa" - quite firmly on his feet, but not averse to go to "mi". Because "fa" is prima, the main sound of the chord, and if it is resolved in "mi" - it will become just a third of a new chord - and it's more pleasant for anyone to be the first guy in the village than a small fry in the city! "La" - the sound is unstable and indecisive, although he smiles. Judge for yourself: "la" is not a leader here either, and after resolution, nothing better shines for him than to be farthest from the tonic. However, "la" is still a major, major third, so it radiates optimism. "Before" is a completely different matter. She is above everyone, she is on the right track, she will become a queen (that is, a tonic) and at the same time she won’t have to lift a finger. "Do" will remain in its place, and honor and respect will come to her themselves. Here is the event "fa-la-do... mi-sol-do" for you, containing a lot of emotions and adventures at once. You can guess that in conditions of a different key, when the F major triad is on a different level, each of its notes will have completely different colors and emotions, weigh differently. Let's make such a conclusion - it's still not enough to know how this or that chord is built! The most interesting thing with this chord will happen only in the key. And from the point of view of harmony, any triad should be called not major or minor - this is not the main thing now - but a triad of one degree or another, or one or another functional group. Moreover, it can be built not only by thirds, do you agree?

Now let's just see what triads we have in major and minor. I do not think that this should be memorized, it will be remembered gradually by itself; just follow. To do this, we take the natural (that is, the main, unchanged) major scale, and from each step we measure the triad. We shouldn't care whether there are large or small thirds, we should only measure steps through one, remaining in this diatonic, okay?

And so on. Having built everything that is possible, we will get the following list for the major: I degree-major; II - minor; III - minor; IV - major; V - major; VI - minor; VII - reduced. And for the minor: I step - minor; II - reduced; III - major; IV - minor; V - minor; VI - major; VII - major.

To summarize: in both modes, the triads of the main steps (I, IV, V) coincide with the main mode. The mediant and submediant (III, VI) have the opposite mode. The triads of the introductory steps (these are II and VII, adjacent to the tonic) just need to be remembered, they do not fit into the symmetrical scheme. So that you do not have to return to the question of where and what triads are located in the key, practice:

1. Find the tonic from the triad (for example, the triad "B-flat - D - F, major: in what keys can it be found; what is the tonic if this triad is the VI degree? Or III-rd? Or IV-th?").
2. Build triads of any steps in any key. For a while! Tips: build triads for now in classical form as learned in music theory lessons. Do not invent any appeals yet. So far, the task is to find out what notes a chord consists of, and the location of the notes, even in what octave, is still unimportant. Secondly, try not to get too used to C-major, try to work in any keys. It depends on your flexibility and independence from the number of key signs in general whether you will be able to apply at least something in life. No information in your head should be stored in the form of note names. Otherwise, knowing that "C-Mi-Sol" is a major triad, you do not recognize the same triad in the notes "A-flat - C-E-flat", understand? Be more versatile! In the next lesson, when you are already clicking these steps and triads like nuts, we will learn how to connect them together and try to color some melody with them.

The musical composition consists of several components - rhythm, melody, harmony.

Moreover, if the rhythm with the melody is like a single whole, then harmony is what decorates any piece of music, what the accompaniment consists of, which you dream of playing on the piano or guitar.

Musical harmony is a set of chords, without which no song or piece will be full-fledged, full-sounding.

Properly selected harmony caresses the ear, ennobles the sound, presenting us to fully enjoy wonderful sounds piano, guitar or instrumental ensemble. Melody can be sung, harmony can only be played. (By the way, it is also possible to sing harmony, but not to one person, but at least to three, and, provided that they can sing, this is what artists of the choir and vocal ensembles learn).

A play or a song without harmony is like an uncolored picture in children's books - it is drawn, but there is no color, no colors, no brightness. That is why violinists, cellists, domrists, balalaika players play accompanied by an accompanist - unlike these instruments, you can play a chord on the piano. Well, or play domra or flute in an ensemble or orchestra, where chords are created due to the number of instruments.

In music schools, colleges and conservatories there is a special discipline - harmony, where students study all the chords existing in music theory, learn to apply them in practice and even solve problems in harmony.

I will not delve into the wilds of theory, but will talk about the most popular chords used in modern compositions. Often they are the same. There is a certain block of chords wandering from one song to another. Accordingly, a lot of musical works can be performed on one such block.

To begin with, we determine the tonic (the main note in musical composition) and remember - together with the tonic, the subdominant and dominant. We take the step of the mode and build a triad from it (notes through one). Very often they are enough to play a simple piece. But not always. So, in addition to the triads of the main steps, the triads of the 3rd, 2nd and 6th steps are used. Rarely - 7th. Let me explain with an example in the key of C major.

Examples of chord progressions

I put the chords in descending order of their popularity:

C major

• C major, F major, G major (these are the main triads of the mode);
• whether minor (this is nothing more than a triad of the 6th degree);
• E major, less often - E minor (triads of the 3rd degree);
• D minor (2nd step);
• si - diminished triad of the 7th degree.

And this is another way to use the 6th degree triad in musical compositions:

But the fact is that these musical harmonies are characteristic only if the note DO is taken as the tonic. If suddenly the tonality of C major is inconvenient for you, or the piece sounds, say, in D major, we simply shift the entire block and get the following chords.

D major

• D major, G major, A major (1, 4, 5 steps - main triads)
• B minor (triad 6th step)
• F# major (triads of the 3rd degree)
• E minor (2nd step)
• to # reduced 7th step.

For your convenience, I will show the block in minor key, slightly different steps are popular there, and it can no longer be said that chords of the 3rd and 2nd steps are rarely used. Not so rare.

La Minor

The standard set of chords in A minor looks like this

Well, in addition to the standard - 1, 4 and 5 steps - bases of any key, the following harmonies are used:

• A minor, D minor, E major (main);
• E seventh chord (related to E major, used frequently)
• in F major (triad of the 6th degree);
• C major (triad of the 3rd degree);
• G major (triad of the 2nd degree);
• A major or A seventh chord (the major of the same name, often used as a kind of transitional chord).

How to find a tonic

A question that plagues many. And how to determine the tonic, that is, the main key, from which you need to start when searching for chords. I explain - you need to sing or play a melody. What note it ends on is the tonic. And the mode (major or minor) is determined only by ear. But I must say that in music it often happens that a song begins in one key and ends in another, and it can be extremely difficult to determine the tonic.

Only hearing, musical intuition and knowledge of theory will help here. Often the completion of some poetic text coincides with the end of the musical text. Tonic is always something stable, affirming, unshakable. Once the tonic has been determined, it is already possible to select musical harmonies based on the above formulas.

Well, the last thing I would like to say. The flight of the composer's creative inspiration can be unpredictable - seemingly completely unpredictable chords sound harmonious and beautiful. It's already aerobatics. If only the main steps of the mode are used in a musical composition, then they say about this - “a simple accompaniment”. It is really simple - with basic knowledge, even a beginner will be able to pick them up. But more complex musical harmonies are closer to professionalism. Therefore, it is called “pick up” the chords for the song. So let's recap:

1. We determine the tonic, and for this we play or hum a melody and look for the main note.
2. We build triads from all steps of the mode and try to remember them
3. Playing the chords in the above blocks - i.e. standard chords
4. We sing (or play) a melody and “select” a chord by ear so that they create a harmonious and beautiful sound. We start from the main steps, if they don’t fit, we “feel” other triads.
5. We rehearse the song and enjoy our own performance.

As a tip, it is convenient to select musical harmonies along with the sound of the original on a music center, computer or tape recorder. Listen several times, and then take a fragment, say, 1 verse and, after pausing, pick it up on the piano. Go ahead. Selecting musical harmonies is a matter of practice.

Let's temporarily forget about temperament and remember that I promised you the connection between the overtone scale and harmony. The development of the overtone scale is associated with the development musical culture generally.
In particular, with the development of "warehouses" musical texture(see Warehouse) - from "monody" to "homophony"

If we take professional music into account, then good example monody will be the music of the Middle Ages. At this stage, we are dealing with the development of intervals, occurring from the edges of the overtone scale. For clarity, you can listen to Gregorian chants. In them, the upper part of the overtone series is given to the melody - seconds (of course, large seconds predominate) and occasionally thirds (we are talking about horizontal presentation), and in the vertical cut we meet: octaves, fifths, quarts - and often in one composition one interval is chosen for parallel duplication of the main voice (usually an octave), or two (fifth and octave) - and dubbing rarely changes in the process. When there are no duplications, we hear pure monody. Currently, this style of music can be heard in church singing.

In this example, there are three options for duplication, in a row. At the end, there is a partial release of the lower voice from the function of duplication.

At the beginning of this example, there is still no "relationship of harmonies" in the sense we are looking for, there is no connection of chords, or at least different intervals - the second voice duplicates the first one by an interval higher - that's all. Before us is the same melody, with its own system, only more voluminous due to doubling. It turned out one layer. But at the end something more interesting happens, but for now the lower voice is tied to the upper rhythm. Surely this fragment was considered the pinnacle of skill. :)

Then, after a couple of centuries, the second voice received freedom - rhythmic and melodic. And here, on each next note of the melody, different intervals began to appear - from that moment on, we can talk about the connection of intervals, although still within the framework of linear logic.

Further development it’s difficult to describe in a nutshell, so I’ll go straight to the bottom line: by the 16th century, polyphony rules appeared, implying freedom and independence of voices within the rules for connecting intervals (that is, a chord was considered their sum) and melodic lines - by the 18th century, this system reached its perfection and changed to another. The freedom of voices was achieved by rhythmic non-synchronism (see Counterpoint). (Rhythmic synchrony was also used, but mainly in church music- in the chorale. Hence the term "choral texture"). In the 18th century, the homophonic-harmonic type of presentation of the material became the leading one (the term itself hints that there is already harmony in the very sense in which we need it) - the division of the texture into 2 layers: melody and accompaniment (complementary, harmonic). The accompaniment took on the function of harmonizing the melody. This system has absorbed some of the rules of polyphony - they are gradually turning into the rules for connecting chords in 4-voices. Here, for the first time, the functional connection of chords within the same key is noticed.

By the 17th-18th century, chords of the tertian structure were fully mastered - the final capture of the overtone scale took place (that zone where we see thirds following each other. Triads and seventh chords officially appear. They also appear in the melody (that is, the melody can now move along the sounds chord - in a row, or from one sound to another in a jump, in any direction).

This whole process is also connected with the expansion of the concepts of consonance and dissonance. I also advise you to read about this in elementary theory.

Also in the 18th century, the concept of tonality appears. And then ... Everything became even more complicated and at the same time there was even more freedom for creativity.

Registers

Above we discussed the importance of the overtone scale for harmony and music in general. Now let's look at it as a source of boring perfect texture. What we see:

In the lower register there are wide consonant intervals: octaves, quarts, fifths.

In the middle register, our main harmonic stuffing of pieces - in this zone, "one-handed" triads and their inversions sound excellent (which cannot be said about them in the counteroctave, for example).

The high register is ideal for a melody moving in a more detailed line, with seconds, embellishments, etc.

That is, if the entire texture is calculated, correlating with the overtone series, we get an idealized version, acoustically monolithic.
The naturalness of this or that type of movement of voices depends on the choice of register. In the lower register there is naturally a smoother, slower movement, in the high register it is faster, more fluid, and in the middle there is something in between.

No one forces you to do this, it is enough just to know that it is most convenient to perceive information in such a placement and tempo match and the listener's brain is minimally stressed. This placement is normal. All sorts of relaxing things, ambient for meditation, etc. are often made in it. In relaxing ambients, everything sounds like this - there is a leisurely bass, there is a shimmering middle, there are some overflows (often on oberons) in a high register. This option informs us about the natural state of rest, about complete and final ordinariness. The unusual begins where movement begins away from this position and rhythms - and it is there that music begins, informing us of states that are different from rest. It turns out that all other uses of registers tell us about the movement ( actors, objects or abstractions), anxiety, threat and other states.

For example, dense triads in the contra-octave, despite the feeling of harmony, will carry a threat or epic power (minor chords will threaten, and major ones will say "calm, these are ours"), since each of the bass tones will give a number of overtones, and they , in turn, will give a feeling of dirt, dissonance, uncontrolled hidden movement (due to the resulting beats in the overtones). And the amplification of the sound in this zone itself did not promise us anything calm since the Paleolithic times, as well as the squeak of a violin or a piccolo flute frozen on one note in the 4th octave.

The fast-moving bass also definitely carries an active character, an imperative. Typical for dance music. Also typical for showing the movement of large objects.

Let's summarize:
● There is a relationship between the pitch of the sound and the size of the intended source or medium of the sound. In this sense high sounds are more likely to be associated with small objects, while low ones are more likely to be associated with large ones.
● Also, the pitch can actually be associated with the height of the object.
● Also, the pitch can be associated with the importance of an object or an ongoing voiced event. The lower - the more important, more significant.
● There are types of object movement environment, which since ancient times inspire peace in a person - in the lower register nothing moves or moves slightly, in the middle - something slowly moves (a flock of sheep, for example), in the upper register - trees rustle, birds chirp, the wind howls.
● A rhythmic element placed in a certain register - bass, middle or high - will be evaluated by the brain for kinetic potential in the context of the register. Depending on the conditions, the sound will be accepted as the movement of an external object, or as a manifestation of one's own activity (for example, in dance music, the rhythm of the barrel is associated with the movement of the legs - steps are perceived by the human senses as a blow, and from music we transfer the movement to ourselves).

Check out this cute scene of the changing seasons in the first Harry Potter movie.

At the beginning, a scene of winter and serenity - the bass in the lower register stands still, above, the harmonies of T S slowly alternate for a while, and a smooth melody sounds above all this.
Then (10th second) active joyful fragment on the same harmonies (T S): lower case not busy, the middle one is busy with moving chords (on an A-flat of a small octave), and a high note froze at the top - E-flat of 3 octaves. In sum, this gave the promise of further movement.
At 18 seconds, the promise is fulfilled - the music unfolds, occupying all registers. The bass moves, supporting magical shifts of harmonies that take us into new tonalities. The smooth melody of the horns moves in the middle register, the more active figurations (shorter durations) - in the strings in the high register. The figurations of the strings have something in common with the image of flight (what we see in the frame), this feeling is reinforced by the "flying" passages of the harp and the strings either gaining height or lowering it. A resonant bass in the lower register gives us a hint that the changes that are taking place are important, significant and "solid". The image of change is mainly shown by movement through different keys.

In music is harmony. It emphasizes the expressiveness of the melody, "finishes", complements the thoughts embedded in it. At the same time, harmony in music is one of the most complex sciences, therefore it is thoroughly studied in musical secondary special and higher educational institutions. Some of the basics of harmony are included in the course of solfeggio for children music schools and children's art schools. What is harmony in music? The definition is what we will try to understand first.

Definition

Harmony is a multifaceted term. The concept of harmony in music includes various facets: it is both a term meaning "euphony", and the science of chords and consonances, and academic discipline. Consider the definitions that are given in the textbooks in more detail.

Harmony is an integral part of artistic thinking

Harmony - pleasant to the ear coherence of sounds in piece of music; same as "benevolence"

Harmony - a word of Greek origin, which means harmony, proportionality, proportionality, consonance.

Harmony can also be a designation of the composer's harmonic style.

Harmony - one or a group of consonances

Harmony - the doctrine of the sequence of consonances

Harmony in a narrow sense is the systemic principles of organizing pitch ratios

Harmony in a broad sense - any pitch intonation conjugation, covering the space-time continuum vertically, horizontally, diagonally, having a structure-forming value and capable of acting as an element (or one of the levels) of a pitch system.

Harmony - combining sounds into consonances and their coherent succession

Harmony is a scientific and educational and practical discipline covering one of the most important aspects of composition technique, studying consonances and systems of connections between them.

Indeed, the definitions of harmony are varied. But they all talk about the importance of this integral part of music. About its importance for composers. After all, in order to write beautiful music, you need to be able to competently build a musical thought. The chaos of sounds is unlikely to be considered a masterpiece (although in contemporary art everything is possible...). The performer also needs to understand harmony, because it is one of the means by which a musical image is created.

IN modern meaning the term "harmony" began to be used around the beginning of the 19th century, before that the concept of general bass was used.

Features of harmony

As can be seen from the definitions, harmony is not an easy science. The main thing that is studied in harmony is the chord. Like harmony in music, the chord has several meanings; different textbook authors interpret it differently.

A chord is a consonance of three or more sounds arranged in thirds

This definition of a chord is the most common. It mainly refers to classical harmony, where tertian chords are most common. There are also fourth, second, and mixed chords.

A chord is a consonance of three or more sounds arranged according to a certain principle.

Each chord has a number of characteristics: the structure, its function in harmony. In the course of teaching classical harmony, a lot of space is devoted to studying the functions of chords, the sequence of their application, the peculiarities of resolving chords of a particular function, the correctness of voice leading when connecting chords (transition of one chord to another).

Types of harmony in music

Varieties of harmony are mainly associated with historical periods and musical styles in which harmony was modified.

The appearance of harmony is associated with polyphonic music. By the 11th century, division into voices appeared in the Gregorian chant, and it became almost impossible to memorize all the chant. This fact is connected with the appearance of musical notation and the development of all musical-theoretical disciplines. Serious works on harmony appeared in the 16th century, one of which was written by Tsarlino.

As a result, 4 main types of harmony can be distinguished:

• In the era of Viennese classicism, the basic rules of classical harmony were formed. All other species are based one way or another on these rules.
• Romantic harmony is characteristic of the 19th century and is associated with the era of romanticism.
• Jazz harmony appeared in the 20th century along with the corresponding musical direction.
• Modern harmony also took shape in the 20th century.

classical harmony

Classical harmony with its rules and laws was finally formed in the work Viennese classics Cast: Joseph Haydn, Christoph Kluck, Wolfgang Mozart, Ludwig van Beethoven.

There are 3 main functions in classical harmony: tonic - T, subdominant - S, dominant - D. The main functional turnover is T-S-D-T. This is the order in which the functions follow their resolution. And, for example, if the options combinations T-S-T, T-D-T, S-D are possible, then the transition of D to S in classical harmony is not allowed. For example, joining chords to form parallel fifths or octaves is not allowed. An important indicator is the stability of chords, the clarity of tonality and functions. Consonant chords predominate - major and minor triads. The leading role belongs to the melody, harmony basically supports it.

A fairly striking example is Diabelli's sonatina in G major.

If you look at the first 4 measures, you can see the following chord progression T 5 3 -II 6 -D 7 -T 5 3. The second step belongs to the subdominant function, so classical sequence functions are fully preserved.

In general, the main indicator of classical harmony is strict observance of the rules.

romantic harmony

Romantic harmony, which gradually replaces the classical one, is much more complex. It first appeared in the work of such composers as Franz Schubert, Robert Schumann, Frederic Chopin, Hector Berlioz, Franz Liszt and Richard Wagner.

On the one hand, in the harmony of romantic composers, much greater freedom in voice leading is allowed, deviations from the strict rules of classical harmony are possible. On the other hand, the consonances themselves, the chords become more complex. The role of dissonant chords is increasing: augmented and diminished triads, seventh chords, non-chords. Altered chords are applied (that is, chords with raised or lowered sounds). Increasing number non-chord sounds. Acquire great importance dissonances, the overall tonal stability is lost. A term such as "extended tonality" acquires meaning, in which much more features. According to Kholopov's definition, various techniques of harmony appear. The harmonic language becomes very individual, before the advent of "nominal chords", the use of chords as a keyharmony. For example, for the work of F. Chopin, a dominant with a sixth is characteristic, for F. Schubert - a VI minor.

In the opera "Tristan and Isolde" by R. Wagner, the so-called "Tristanaccord" appears, from which the work begins, it characterizes the entire harmonic style of the composer.

The overture to the opera "Tristan and Isolde" is especially indicative from the point of view of the peculiarities of romantic harmony: instability, dissonances (tritones are highlighted in color, sometimes even 3 tritones are found in a measure), an abundance of non-chord sounds (indicated by crosses above notes), alterations, dissonant triads - all this is found even in a small fragment above, but the music is simply mesmerizing!

These are the main features of romantic harmony. If we talk about the relationship in music: melody / harmony, then here more attention is paid to the colorfulness of harmony, it is she who begins to play a more significant role.

jazz harmony

The seventh chord becomes the main harmony in jazz, the role of dissonance is very large. Voice leading in this type of harmony is even freer. Probably jazz harmony is one of the most democratic types.

One of important achievements jazz harmony is a jazz notation for chords. It is to some extent much easier for quick mastering, it is often used by people who do not have a musical education.

Instead of the usual functions - T-S-D-T - the main tones of the chords are used, for example, in C major, the sequence consisting of the main triads will look like this: C-F-G-C. The letter designations generally correspond to the classical ones:

• C - before;
• D - re;
• E - mi;
• F - fa;
• G - salt;
• A - la.

Only the note si occurs in two versions, and B - does not always denote si-flat, as in classical harmony.

• H, B - si

A special feature is that instead of the small letters used in classical harmony, the letter m is simply added to indicate minor triads in the jazz system. The designation of sixth chords is also unusual, the number 6 next to the letter denoting a triad means that a sixth has been added to the triad. That is, C 6 is not mi-sol-do, but do-mi-sol-la. To designate a sixth chord, a bass is written through a dash, for example, C / E - C major with bass E.

• M, maj, maj7, Δ - major seventh (only applies to the seventh in the chord)
• m, mi, min - minor (always refers only to the third in a chord)
• °, dim, verm - reduced (reduced seventh chord)
• Ø - small reduced (half-reduced seventh chord)
• aug - enlarged
• 7, x - small major (dominant)
• add - added stage
• sus - delay (replacement of a step, as a rule, a third, for example: Csus4- it turns out instead of a third in C major there will be a quart or Csus2 - a big second)
• omit - step skip
• - , ♭- decrement of the chord
• +, ♯ - raising the degree of the chord (always applies only to fifth or none)

The number of seventh chords can be seen in the work of E. Medvedsky - "Gamma Jazz".

There are almost no triads in this work, it is especially surprising that dissonances only enhance the cheerfulness of this music.

Modern harmony

Modern harmony is a field much less explored due to its complexity and incredible freedom and individuality. This includes dodecaphony, artificial frets, and much more. IN contemporary music rare tonal stability.

You can catch this by listening to Arnold Schoenberg's vocal cycle - "Moon Pierrot".

Harmony Tutorials

The main textbook, which is studied by almost all musicians in secondary specialized educational institutions, is the brigade harmony textbook. It was compiled by 4 authors: I. Dubovsky, S. Evseev, I. Sposobin and V. Sokolov. In this textbook, in detail, with examples, all the necessary rules are sequentially stated in order of increasing complexity and importance of chord functions. First, the main triads of the mode are run through (as well as the most used seventh chords), then the side triads are added. Then larger themes begin.

An alternative is A. Myasoedov's textbook. The logic of presentation in this textbook is different. If triads are studied, then all at once (main and secondary). Similarly, seventh chords. In general, the logic is interesting, however, one should be very careful about the text - sometimes there are inaccuracies.

There are also works by E. Abyzova, T. Muller.

A grandiose, thorough work on harmony was created by V. Berkov. Many topics are covered in the textbook in much more detail than in the previous two. But, nevertheless, it is better to first study the brigade textbook, and then proceed to more complex manuals.

For the most courageous, courageous people who study harmony, there are the works of Y. Kholopov. It is better not to open this book without basic knowledge of harmony. How not to open it if you are afraid of a lot of scary words. There are 2 textbooks by this author: a theoretical course, where Yuri Nikolayevich's theory is presented in thematic blocks, and a practical one, where you can get acquainted with the harmony of different eras on practical tasks.

Quite difficult to understand and, at the same time, very interesting is the textbook by L. Dyachkova. To fully understand what in question, you will have to thoroughly study the textbook by Yu. Kholopov. The most curious are 2 books: Harmony in Western European Music of the 9th - early 20th century and Harmony of the 20th century.

Harmony is one of the most amazing areas musical art which is interesting to study despite its complexity.