Natural scale: description of the concept, construction order

Today's music practice is based on a system that is a series of sounds. Between them there are certain high-altitude relationships. Their location in height is usually called the scale. Every sound in it is a step. There are about a hundred sounds in the full scale of this system. Their frequencies vary greatly and are concentrated in the range of 15-6000 oscillations per second. These sounds are distinguishable by the human ear. And the exact definition of their height depends on the degree of development of musical ear.

The main steps of the scale are the names of the main notes, from “To” to “C”. And then what is a natural scale? And what is the relationship of sounds in it? And what role does partial tones play in it?

Definition

A natural scale is a sound series that includes the fundamental tone and harmonic sounds (their other name is overtones).

The vibration frequencies of sounds here interact in such a way that a natural number series is obtained: 1, 2, 3, 4 ... Due to the presence of overtones, this scale is called the natural overtone scale.

Some overtones are superior to the main sounds in pitch, while other overtones, on the contrary, are inferior to them in this regard.

What are the partial tones?

Natural scale is also characterized by the presence of partial tones. Their number in different octaves and from each note is different:

Designations: A - la; D is re; E - mi, F - fa, G - salt, B - si; # - sharp.

The sound wave has a very complicated configuration. The reason for this is (for example, a guitar string): an oscillating element (string) vibrates, the sound is refracted in equal proportions. They produce independent vibrations in the total vibration of the body. Another wave is created that is identical to their length. And they generate partial tones.

These tones may vary in height. After all, the dynamics of oscillations of the waves that formed them has different parameters.

If the string formed only the basic tone, then its wave would have a simple oval shape.

The second partial tone arises from half of the initial sound wave of the string. Its wavelength is half that of the pitch. And in frequency of oscillations, it is twice as high as the fundamental tone.

Wave flows from the third sound are already three times more dynamic than the waves of the initial sound. From the fourth - four times, from the fifth - five, etc.

The initial sound (the main tone), more precisely, the number of its vibrations, can be displayed as a unit. That number of oscillations of the arising tones can be expressed by primes. Then we get a simple arithmetic series: 1,2, 3, 4, 5 .... This is a natural scale. It remains to deal with its construction.

Building issue

How to build a natural scale? To answer this question, the simplest example is proposed.

The main tone here is the note "Do", located in a large octave. From it, the construction of a sound series having frequencies according to the indicated regularity is organized.

The result of this construction is obtained:

Man does not consciously perceive such a complex structure of a natural scale from a single string. And here such reasons appear:

1. Many sounds have a similar structure.

2. The amplitudes of the sounds significantly lose the amplitude of the main frequency emanating from the string.

Building from notes

You can build a natural sound range from any note. It is important to take into account the tonality. It can be minor or major. For the first, the construction scheme is as follows:

T - P - T - T –P– T - T

The scheme for the second is as follows:

T - T - P - T - T - T - P

Designations here: T - tone, P - half tone.

Thus, when constructing from “A” in minor we get the following picture:

A - B - C - D - E - F - G - A

The same row, but in a major scenario, looks like this:

A - B - C # - D - E - F # - G # - A

The note from which the series is built is called the tonic.

The following are examples of construction from Re and Fa.

Work from "Re"

Natural scale from "Re" is also built depending on the key. In minor construction, the following result is obtained:

D - E - F - G - A - A # - C - D

In a music notebook this is written like this:

In the major scenario, the situation is as follows:

D - E - F # - G - A - B - C # - D

And in the notebook (or the program "Guitar Pro"), the entry is entered as follows:

But there are still nuances. The same scale can exist in harmonic modification. In it, before the tonic, an additional semitone occurs.

In a minor example, the picture is as follows: D - E - F - G - A - A # - C - C #. The sound is obtained with an oriental touch.

Work from the Fa

The natural scale from "F", built according to the major scheme, has the same signs as the minor row from "Re". These are two parallel keys.

And the major structure of a natural scale built from the Fa is as follows:

F - G - A - A # - C - D - E - F

Records on musical lines are obtained as follows:

Picture of minor construction:

F - G - G # - A # - C - C # - D # - F

The following notation is obtained on musical rulers:

Here the signs are the same, but are indicated by flat: A - flat = G #. B flat = A #. D flat = C #. E flat = D #.

About natural intervals

On the main steps of natural structures there are only corresponding intervals. These include an enlarged quart and a reduced fifth.

The total number of intervals with an equal step parameter is always identical to the number of main steps. And at any stage any such interval is built.

In parallel keys, the group of intervals is always unchanged. But the steps at which they are being built vary.

The following table is provided to reflect these principles:

Designations in the table:

B - big. M is small. H - clean. Uv - increased. The mind is diminished.

About Tone Signs

Such signs are sharps (indicated by the symbol #, indicate an increase by half) and flats b (indicated by the symbol b, indicate a decrease by half). In the natural interval, they are not set at the same time.

There is an important nuance here: the note “A” lacks a sharp, which is the fifth in order.

This nuance indicates that in the key, where there are at least 5 sharps, this interval does not appear.

Then the big sixth (b.6) from "A" (A - F #) is found only in majors and minor, in which there are a maximum of 4 sharps.

Under such a criterion, such tonality falls:

1. Major: G, D, A and E.
2. Minor: Em, Bm, F # m, C # m

Working at intervals without signs of raising or lowering the tone, you need to calculate which sound is first formed with such a sign. Further work is based on the indicated principle.

Example: there is a search for tonality with a small third E - G. You can follow along the fifth circle in the direction of the sharp. Then the sign should appear on the note “Salt”. But he does not appear in this position. Then structures with a minimum of 3 # do not contain this third.

You can go in the same circle, but to the flat. Then a flat should form near the "Mi". However, he is not. Then the indicated interval does not appear in structures where there are at least 2 flats.

As a result of the search, the minor third E - G is present in such minor and major structures, where:

• no characters with a key;
• there are 1-2 sharp;
• there is 1 flat.

Further, tonality is specified by the names and steps at which this interval is constructed.

This principle will help in this: there are 7 main steps in the fret. And there are 7 seconds, as many thirds and other intervals. They may differ in tone value. This factor is determined by the construction of a certain level.

Example: there are major and minor structures. Here a small second appears twice. In the first case, at 3 and 4 steps. In the second - at 2 and 4 steps.

Then on the other five steps only big seconds line up.

Music practice

There are instruments that differ in that they extract only natural scale. This is about:

1. Horne and fanfare.
2. All kinds of horn.
3. The pipe.
4. French horn.
5. Flute overtone type, such as Russian kalyuk.

That is, basically they are representatives of the wind instrumental category. And the natural scale of wind instruments from this list is often perceived as a clean system. This is mistake.

So in a clean system m.7 (small fifth) is formed by the addition of part 5 and part m. 3 (add up clean: fifth and small third). The frequency parameter of its sound is 1017.6 c. And in natural septime, it reaches 968.8 c.

The indicated scale is often involved in ethnic singing. Examples:

1. Indian stew.
2. Throat Tuvan singing.
3. Singing of the African Kosa tribe (emphasis on the first syllable).

Academic music knows rare examples of using natural scale. The most striking of them are the first and final parts of Britten's Serenade. A horn is played there solo.