Natural scale: description of the concept, order of construction

2024 Author: Leah Sherlock | [email protected]. Last modified: 2024-01-17 12:35

Today's musical practice is based on a system that is a series of sounds. There are certain high-rise relationships between them. Their location in height is usually called the scale. Each 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 audible to 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 “Do” to “Si”. And what then is the natural scale? And what are the relations of sounds in it? And what role do partial tones play in it?

Definition

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

The vibrational 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 exceed the pitch of the main sounds, while other overtones,on the contrary, they are inferior in this respect.

What are partials?

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

note	octave	counter-octave	big octave
C		32	65
C		34	69
D		36	73
D		38	77
E	20	40	82
F	21	42	87
note	octave	counter-octave	big octave
C		32	65
C		34	69
D		36	73
D		38	77
E	20	40	82
F	21	42	87
F	23	44	92
G	24	46	103
G	25	49	110
A	27	51	116
A	29	55	118
B	30	58	123

Denotations: A - la; D - re; E - mi, F - fa, G - s alt, B - si;- sharp.

A sound wave has a very complex configuration. The reason for this is (on the example of a guitar string): the vibrating element (string) vibrates, refraction of sound is created in equal proportions. They produce independent vibrations in the total vibration of the body. Another waves are created, identical to their length. And they generate partial tones.

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

If the string formed only the fundamental 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 twice as long as the wavemain tone. And in terms of vibration frequency, it is twice the main tone.

Wave streams 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 (fundamental tone), more precisely, the number of its vibrations, can be displayed as a unit. The number of oscillations of the resulting tones can be expressed in simple numbers. Then a simple arithmetic series is obtained: 1, 2, 3, 4, 5…. This is already a natural sound. It remains to deal with its construction.

Build question

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

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

The following result of this construction is obtained:

Such a complex structure of the natural scale from one string is not perceived by a person consciously. And the following reasons appear here:

1. Many sounds have a similar structure.

2. The amplitudes of overtones are significantly inferior to the amplitude of the main frequency coming from the string.

Building from notes

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

T – P – T – T –P– T – T

Scheme forthe second is as follows:

T – T – P – T – T – T – P

Notation here: T - tone, P - semitone.

Thus, when building from "A" in minor, the following picture is obtained:

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"

The natural scale from "Re" is also built depending on the key. Minor building produces the following result:

D - E - F - G - A - A - C – D

In the music book it is written like this:

In the major scenario, the situation is as follows:

D – E – F - G – A – B – C - D

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

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

In the minor example, the picture looks like this: D – E – F – G – A - A - C - C. The sound is oriental.

Work from Fa

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

And the major structure of the natural scale, built from "F", is as follows:

F – G – A - A - C – D – E – F

Records on musical lines are obtained as follows:

Minor construction pattern:

F – G – G - A – C – C - D - F

The following designations are obtained on the musical rulers:

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

On natural intervals

There are only corresponding intervals on the main steps of natural structures. These include both the augmented fourth and the diminished fifth.

The total number of intervals with the same step parameter is always identical to the number of main steps. And any such interval is built at a different step.

In parallel keys, the group of intervals is always the same. But the steps on which they are raised vary.

The following table is provided to show these principles:

Intervals	Their main types	Steps with their presence	Their number
Natural. major	Natural. minor
Prima	Ch.	At all	At all
Second	M	3 and 4	2 and 5
- »-	B	1, 2, 4, 5 and 6	1, 3, 4, 6 and 7
Thirtia	M	2, 3, 6 and 7	1, 2, 4 and 5
- »-	B	1, 4 and 5	3, 4 and 7
Quart	Ch.	1- 3, 5 -7	1 – 5, 7
…..	Uv.	4	6
Quint	D.	7	2
…..	Ch.	1 - 6	1, 3-7
Sexta	M.	3, 6, 7	1, 2 and 5
-» -	B.	1, 2, 4 and 5	3, 4, 6 and 7
Septima	M.	2, 3, 5-7	1, 2, 4, 5 and 7 I
- »-	B.	1 and 4	3 and 4
Octave	Ch.	At all	At all

Notation in the table:

B is big. M is small. H -clean. Uv - increased. Mind - reduced.

About tone change signs

These characters are sharps (denoted by the symbol, meaning an increase by half a tone) and flat b (denoted by the symbol b, they indicate a decrease by a half tone). In the natural interval, they are not set simultaneously.

There is an important nuance here: the note "La" does not have 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 "La" (A - F) is found only in majors and minors, in which there are a maximum of 4 sharps.

The following tones fall under this criterion:

1. Major: G, D, A and E.
2. Minor: Em, Bm, Fm, Cm

Working with intervals without rising or falling signs, you need to calculate which sound is first formed here with this sign. Further work is built according to the indicated principle.

Example: searching for a key with a minor third E - G. You can follow the circle of fifths towards the sharps. Then the sign should appear at the note "Sol". But he does not appear in this position. Then structures with at least 3do not contain this third.

You can go in the same circle, but to flats. Then the flat should form near "Mi". However, he is not. Then the indicated spacing does not appear in structures where the minimum is 2 flats.

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

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

Next, the tonality is specified by name and the steps on which this interval is raised.

The following principle will help with this: there are 7 main steps in harmony. And here there are 7 seconds, the same number of thirds and other intervals. They may differ in tone value. This factor is determined by the construction from a certain level.

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

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

Music practice

There are instruments that differ in that only the natural scale is extracted on them. It's about:

1. Horn and fanfare.
2. All kinds of horn.
3. Pipe.
4. Horn.
5. An overtone-type flute, such as Russian Kalyuka.

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

Thus, in pure tuning, m.7 (minor fifth) is formed by adding ch.5 and ch.m. 3 (pure ones add up: a fifth and a minor third). The frequency parameter of its sound is 1017, 6 c. And in natural seventh it reaches 968.8 c.

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

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

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