What are the intervals in music, in mathematics?

What is the relationship between music and exactsciences, for example, mathematics? This question people began to ask from ancient times. Modern scientists have proved that the thought processes that occur in solving mathematical problems are similar to those that occur during the performance of musical works and the study of subjects of the musical-theoretical cycle.

For example, the definition of musical intervals onhearing is an action to find the distance between sounds of different heights. On the basis of this, it was concluded that the parallel occupation of music and mathematics can greatly facilitate the assimilation of both sciences.

There is also an obvious similarity between someelements of musical-theoretical and mathematical terminology. This is partly due to the use in both sciences of a number of terms that are of Latin origin, but still there is such a similarity. This article presents the definitions of intervals from the point of view of music theory and answers the question: what are the intervals in mathematics. Also in the article there are examples of the use of the term "interval" in some other spheres.

General concept

To begin with, we should consider the very meaning of the word "interval" and its origin.

So what are the intervals?

The word "interval" has Latin roots and canbe translated as a gap or a distance. This term, in addition to music and mathematics, is used in such fields of knowledge as: military affairs (means the distance between two military personnel, military units, and between units of military equipment), medicine (used in cardiography), is of key importance in the theory of relativity. in the calculation of the time of floods, volcanic eruptions and the like natural phenomena.

What are intervals in music?

In musical-theoretical disciplines, the intervalin the broadest sense of the word is called the distance between two musical sounds, and in the narrow sense - the consonance of two sounds that can be played simultaneously or sequentially. If the sounds of the interval are taken simultaneously, then such an interval is considered harmonic, and if successively - melodic.

The musical intervals can be expressed as inmathematical numbers, denoting the number of prisoners in the interval of steps, and in acoustic units - cents. The intervals have a Latin name, according to the number of stages of the scale in them: prima (translated as "first") - one stage, second ("second") - two steps and so on. They can also be simple and complex. Simple intervals are eight (an octave and all intervals are less than it).

Considering the question of what are the intervals inmusic, it is worth mentioning one more value that characterizes them, namely, the number of semitones contained in them. On this basis, the intervals are divided into large and small, clean, reduced and enlarged.

Other features of musical intervals

An inversion of an interval is the transfer of itThe bottom sound is an octave higher. At the same time, the quality component changes to the opposite one - large ones turn into small ones, enlarged ones into smaller ones, and so on. Clean intervals always turn only to clean ones. The sum of the numerical designations of the consonants in each other is nine.

Thus, the prima turns into an octave, thirdsin the sixth and so on. For compound intervals, the rules are somewhat different: two interval sounds should be shifted by an octave, the upper one by an octave upward, and the interval base by an octave down. The sum of the numerical designations in this case must be equal to the number sixteen.

Interrelation of two sciences

From the previous information it is clear thatmusical and theoretical knowledge is largely based on mathematical calculations. So, the benefit of parallel learning of both disciplines is obvious. After all, students of music schools decide in harmony classes for the task, I use all the same arithmetic calculations. Except for happy owners of the so-called "absolute hearing", for which this work is greatly facilitated by natural data.

The use of music for developmentmathematical abilities and the development of logical thinking in general was experimentally confirmed by the Hungarian teacher-innovator Zoltan Kodai in the middle of the last century.

He founded several schools with an in-depthstudying music. And the number of music lessons was increased due to the reduction of hours allocated to other subjects. The control section, conducted in all subjects at the end of the training cycle, revealed a level of knowledge in students of experimental schools that exceeds the knowledge of pupils of schools with traditional education.

What are the intervals in mathematics?

In mathematical science, most oftenTwo terms are used, denoted by the word "interval". The definitions of these two concepts constitute the answer to the question: what are the intervals from the point of view of mathematical science.

So, the most common in mathematics are the intervals of monotony and law-constant. Let us consider their definitions.

What are intervals of monotonicity?

These are such intervals of the value of the argument of the function, under which the function becomes only increasing or only decreasing.

And what are intervals of sign-standing?

These are such intervals of the domain of definition for which the sign of the function remains unchanged.

In both cases, we are talking about certain gaps, as in the case of musical intervals.

Perhaps the most vivid example of the use of the word "interval" in a particular industry is the well-known computer program "Vord". Let's study this moment as well. What are the intervals in the "Word"?

Application in the "Word"

It is known that in this program three types of gaps are involved:

1. The gap between the lines.
2. Between separate paragraphs.
3. Between adjacent pages.

There is no need to consider the detail valueeach of the above three intervals, used in the program "Word", as it is devoted to a lot of literature. It should be noted that in this case we are talking about a phenomenon that has, albeit a distant, but similarity with musical intervals.

Finally

In this article, the issue of communicationmusic with mathematical science. It was revealed that such a connection does exist, which is proved both by experiments in pedagogical science and by analysis of thought processes in both activities. Also considered is the question of what are the intervals in music and mathematics. Here, too, some common points in the definitions of mathematical and musical terms are revealed. Now it becomes clear what intervals are. And this proves once again that the realm of contact between the two spheres, mathematics and music, really exists.