What is the relationship between music and the exact sciences, for example, mathematics? People began to ask this question since ancient times. Modern scientists have proved that the thought processes that occur when 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 by ear is the action of finding the distance between sounds of different heights. Based on 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 some elements of musical-theoretical and mathematical terminology. This is partly due to the use in both sciences of a number of terms of Latin origin, but nevertheless such a similarity holds. This article presents the definitions of intervals from the point of view of music theory and answers the question: what are intervals in mathematics. Also in the article there are examples of the use of the term "interval" in some other areas.
General concept
To begin with, one should consider the very meaning of the word "interval" and its origin.
So what are intervals?
The word "interval" has Latin roots and can be translated as a gap or distance. This term, in addition to music and mathematics, is used in such fields of knowledge as: military science (denotes the distance between two military personnel, military units, as well as between units of military equipment), medicine (used in cardiography), is of key importance in the theory of relativity, it is used in calculating the time of floods, volcanic eruptions and the like, natural phenomena.
What are intervals in music?
In musical theoretical disciplines, the interval in the broad sense of the word is the distance between two musical sounds, and in the narrow sense, the harmony of two sounds that can be played simultaneously or sequentially. If the sounds of the interval are taken at the same time, then such an interval is considered harmonic, and if in sequence - melodic.
Musical intervals can be expressed both in mathematical numbers, indicating 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 enclosed in them: prima (translated as “first”) - one stage, second (“second”) - two stages and so on. They can also be simple and compound. There are eight simple intervals (an octave and all intervals are less than it).
Considering the question of what intervals in music are, it is worth mentioning another quantity that characterizes them, namely, the number of halftones contained in them. On this basis, the intervals are divided into large and small, clean, reduced and increased.
Other features of music intervals
The inverse of the interval is the transfer of its lower sound an octave up. At the same time, the qualitative component is reversed - large ones turn into small ones, enlarged ones into smaller ones, and so on. Clean intervals always turn to pure ones. The sum of the numerical designations of the consonants converted into each other is nine.
Thus, prima turns into an octave, a third into sextus, and so on. For composite intervals, the rules are slightly different: the two sounds of the interval should be moved an octave, the top one should be moved up an octave, and the bottom of the interval must be moved down an octave. The sum of digital designations in this case should be equal to sixteen.
The relationship of the two sciences
From the previous information it is clear that musical-theoretical knowledge is largely based on mathematical calculations. So, the benefits of parallel study of both disciplines are obvious. After all, students of musical educational institutions solve problems in harmony classes, I use all the same arithmetic calculations. With the exception of the lucky owners of the so-called "absolute hearing", for whom this work is greatly facilitated by natural data.
The use of music for the development of mathematical 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 in-depth study of music. Moreover, the number of music lessons was increased due to the reduction of hours allocated to other subjects. A control slice, conducted in all subjects at the end of the curriculum, revealed in students of experimental schools a level of knowledge that exceeded the knowledge of students in schools with traditional education.
What are intervals in math?
In mathematical science, two terms are most often used, denoted by the word "interval". The definitions of these two concepts make up the answer to the question: what are intervals from the point of view of mathematical science.
So, the most common in mathematics are intervals of monotony and consistency. Consider their definitions.
What are intervals of monotony?
These are such intervals of the value of the function argument at which the function becomes only increasing or only decreasing.
And what are intervals of constant sign?
These are the intervals of the domain of definition at which the sign of the function remains unchanged.
In both cases, we are talking about certain intervals, as is the case with musical intervals.
Perhaps the most striking example of the use of the word “interval” in a specific industry is the well-known computer program “Word”. We will also study this moment. What are intervals in Word?
Application in "Word"
It is known that three types of intervals are involved in this program:
- The spacing between the lines.
- Between separate paragraphs.
- Between adjacent pages.
There is no need to consider in detail the meaning of each of the above three intervals used in the Word program, since a lot of literature is devoted to this. It should only be noted that in this case we are talking about a phenomenon that has, albeit distant, but similarity with musical intervals.
Finally
This article examined the issue of the relationship of music with mathematical science. It was revealed that such a relationship really exists, which is proved both by experiments in pedagogical science and by an analysis of thought processes in both types of activity. The question of what intervals in music and mathematics are also considered. It also revealed some common points in the definitions of mathematical and musical terms. Now it becomes clear what the intervals are. And this once again proves that the area of contact between the two spheres, mathematics and music, really exists.