JP5487507B2 - Three-square theorem and scale visual learning tool - Google Patents

Description

  The present invention relates to a three-square theorem and a visual scale learning tool that can learn the three-square theorem (Pythagorean theorem) and can also learn the formation of a scale.

  Today, so-called separation from science is becoming a problem in Japanese education. The development of various semiconductors, integrated circuits, etc., has led to the black boxing of equipment, and one of the major reasons is that children are not able to visually grasp the principle of things. If children have an opportunity to understand and understand the fundamental principles of mathematics and music, it will be an opportunity to wake up to the fun of science.

It's not without learning tools that make things visible.
For example, Japanese Patent Application Laid-Open No. 2005-181786 describes a device for teaching a theorem for a circumferential angle. Japanese Unexamined Patent Application Publication No. 2005-115303 describes a regular polyhedron set for the purpose of teaching mathematics and geometry. Japanese Patent Application Laid-Open No. 2009-205120 describes a scale and a chord transposition quick reference table instrument.

JP-A-2005-181786 JP 2005-115303 A JP 2009-205120 A

  However, so far, visual learning that helps to understand the three-square theorem and makes it easier to understand not only the auditory sense, but also the invisible scale and pitch. I don't see any ingredients.

  Greek philosopher and mathematician Pythagoras was a person who had the idea that this world was all made up of numbers. In Japan, he is famous for the three-square theorem (Pythagoras' theorem) that he studied in the third grade of mathematics. It is.

Pythagoras, on the other hand, is also the person who laid the foundation for the scales of Western music. However, this is not unexpectedly known.
Pythagoras made an instrument called a mono chord, and clarified that a sound with a double frequency is one octave above the same string. For example, there is a 2: 3 frequency relationship with the sound of “de”. It is said that the scale is defined by the frequency, such as “Seo” for a certain sound (in other words, a sound having a frequency 1.5 times that of the sound).

  The present invention helps the understanding of the three-square theorem, and makes the invisible scale and pitch appeal not only to the auditory sense but also to the visual sense so that it can be easily understood. It is an object to provide a visual learning tool for a musical scale.

  Among the right triangles, 3: 4: 5 is the simplest integer ratio of three sides. The present invention can be embodied so that when a string is stretched with the same tension at that ratio, the right triangle can be seen, touched, and measured, which helps to understand the three-square theorem. It is easy to understand visually with sound that the ratio of string length, and hence the ratio of frequency, determines the scale and pitch from the sound generated by playing the nail of the prepared string. I found what I could do.

The present invention is based on the above findings.
A base, the same first, second, third and fourth pulleys rotatably supported by the base, one end connected to the base and the other end provided on the base The first and fourth pulleys are arranged in two stages so as to be able to freely rotate with respect to each other, with the first and fourth pulleys aligned with each other. The distance between the rotation centers of the first and second pulleys is L1, the distance between the rotation centers of the second and third pulleys is L2, the distance between the rotation centers of the third and fourth pulleys is L3, and L1: The relationship of L2: L3 = 5: 4: 3 is satisfied, and the strings are wound around the first, second, third and fourth pulleys in this order, and the first and second pulleys. The three-square theorem and scale stretched between the second and third pulleys and between the third and fourth pulleys, respectively. To provide a visual learning tool.

  In the learning tool according to the present invention, the length of the vibrated portion of the string stretched between the first and second pulleys is the above-described L1, and is stretched between the second and third pulleys. Further, it is assumed that the length of the vibrating portion of the string is L2 described above, and the length of the vibrating portion of the string stretched between the second and third pulleys is L3 described above. There is no problem in practical use.

  In the learning tool according to the present invention, the distances L1, L2, and L3 between the pulleys, in other words, the lengths L1, L2, and L3 of the strings that can be vibrated between the pulleys are L1: L2: L3 = 5: Since the 4: 3 relationship is set, a right triangle with three sides L1, L2, and L3 is formed here, and the learner touches or sees this learning tool, or the interior angle of the triangle. Or the distances L1, L2, and L3, and the three-square theorem that the square of L1 is equal to the sum of the squares of L2 and L3 I can understand.

  In addition, in this learning tool, the string portion having the length L1, the string portion having the length L2, and the string portion having the length L3 are in a relationship of L1: L2: L3 = 5: 4: 3. The frequency at which each string portion is nailed is different, and the string portion having the length L1, the string portion having the length L2, and the string portion having the length L3 are, in terms of the scale, “do” in which the sound increases in sequence. The relationship is “Mi” and “La”. That is, if the chord length is stretched in the relationship of 5: 4: 3, the relationship of “do”, “mi”, “la” is obtained, and the frequency is inversely proportional to the chord length. From the ratio, it can be easily and visually understood that “la”, “mi”, and “do” are 5: 4: 3.

In the learning tool according to the present invention,
Further, a fifth pulley is rotatably supported on the base, a distance between the rotation centers of the fourth and fifth pulleys is L4, and a relationship of L1: L4 = 3: 2 between the L1 and the L4. And the string may be wound around the fourth pulley from the fourth pulley to be stretched between the fourth and fifth pulleys.

  In this learning tool, the length of the string portion stretched between the first and second pulleys is L1, and the length of the string portion stretched between the fourth and fifth pulleys is L4. There is no problem in practical use.

  Further, the string portion having the length L1 and the string portion having the length L4 are in a relationship of L1: L4 = 3: 2, and therefore, the frequency when the nail is played is different. In terms of the scale, the string portion and the string portion having the length L4 have a relationship of “do” and “so” in which the sound becomes higher sequentially. That is, when the chord length is stretched to a 3: 2 relationship, the relationship between “do” and “so” is obtained, and from the frequency ratio, “so” and “do” are set to 3: 2. Can be easily and audibly and visually understood.

Thus, with this learning tool, the scale relationship of “do”, “mi”, “so”, “la” is obtained.
For reference, the released string scale of the 4-string ukulele is “So”, “De”, “Mi”, “La”.

In the learning tool according to the present invention, when the tension of the string is tensioned by the string winder, the pulleys are arranged on the base in order to make the string partial tension between the pulleys more accurate and constant. A pulley that rotates integrally with the outer ring portion of the ball bearing may be used.
As for the strings, metal guitar strings having high tension resistance may be used.

  The base includes a soundboard and a pulley support frame mounted on the soundboard so that a larger sound can be produced when a string is struck, and the pulley can be supported more stably. be able to. In this case, each of the pulleys can be rotatably supported by the pulley support frame.

  The soundboard may be a wooden soundboard, as a wooden soundboard is adopted for a stringed musical instrument. The pulley support frame may be a metal frame (for example, a stainless steel frame) so as to support the pulley more stably and firmly and to facilitate sound transmission to the soundboard.

  As for the connection of the strings at both ends to the base, for example, the one end of the string faces the first pulley and is connected to the pulley support frame with a connector, and the other end of the string is connected to the base. There may be mentioned a case of connecting to a string take-up feeder attached to the soundboard facing the fifth pulley (the fourth pulley when there is no fifth pulley).

  As described above, according to the present invention, it is easy to understand the scale and pitch that are invisible, not only to the auditory sense but also to the visual sense, as well as helping to understand the three square theorem. It can provide a three-square theorem and a musical scale visual learning tool.

It is a front view of an example of the visual learning tool of the three square theorem and scale according to the present invention. It is a rear view of the learning tool of FIG. It is a top view of the learning tool of FIG. It is a bottom view of the learning tool of FIG. It is a right view of the learning tool of FIG. It is a left view of the learning tool of FIG. It is a left view which shows the learning tool of FIG. 1 in a standing state.

  FIG. 1 to FIG. 6 show an example of the triple square theorem and scale visual learning tool according to the present invention. 1 is a front view, FIG. 2 is a rear view, FIG. 3 is a plan view, FIG. 4 is a bottom view, FIG. 5 is a right side view, and FIG.

  The illustrated learning tool 10 includes a base 1. The base 1 includes a flat wooden sound board 11 having a substantially constant thickness, and a metal frame 12 attached to the sound board 11 in parallel with the sound board 11 and slightly lifted from the sound board surface. The metal frame 12 is not limited to this, but in this example, a metal plate made of stainless steel having a constant thickness is formed by punching two places into a triangular shape when viewed from the front.

  In the frame 12, pulleys are rotatably provided at portions corresponding to the respective corners. That is, in FIG. 1, the first pulley 21 and the fourth pulley 24 are in the upper right corner portion, the second pulley 22 is in the lower left corner portion, the third pulley 23 is in the lower right corner portion, and the fifth pulley is in the upper left corner portion. Each pulley 25 is rotatably provided. The first pulley 21 and the fourth pulley 24 are provided so that their rotation centers coincide with each other so that they can rotate freely in two upper and lower stages.

Each pulley is a pulley formed integrally with an outer ring portion of a ball bearing 20 provided at each corner portion of the metal frame 12.
The respective rotation center lines of the pulleys 21 to 25 are perpendicular to the surface of the soundboard 11 and are parallel between the pulleys.

  The distance between the rotation centers of the first and second pulleys 21 and 22 is L1, the distance between the rotation centers of the second and third pulleys 22 and 23 is L2, and the third and fourth pulleys 23 and 24 are. The distance between the rotation centers is L3, and the distance between the rotation centers of the fourth and fifth pulleys 24, 25 is L4. The relationship of L1: L2: L3 = 5: 4: 3 is satisfied, and the relationship of L1: L4 = 3: 2 is satisfied.

  A string 3 is wound around these pulleys, and a connection tool 4 for connecting one end portion 3a of the string 3 to the frame 12 is erected in the vicinity of the pulleys 21 and 24. One end 3 a of one string 3 is connected to the frame 12 and thus to the base 1. Although not limited thereto, the string 3 here is a metal string used in a guitar.

  The string 3 is wound from the coupling 4 to the upper side from the right outer side of the first pulley 21, further obliquely extends to the second pulley 22, and wound from the outer side to the lower side of the second pulley 22 to the third pulley 23. It extends from the lower side of the third pulley 23 to the right outer side and extends upward to the fourth pulley 24, and is wound from the right outer side of the pulley 24 to the upper side to extend to the fifth pulley 25, and above the pulley 25. It is wound and connected to the string winder / feeder 5 at the other end 3b.

  The string winder 5 is a tool similar to that used for winding, feeding, and adjusting the string tension in a guitar or the like, and is already known per se. By manually turning the handle knob 51, the tension of the string 3 can be adjusted.

  In this learning tool 10, when the tension of the string 3 is adjusted by the string take-up / feeding device 5, the string portion 31 stretched between the first pulley 21 and the second pulley 22, the second pulley 22, and the third pulley 23. The string portion 32 stretched between the third pulley 23 and the fourth pulley 24, and the string portion 34 stretched between the fourth pulley 24 and the fifth pulley 25. Each is set to the same tension by employing rotatable pulleys 21-25. In particular, since each pulley is integrally supported by the outer ring portion of the ball bearing 20, each of the string portions 31 to 34 is more easily and easily set to the same tension.

  A handle 6 is provided on the back side of the soundboard 11, and a standing protruding member 7 is provided on the opposite side.

  In the learning tool 10, the first pulley 21 and the fourth pulley 24 are arranged in two upper and lower stages, but the heights of the pulleys 22, 23, 24, 25 from the soundboard 11 are the same, and the pulley 21. The difference in height from the soundboard 11 of 24 is about several millimeters compared to the distance (for example, about 250 mm) between the rotation center lines of the pulley 21 and the pulley 22 and is negligible.

  Therefore, the length of the vibrated portion 31 of the string stretched between the first and second pulleys 21 and 22 is L1, and is stretched between the second and third pulleys 22 and 23. In addition, the length of the string oscillating portion 32 is L2 described above, and the length of the string oscillating portion 33 extending between the third and fourth pulleys 23 and 24 is L3 described above. The length of the string vibrating portion 34 stretched between the fourth and fifth pulleys 24, 25 is considered to be L4 as described above.

  Then, the relationship of L1: L2: L3 = 5: 4: 3 is set for the lengths L1, L2, and L3 of the vibratable portions 31, 32, and 33 of the string 3, and L1, L2, and L3 are set to 3 here. A right triangle is formed as a side, and the learner touches or sees this learning tool, measures the interior angle of the triangle, or measures the distances L1, L2, and L3. It can be easily understood by realizing the three-square theorem that the square of L1 is equal to the sum of the squares of L2 and L3.

  Further, in the learning tool 10, the string portion 31 having the length L1, the string portion 32 having the length L2, and the string portion 33 having the length L3 are in a relationship of L1: L2: L3 = 5: 4: 3. When the strings are struck, their vibration frequencies are different from each other, and the string portion 31 having the length L1, the string portion 32 having the length L2, and the string portion 33 having the length L3 are, in terms of the scale, the sound sequentially increases. “Do”, “Mi”, “La”. That is, if the chord length is stretched in the relationship of 5: 4: 3, the relationship of “do”, “mi”, “la” is obtained, and the frequency is inversely proportional to the chord length. From the ratio, it can be easily and visually understood that “la”, “mi”, and “do” are 5: 4: 3.

  Further, the string portion 31 having the length L1 and the string portion 34 having the length L4 are in a relationship of L1: L4 = 3: 2, so that the frequencies when the nails are played are different, and the length L1 is different. The string portion 31 and the string portion 34 having the length L4 have a relationship of “do” and “so” in which the sound becomes higher in terms of the scale. That is, when the chord length is stretched to a 3: 2 relationship, the relationship between “do” and “so” is obtained, and from the frequency ratio, “so” and “do” are set to 3: 2. Can be easily and audibly and visually understood.

  Thus, with this learning tool 10, the musical scale relationship of “do”, “mi”, “so”, “la” is obtained.

  The learning tool 10 can be placed on a table such as a tabletop with the handle 6 and the protruding member 7 on the back of the soundboard 11, and the edge of the sounding board 11 on the side of the protruding member 7 as shown in FIG. It is also possible to stand on the table top or other table 8 with the projection member 7 and the like.

  INDUSTRIAL APPLICABILITY The present invention can be used to provide a three-square theorem and a musical scale visual learning tool that can learn the three-square theorem (Pythagorean theorem) as well as the formation of the scale.

10 Three-square theorem and scale visual learning tool 1 Base 11 Soundboard 12 Metal frame 21 First pulley 22 Second pulley 23 Third pulley 24 Fourth pulley 25 Fifth pulley 20 Ball bearing 3 String 3a One end of the string 3b The other end L1 of the string L1 The distance between the rotation centers of the pulleys 21 and 22, the length L2 of the string portion 31 stretched between the pulleys The distance between the rotation centers of the pulleys 22 and 23, and the tension between the pulleys Length L3 of the string portion 32 Distance between the rotation centers of the pulleys 23 and 24, Length L4 of the string portion 33 stretched between the pulleys Distance between the rotation centers of the pulleys 24 and 25, and tension between the pulleys Length of string portion 34 Connector 5 String take-up feeder 6 Handle 7 Projection member 8 units

Claims (5)

  A base, the same first, second, third and fourth pulleys rotatably supported by the base, one end connected to the base and the other end provided on the base The first and fourth pulleys are arranged in two stages so as to be able to freely rotate with respect to each other, with the first and fourth pulleys aligned with each other. The distance between the rotation centers of the first and second pulleys is L1, the distance between the rotation centers of the second and third pulleys is L2, the distance between the rotation centers of the third and fourth pulleys is L3, and L1: The relationship of L2: L3 = 5: 4: 3 is satisfied, and the strings are wound around the first, second, third and fourth pulleys in this order, and the first and second pulleys. Between the second and third pulleys and between the third and fourth pulleys. Visual learning tool of the theorem and scale of.   Further, a fifth pulley is rotatably supported on the base, a distance between the rotation centers of the fourth and fifth pulleys is L4, and L1: L4 = 3 between the L1 and the L4. 2. The relationship according to claim 1, wherein the string is wound around the fourth pulley from the fourth pulley and is stretched between the fourth and fifth pulleys. Square theorem and scale visual learning tool.   3. The three-square theorem and musical scale visual learning tool according to claim 1, wherein each pulley is a pulley that rotates integrally with an outer ring portion of a ball bearing disposed on the base.   The said base | substrate contains the sound board and the pulley support frame mounted in the said sound board, Each said pulley is rotatably supported by this pulley support frame. Square theorem and scale visual learning tool.   5. The three-square theorem and musical scale visual learning tool according to claim 4, wherein the soundboard is a wooden soundboard, and the pulley support frame is a metal frame.