Introduction
There are a lot of speculations concerning the relationship between mathematics and music. The best dimension thou in which an individual can comprehensively understand the relationship between these two subjects is in participatory of both entities. Without participating it would be difficult to blend and understand the two subjects. Without participating again individuals are seen to be left in wonderment since they perceive it as a rear marriage. While pursuing this matter it is important to understand note that mathematical formulas together with the numbers that go with them are not lifeless. It is also imperative to realize that music encompasses tangible number incarnations. These two aspects are seen to reflect the emotion and beauty accompanying music and mathematics. Therefore this paper seeks to establish this relationship, show the usage of mathematics in music, avail information on the effects of listening to music on mathematics, highlight the effects of learning and making music or mathematics, and conclude by showing the compatibility of the subjects in question.
The use of mathematics in Music
Mathematics is used in nearly everything done in life and music is one of these. Mathematics is used when arranging a melody, using a Pythagorean scale, calculating frequencies and intervals, and measuring songs by beats. Music also uses mathematics in mathematical expression theories like abstract algebra and set theories: instrument turning to work on specified frequencies: for Fibonacci numbers and golden ratio is used: the making of compatible disks and in the pitching of instruments
Ratio and Frequency
Different sound pitches are caused by wave spacing. When the waves come closer the tone becomes high. The space between a wave and another is referred to as a wavelength. Long wavelengths are not heard as frequently as shorter ones. So frequency is how often wave peaks go by. This is calculated in Hertz. The sound that a person can hear starts from 20 to 17,000 hertz. Long wavelengths have lower frequencies while short wavelengths have higher frequencies. Frequency relationships are written and calculated in form of ratios. An example can be the frequency ratio #5 to frequency #7 equals X. This is written #5 = X #7
Pythagorean Scale
Pythagorean scale is responsible for the discovery of how different lengths and ratios of vibrating strings forms pleasing music. The scale itself is a turning for a three-set major triad consisting of ratios 4:5:6 frequencies in octaves. The Pythagorean scale 9:8 and 256:243 intervals. This frequency tuning relates to intervals on a basic ratio of 3:2 (the oldest tuning of the chromatic scale).
Measuring Songs By Beats
A song’s timing is usually calculated in BPM (Beats per Minute).
This works as a guideline to the momentum of a song. An example is when 120 beats are played per minute, this means, and 120 counts in 1 minute = 2 beats in a second.
The Effects of Listening Music on Mathematics
There are some researches indicating that listening to music may improve mathematical skills. Music stimulates the use of a part of the brain that is also used in mathematics. Therefore, by listening to music, mathematic skills improve. Listening to music enhances math capabilities. This is shown by studies on young children who indulge in music at an early stage. A study carried out on first-grade students displayed the fact that mathematical performance was after a certain period of time in music education and training. These students have been exposed to sequence-related abilities of development and musical training encompassing pitch and rhythm. This was done for about half a year, after this, the students taking music lessons were seen to excel in mathematics over those who did not do music at all. In this study, music is seen to be an enhancement of ST (spatial-temporal) and LA (language analytical reasoning). Language analytical skills are responsible for dealing with equations and getting quantitative results. Spatial-temporal on the other hand is responsible for thinking beyond a current situation. This is brought out in the Mozart issue which got its fame after finding out that Mozart music (sequential music) creates enhancements for spatial-temporal thinking.
Music + Math = Success
Researchers carried out a study on students participating in music programs. They found out that the students who initially had average scores in mathematics started performing better. The experiment continued and later music students were better in class. This is shown by a result of mental stretching useful for learning mathematics. Further evidence displays enabled focusing ability and alertness students.
The Affects of Learning and Making Music on Mathematics
Music is used to understand how brains work. When learning or playing music people’s minds tend to develop the ability to think in pictures, which after research was found to also improve mathematical skills?
Spatial Temporal
Spatial temporal is significant in the generating and the conceptualization of solution to problems arising in mathematics. A study has even shown that two thirds of good mathematicians have spatial temporal kind of reasoning. The research also established that training in music was a way of enhancing spatial thinking. Music and several other cognitive tasks contribute to intrinsic neurotic patterns present in spatial temporal in the cortex. In the research students took part in music lessons for four months. These students were found to be better in mathematics than those who did not take any music lesson. The study also proposed that for spatial temporal development cortical pattern enhancement needs to be facilitated. The key skill enhancing features in spatial temporal are; symmetries of cortical firing patterns used to compare and contrast images, natural sequences for inherent cortical patterns and the transformation, visualization and relation of mental pictures. This is enhanced by taking of music lessons. The areas requiring temporal kind of thinking are calculus, geometry and vectors, the capability to write proofs related to mathematics since the writing of proof requires intuitive sequences and the skill to reason a step further.
Conclusion
Consequently music correlates and helps a great deal in the understanding of mathematics. On the other hand mathematics is equally essential in music and musicians. This is evidenced by several processes in the life of musicians. They include changing money in foreign countries, connecting of chords, building musical systems from integers, arranging instrumental melodies, playing musical melodies, composing music and the necessity to hear music from different angles. Therefore as shown in this paper better mathematical quality can be realized through participating in music. As a result of this parents and teachers should try to approach the issue of mathematics from a musical point of view.