## Introduction

### Research Background and Content Preview

As the world becomes a global village, the growth and development of music have depicted the societal way of life. Specifically, the depiction covers the tradition and culture of people. Across the world, different societies use instruments and tools in music composition (John, 2013). Basically, learning music and different accompanying instruments depends on the ability of an individual to understand concepts such as ratios and fractions, which are significant in the fields of mathematics and financial economics (Castanedo, 2016). Therefore, this research paper will attempt to establish the existing relationship between music and fields of mathematics, economics, and finance.

### Research Question

- How can music help in the field of mathematics and financial economics?

### Research methodology

The researcher opted for secondary data to carry out a qualitative analysis of different musical attributes that are related to economics, mathematics, and finance.

## Findings and Analysis

As an art, music is a medium fusing silence and sound to appeal to the listener. The sound-making up music is controlled by beats, dynamics, and rhythm. Music composition comprises of fusion of sound and beats, depending on the genre. Previous studies have endeavored to link mathematical achievements to musical training in the form of instrumentation (Castanedo, 2016).

In one of such studies, the findings revealed that students with high musical training tended to excel in mathematics and accounting subjects more than their counterparts with no musical knowledge. Such students had high standardized scores for different computation tests (Bergman, 2013). This means that music and finance or mathematics have a close relationship, whose origin can be traced to several centuries back to the beginning of civilization and musical instrumentation.

Music basically involves pattern creation of sound to form consistent notes. On the other hand, the field of mathematics and finance involves studying patterns and figures to make sense of different phenomena (John, 2013).

This means that everything in music, such as harmony, melody, and timbre, can be studied from a series of mathematical perspectives. For instance, rhythm can be studied by application of mathematics perspectives such as differential calculus, signal processing, trigonometry, and number theory or geometry (Pitts, 2012). Moreover, most of the modern electronic and electrical tools that are used to create music functions on the ability to understand the connotation of how these musicals work.

As is the case with rhythm in music, which involves the creation of notes that make a beat, mathematics works with periodic functions. For instance, in the compositions of Milton Babbit and other composers of the 20^{th} century, their music composition involved the artistic fusion of dynamics and tempo to create deep rhythm (Gaab & Zuk, 2017). In a gradual manner, the tempo of such compositions harmonized proficiency to balance the andante, allegro, and moderate swings.

Specifically, the hypnotic quality of the beats forming a rhythm in these compositions was perfectly balanced and introduced at specific intervals. In order to create such compositions, there has to be a balance in changing the tempos to avoid veering off the flow of beats (Pitts, 2012). In relation to the field of mathematics and financial economics, the principle of periodic function that is similar to a rhythm is applied to solve different accounting challenges. Since music works with rhythm, mathematics, and accounting principles operate on the ability to create a purposeful periodic function.

Melody is an important element of music. Specifically, any musical note is a collection of different waves, which are created by vibrations of stringed instruments such as piano, guitar, and harps. These vibrations originate from an air column of trumpet or saxophones and membranes of drums. In the creation of music, the high-frequency vibrations are heard as a set of progressive sounds associated with peculiar timbre and pitch (Gaab & Zuk, 2017).

This means that it is almost impossible to isolate vibrations into discrete rhythms. The peculiar notes, “which sound pleasurable when played in a sequence as a melody, often have a particular mathematical relationship” (Bergman, 2013, par. 11). In the same way, it is very difficult to isolate dependent variables in mathematical or financial computations, as long as the functional principle is determined by a particular formula.

In music, an interval refers to the existing gap between musical notes. The most significant number in the gap is the frequency ratio between musical notes. Irrespective of the musical genre, cultures across the globe prefer hearing particular sequences of different notes. In order to create music, the interval must involve a series of integer ratios in the note frequencies. For instance, the perfect fifth is an interval between the C and G in classical music of the 20^{th} century (Pitts, 2012).

The notes ‘Sa and Pa’ and ‘Do and So’ were very common in the compositions of the past century associated with artists such as Alexander Mackenzie and Robert Fuchs. In the composition, *The Cricket on the Hearth*, Mackenzie applied the perfect fifth interval to create a dynamic string of frequencies (Bergman, 2013). In such intervals, the ratio between any two successive frequencies is 2:3. This means that such ratios are perfect and often lead to a particular note sequence. Therefore, in the creation of an instrument such as a piano, these ratios are used to determine the pitch of each note (Gaab & Zuk, 2017). The same principle is applied in mathematical and financial calculations, where different formulas are used to solve particular equations to arrive at a similar result.

Harmony in music is created by melody of notes at intervals that sound good. A perfect harmony is created by playing different notes at once in different intervals. For instance, a chord that is played in a piano has more than three notes that must play in a quickly sequence or simultaneously (Williamson, 2014). The notes should overlap to ensure that such a chord sounds harmonious. Thus, the integer intervals must be balanced to create a melodious sound. The same principle has been applied in creation of programs or musical intervals for training sound engineers on ear attention to notes. For instance, there are mathematical programs that can demonstrate complex sounds and pure tone.

In this era of computer aided learning, mathematic principles have become a central part algorithmic musical composition. Specifically, it is now possible to use different computer codes and mathematical models to generate music of different genre. Some of the mathematical principles are accompanied by specific functions or alternation of different quantum mechanics, which are just “harmonics of the electron field’s vibrations” (Castanedo, 2016, par. 7).

In the 20^{th} century music, the absolute pitches in these compositions have become a staircase for understanding logarithm principles in mathematics. In determining loudness and decibels in the composition, *Six Irish Rhapsodies*, by Charles Villiers Stanford, the principle of symmetry is applicable (Bergman, 2013). Particularly, this principle relates music to events of a time towards a musical plane. In application, the use of pitch continuum through scale and system tuning has become discrete mathematical systems for relating pitches to modular arithmetic.

The basic mathematics is applicable in understanding different sections of musical theories. For instance, Fourier analysis is important in studying overtones in music, beat phenomenon, and tone difference. Particularly, the note variations in music are basically rational beat numbers. Moreover, studying music fractions in the sphere of fifths is a modular arithmetic process (Pitts, 2012). This means that music is inspired by different mathematical principles, which are also applicable in financial economics.

Apparently, most the 20^{th} century music was inspired by mathematical principles in balancing the rhythm, creating different notes, and forming perfect harmonies between two concurrent frequencies. Comparatively, in studying financial economics, multivariable equations, calculus, and statistics are applied alongside other mathematical principles to create a systematic line of thinking in solving problems (John, 2013). Therefore, studying mathematics and financial economics would facilitate proactive understanding of how to compose or play music.

## Conclusion

The case study has established a connection between music and the field of mathematics and financial economics. The relationship between these fields was established as them being part of the embody abstraction of art to study science. The musical principles such as interval, rhythm, note, and frequencies are applied in financial computation in measuring physical values. For instance, understanding the harmony patterns, tuning systems, constrained note forms, rhythm, and other classical instrumentation involve complex arithmetic thinking.

Since music often fulfill some emotional needs, it is probable to note these desires have psychological motivational effect in pursuing abstruse mathematically related fields such as financial economics. Apparently, the 20^{th} century compositions had interesting harmony of tempo to create perfect notations, which is a mathematic principle called algorithm.

## References

Bergman, M. (2013). *In the groove: Form and function in popular music*. San Diego, SD: Cognella University Press.

Castanedo, M. (2016). *Is there a relationship between music and finance?* Web.

Gaab, N., & Zuk, J. (2017). *Is there a link between music and math?* Web.

John, Y. (2013). *What is the relationship between music and math*? Web.

Pitts, S. (2012). *Chances and choices: Exploring the impact of music education.* Chicago, Ch: Oxford University Press.

Williamson, V. (2014). *You are the music: How music reveals what it means to be human*. New York, NY: Icon Books Ltd.