Mathematics and its Relation with Music and its Harmonics

Pythagoras also contributed to the music world. He expressed the musical harmony in formulas. He created a scale layout with gongs in different sizes and he proved that in the resonance of the gongs he hit, 1 octave interval is equal to 2:1 proportion, the perfect fifth is equal to 3:2 proportion, perfect four is equal to 4:3 proportion and whole notes are equal to 9:8. This, later started to be known as “Pythagorean Tuning.”

The unique tone painting reflects the meaning, symbolism, and characteristics of the movement, shaping and characterizing the harmonic, melodic, and rhythmic elements. The time signature and key signature of the second movement draw attention to both the lively and calming outdoors. Beethoven expressed the sounds of nature through the instruments in the movement, setting the scene in the countryside. The perception of nature is fulfilled stylistically with instruments imitating flowing water by repeated notes. The instruments also imitate bird song by playing trills, grace notes, embellishments, ornamentation, and bird indications.

Western musical styles have developed into the music what we listen to today in the twentieth century. Throughout time composers have created new ways to enhance music by adding harmonies, phrases, dynamics, and much more. At the start of music, composers kept a simple melody using the same frame of pitches in simple tunes. As we became more educated, so did our music and we are now able to create songs with texture and countermelodies all within a plethora of genres. The use of notation has changed our music we have allowed music to obtain variety, depth, and be shared amongst people for thousands of years. Without notation, music would have no way to thrive and expand on what composers discovered and experimented with. We can see how western music developed throughout the musical notation of the eras. Starting in the Middle Ages, we can see the basics of Western music and where it all began.

Each instrument produce a different harmonic sound. Any sound that is produced by any musical instrument can be very complex where they contain infinite amount of sine waves of different frequency levels, one of the most common genres is the pitch called for the fundamental frequency. There is 3 types of complex waves associated with sound the triangle wave, sawtooth wave and the square wave which are all made from the different harmonic sounds which show the difference between each individual harmonic as explained

In conclusion, music has always had a relationship with music. A composer must take in to account all the instruments when writing a symphony. The only logical reasoning to suggest this is math. How else would he know when to have the bass come in and the violins to carry a note? The composer must figure out the timing of each beat, timing is everything. Music often repeats patterns, same as math. One could also suggest that a dancer uses math when choreographing dance

As a piano student in Indonesia with an upcoming exam just a few months away, I discovered that my practicing would be less grueling if I analyzed the piece first. Soon afterwards, I began to incorporate music theory into my piano teaching, and the result was impressive, my students were able to progress faster and their performances improved significantly. From that moment, music theory became an inseparable part of my piano teaching. My determination to be an effective teacher compelled me to keep learning, and as I was learning, I found myself immersed in my new subject matter, music theory. I had a chance to study music further when I was in the US.

Math can be seen in all aspects of life, whether you notice it is prevalent or not. As a result, almost every aspect of life can be boiled down to a specific group of mathematical concepts. Similarly, art forms, especially music, can be analyzed through the eye of math and therefore be fully inspected, observing how certain chords and notes sound more harmonious than others.

The main concept which Romantic music rotates around is the idea that the instruments can be adapted and adjusted to create different sound; Beethoven, along with others, custom built and adapted pianofortes to fully create music. Further, their musical compositions are full of emotion, with its decrescendos and crescendos, key and tempo changes resulting in a rich and varied portrait. Combined, they create a full and complete composition in a similar manner to what the Romantic philosophers believed a well-rounded human being to be, with unique traits and characteristics formerly believed to be unnecessary by Enlightenment

is an example polyphonic texture and Beethoven - Symfoni nr 6 Pastorale DRSO Rafael Frühbeck de Burgos is an example of homophonic texture. Texture is one of the most essential fundamentals of music. When dealing with different textures of music, one would know and expect different levels to the music. Monophonic texture is describe when music only contains a melody line with no harmony. It might be played by one person on their own, or by many people playing the same melody. Heterophony texture music is a type of musical texture that characterizes the simultaneous

While music and mathematics are worlds apart at first glance, there is a strong underlying structure of mathematics, even though it’s invisible to the casual observer. As in many areas of life, a strong thread of mathematics makes music work.

of white noise, in contrast to the variations in tone and melody of normal music.

One of the earliest discoveries of how string function comes from the Greek philosopher, Pythagoras. The wavelength and pinches between strings are what differentiate the varying notes. As shown in Diagram 1, the wavelengths have specific spacing in between, which are directly related to mathematics. Nodes, or pinches, are strategically and mathematically placed to resonate precise pitches, and particular ratios are able to be derived from these intervals. For example, an octave describes two notes that are eight notes apart. In order to create the perfect first octave, the string is pinched into perfect halves, making the mathematical ratio , as 2 parts are created from the whole with one pinch. By pinching the string in half, the frequency becomes twice as fast , producing a higher tone of the same note. One octave higher than an A

Music Theory can be understood as chiefly the study of the structure of music. With the idea of both written and oral notation, it may be understood through recognized systems of indication, and used as systems of memorizing and transmitting the theories themselves. Western music theory is significant for its quantity and range whilst those of non-Western traditions are also notable in possessing major works of theoretical oration and literature.

In Mathematics, it is rare that a new branch of mathematics is introduced. That means that even branches of math that have been around for hundreds of years are still technically new, or at least relatively new. One such branch of mathematics is probability. Probability is only three hundred to four hundred years old, so it easily falls into this category when compared to branches of mathematics such as Geometry which dates back all the way to ancient Egypt in around 2900 BC, when it first became important when an Egyptian pharaoh wanted to tax farmers who raised crops along the Nile River. To compute the correct amount of tax, the pharaoh’s agents had to be able to measure the amount of land being cultivated. Later it was used to build the pyramids.

The unit of frequency in SI (System International) is the hertz (Hz), where one hertz is equivalent to one cycle per second. Human beings can hear sound from vibrating objects in the range between 20-20.000 Hz (this range may vary depending on age, health, e.t.c.). Pitch, on the other hand is the human sensation of frequency, the ability to tell the difference between different frequencies of sound, which are organized into classes of pitches. A high pitch sound corresponds to a high frequency sound wave and a low pitch sound corresponds to a low frequency sound wave. In music, pitch is a technical term, used to describe how high or low a note is.