Mathematics of Harmonic Relationship in music
Introduction In music, harmonic relationship between pitches is a fundamental component, it sonically structures a composition of music, it adds texture, depth and dimension. It is the relation of one pitch to another. From a young age, my personal interest for music has been steadily high, playing instruments such as drums, guitar and electric bass have become a part of my day to day hobby, including my own compositions. And now with a more developed understanding of music, my interests have deepened. Mathematics integrates with music in many different aspects. In tuning, pitch, frequency, volume, rhythm and tempo, to mention a few, all integral elements of music. However, I have placed my focus
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Starting with the staff. The staff is a groundwork where music is placed on. These include notes, rests, dynamic markings and tempo markings. It is represented by 5 lines and four spaces, upon where the notes are placed. Clefs are placed at the start of a staff and act as a point of reference where the notes are located within the staff. There are two main types of Clefs, the Treble and Bass. In music there are twelve notes. The relationship from one note to another is expressed using semi-tones and full-tones. A semi-tone is the difference of one pitch up or down from a starting pitch for example: G and G sharp, the difference between the two notes is one semi-tone as well as G and G flat where G flat is one semitone below G. The twelve notes are specified by the following: A, A#, B, C, C#, D, D#, E, F, F#, G, G# these can be also expressed as: A, Ab, G, Gb, F, E, Eb, D, Db, C, B, Bb. The “#” symbol represents sharp and the “b” represents flat. Both can be interchanged, by looking at the scale, for example, Ab would be the same musical value as G#. Another important anomaly of the musical scale would be to point out there are no real musical values for “B# / Cb” and “E# / Fb”. The relationship from B to C for example is counted as a semitone. Including the pitches of E to F. On the staff below, an annotated diagram reveals the position of the notes C and C# in the treble clef. The lines placed in between the staff are known as bar lines and indicate the end and start of a new bar. A bar acts as a limit to how many notes can be played at a
Next we come to a point in time where a great leap had to be made. Musicians had made positive steps forward in the way of pitch and time but of only one or two notes at a time. What was needed was an in instrument that gave players control of many pitches simultaneously. The mechanism ...
According to Laurence O’Donnell, “Music is thought to link all of the emotional, spiritual, and physical elements of the universe.” This proves that music is more than a simple class teaching random notes. It is a common denominator between mind, body, and learning. One scholar shows that music causes a response that can affect a person’s mood; this is directly related to how a person acts upon their emotional response to music. He later talks about how music can have a positive effect on memorization and brain function (O’Donnell). The Center for New Discoveries in Learning stated, “Learning potential can be increased a minimum of five times by using 60 beats per minute music” (qtd. in O’Donnell). Most of the music that follows these types of beats is classical music such a Mozart and Bach. This is the type of music taught in schools, thus, enhancing a student’s ability to learn.
When analyzing musical sound there are many factors to pay attention to during the performance. Important things to listen for are the pitch, scale, timbre, tone quality, rhythm, melody, and form. While listening to the Marching Band the pitch of the performance varied. At some moments during the performance the pitch would sound low and that is when the bass instruments are heard. The pitch sounded high when the other instruments joined. Using a standard pitch enables a large number of instruments to be played together with out sounding out of tune. In many musical traditions people are not concerned with a standard pitch, and they tune instruments to sound well with other instruments for a specific occasion or even to suit the convenient level for a singer (Kaemmer:58). A pitch also contains intervals, which refers to the difference between tones of two different pitches. An example would be the octave, it represents two tones the bands performance had an octave. The marching band used a chromatic scale because of all the instruments and in a chromatic scale there are twelve notes within an octave. This allows the other members of the band to join in the...
The main goal of the very talented English music composer and conductor Benjamin Zander was to convince his audience through his very interesting and inspirational video, “The Transformative Power of Classical Music” that ‘Classical Music is for every one’. He was not only able to keep the attention of his audience growing with his splendid performance but also was able to make them understand the depth of classical music. He chose the most beautiful piece of classical music in order to make sure that his audience love it.
Music has a great influent on people in our daily life, just like technology’s effect on the music. In the last 100 years, pop music has been a major part of American culture. There’s always discussion on how great can a pop music affect one’s daily life. Both technology and music can affect one’s life in either good or bad way such that they are also related to each other. Technology had always had a dominant role in human history like music since the 1900s. Since then, the advancement of technology had create ‘miracle’ with music such that people won’t be able to imagine the effect back in 19th century. The effect of the technology on pop music can be observed through the instruments, composition and mainly the recording and transmission technique.
It is undeniable that Iannis Xenakis made use of many different mathematical theories such as the golden section, the Fibinacci series, and stochastic laws, in his music. In this essay, I will show the reader how extensively these principles governed much of his compositional process. I will also present the reader with examples where these different principles and theories are evident in his music.
Composition music theory is the study of which you learn to write and develop a creative ability to compose. There are many ways for you to learn about what it can lead to in a career and to create a greater understanding in music. It has many ways of affecting a mind and how it affects a person’s abilities
Music is far more than the sum of its parts. It can be thought of in a highly mathematical sense, which leaves one in awe of the seemingly endless combinations of rhythm, tone and intervals that a good musician can produce. Admiring music in this way is a lot like admiring an intricate snowflake, or shapes in the clouds; it's beautiful, but at the same time very scientific, based on patterns. All of the aforementioned qualities of music have one thing in common: they can be defined with numeric, specific values. However, the greatest aspect of music lies elsewhere, and cannot be specifically defined with words. It is the reaction that each individual has when they are confronted with their favorite (or least favorite) kind of music.
The relationship between the two gets even more intriguing when applied to actual notes being played. The best sounding music is that which uses flawless mathematics. It is common knowledge that each note has a letter name—A through G—but also has a number value, measured in hertz. An A4 for instance is 440 hertz. In Beethoven’s “Moonlight Sonata,” there exist triads in triplet form. These triads are made up of D, F#, and A. Since sound is a vibrational energy, notes can be graphed as sine functions. When the triad notes are graphed, they intersect at their starting point and at the point 0.042. At this point the D has gone through two full cycles, the F# two and a half, and the A three. This results in consonance, something that sounds naturally pleasant to the ear. Thinking about this opened my eyes to all the aspects of my life with which I utilize math to
The book is divided into four chapters: 1) Humanly Organized Sound, 2) Music in Society and Culture, 3) Culture and Society in Music, and 4) Soundly Organized Humanity. In chapter one, Blacking discusses the analysis of sound. He begins by describing music as humanly organized sound. His overarching theme is that “the function of tones in relation to each other cannot be explained adequately as part of a closed system” (30). In other words, music can’t be analyzed simply by one set of rules. This is because every single culture has a different system that they use to structure and compose their music. In order to adequately analyze a society’s music we have to study their “system.” We must learn what music means to them. Then, and only then, can we accurately and completely analyze what a particular type or piece of music means to a particular society and culture.
Music and the relationships of music have changed drastically in our society. The course of studies and the evaluations of the applications of the technology of music, the making and the listening of music have changed in the way we listen to music, the styles of music in our society and in the media. The importance of the technology in music today, has, over the past century been charted through the study of musical examples and through viewing how human values are reflected in this century's timely music. There are very many different types of music that are listened to. There are readings, writings, lectures and discussions on all the different types of music.
Pitch is the general perception of the highness or lowness of a sound which depends on the frequency complexity, and loudness of the sound [11]. On the other hand, in music pitch is related to notes that are being played. The vibrations caused by a disturbance such as a vibrating string create areas of compression and rarefaction of the molecules in the medium that the vibrations are traveling through. Sound is only produced when these vibrations travel through a medium. An observer is able to hear sounds because these areas of compression and rarefaction are picked up by the observer's ears, and translated to the brain from longitudinal sound waves.
When students see a quarter note, they should clack their rhythm sticks together a single time. A quarter note looks like a dark, filled-in circle with a stem coming off the side. The teacher must explain that half notes look like quarter notes that are empty inside the note head, and whole notes look like half notes without a stem. Half notes hold for two beats, while whole notes hold for four. Demonstrate how to play these note values with rhythm sticks by playing each note value for the class.
Dobrian, Chris. "Music and Artificial Intelligence.” In University of California, Irvine Department of Music. UCI.edu,
Music of the Romantic Era had many distinct qualities. The characteristics of Romantic Music are individu...