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Physics and mathematics in music - why does it matter?

Have you ever asked yourself, what physics and mathematics have to do with music? Why it is a critical tool for composers to write great pieces? Well, then it is your lucky day! Ali Latif-Shushtari has mastered both disciplines. Read this short interview and learn more about physics and mathematics in music.

music sound waves guitar
Guitar strings produce unique sound waves

Hi Ali! Tell us a bit about yourself.

I am Ali. I was born in Iran. I studied math in high school. In Iran, I studied physics and I finished my MSc in 2017. I was always passionate about music and parallel to my studies I educated myself in classical music. Finally, in 2019 I came to Bern for an MA in music composition and now I pursuing my Ph.D. in composition. I could never detach myself completely from these two majors I studied. Naturally, I was driven towards a path where I could relate to both. Although I must say that I am a far better composer than a physicist.

What do physics and mathematics have to do with music?

All our knowledge about sound comes from physics. From acoustics to the structure of instruments and how they function, physics provides deep and thorough insights through observation and calculation and we need mathematics for that. Take a guitar string for instance. Everybody knows that plucking the string generates the sound. We use physics to understand and describe what is happening and math to formulate our physical notions. We can calculate the relations between the length or thickness of the string and the frequency and how they function. We can calculate where and why the harmonics happen. We can understand with certainty why plucking the string in different places creates different colors of the same pitch, and so on.

Can you give us a few practical examples of physics?

For example, the question of timbre in instrumentation is an extremely physical phenomenon. By understanding the basics of the physics of sound, one can learn many useful insights about instruments and how to use them. Many things that take a long time to learn by musical experience, can be learned quite easily when you know the science behind it.

The harmonics of a string are an obvious example of this. Or in electric guitars, what are pick-ups, what does the amplifier do? Or how can you achieve a sound color by turning these knobs on the amp? This brings us to the third example: the vast applicability of physics in electronic music. Almost all the technical terms in electronic music and sound engineering, from amplitude, phasor, and gain to modulation, compression, and normalization, come from physics. Understanding these physical phenomena helps you understand what are the whys and hows in this genre.

Ok, understood! But what about mathematics?

Mathematics is generally a calculation tool. To use physical concepts, one must also know basic mathematical methods. Many composers have used mathematical calculations to create their pitch material, especially in modern music. For example, the idea of atonal theory in music can be learned from a mathematical point of view.

At the beginning of the 20th century, many composers fed up with the classical theory of harmony, what we know as tonal theory, tried to go beyond the norms and create new systems for composition that had not been practiced yet. Schoenberg invented serialism to create music that is not tonal at all. To briefly explain, serialism follows certain rules in order to avoid tonality and this requires some mathematical calculations.

In the next generation of Schoenberg, some composers appeared known as integral serialists such as Boulez and Stockhausen who started to use serialism in all possible levels of their compositions. This made things much more complicated, making them use a bit more complicated math as well. I have seen many students who find these topics very difficult simply due to a lack of mathematical practice. Also, many teachers try to avoid going into mathematical details due to obvious reasons.

How does it differentiate from music theory in general?

Music theory is the study of musical signs, language, and rules. Through music theory, you basically learn how to represent your musical thoughts in a symbolic and meaningful way. For example, imagine that you are sitting behind the piano and suddenly playing a beautiful melody. Music theory teaches us how to notate that melody and what other melodies or chords sound beautiful when played together with your original melody. But, the questions of physics are rather more fundamental. In music theory, we study the result of a physical phenomenon which is the sound traveling. Music theory cannot tell you how sound works! Knowing this can give a more comprehensive vision of your musical knowledge.

What makes a great composition great?

There are many aspects to a great piece of music. Although judgment is subjective (I talk about such topics and discussions in my composition course where I constantly borrow from philosophy) there are certain elements that can help us to have a better understanding of a musical composition. Form and structure are extremely important. When you listen to a piece, imagine that you are hearing a story. You can ask yourself many questions: Think about what comes first and why? Which musical ideas are repeated? Is it an exact repetition or there are variations? Etc. Another important element in a great composition is the instrumentation. Listen to the colors and how they change and develop through the piece. Such questions are completely regardless of the era in which the piece is composed.

Does your practice work for every instrument?

Yes. Any musical instrument can be studied from a physical point of view. We study how the sound is generated and what are the acoustical properties of every instrument. Almost all instruments follow the same structural logic. They all have a sound (vibration) generator. This can be a string, a membrane, a mouthpiece, or a reed. Then there should be a resonator, something that amplifies the sound. This can be a hollow wooden box or a tube. And finally, something to control the pitches; Keys, frets, holes, etc. Take a clarinet for instance. We blow into the mouthpiece where the reed is. Vibrations of the reed generate a sound that is directed into the resonating tube. With the keys, we manipulate the length of the tube which naturally changes the resulting pitch for us.

Why should music students or teachers be bothered about learning the mathematics and physics of music?

Especially in modern and contemporary music, to understand many pieces, it is necessary to have a knowledge of physics and math. But for me, the most valuable result of learning physics is the power of fundamental vision, and the ability of theoretical and critical thinking. Studying physics improves your abstract thinking which can lead to a better understanding of music theory and analysis.

How can music students or teachers incorporate your theory into their practice?

The size of your imagination depends deeply on your knowledge. Students, by learning the reality (physics) behind an instrument can develop a great understanding of it which allows them to imagine its sound more creatively. This applies to both composers and performers. Also, understanding these topics can help teachers to develop a more practical and smooth way to communicate with their students when it comes to such subjects.

What do music student beginners learn in your first lessons?

The first thing you will learn in my lessons is “What is sound?” Answering this question opens the door to the world of physics and music. It is followed by questions such as “How does sound travel?” and “How is sound generated?” These two questions lead us more toward acoustics and instrumentation. Of course, different people have different priorities therefore the lessons can and should be oriented regarding their preferences and what they would like to learn more.

What about music teachers or musicians?

There is this tendency in our time that everybody to be focused on their own specialties. It is very recent that composers have actively started to go beyond their one-dimensional thinking. In my Ph.D. research, I am learning about interdisciplinarity in composition and such orientations which I believe is very interesting but not enough. When you try to engage with new ideas in order to create original creative results, there is a typical trap that you can fall into and that is surface learning.

I have seen many musicians who try to come up with original ideas using math and physics but unfortunately, the results were shallow and unconvincing. Technique is immensely important and valuable, but without vision and deep understanding, it can lead to long-term problems. Let me give a very simple example: Imagine an extended technique on an instrument. Knowing the physics behind it can have many fruitful results: If you are a composer, you can with certainty imagine how it will sound, therefore you can notate it more clearly and have much better communication with your performers. If you are a performer, you know exactly what to do on your instrument to get that desired sound result without going through endless trying and experiments. And in both cases, when you teach, you know exactly how to inform your students and make them understand the reality behind that technique. And it is not just that technique, this can and should be applied to many different levels of our understanding of music.

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