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Music as a language
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In this equally fascinating video, they talk about pattern and structure in music, and how in the deaf Beethoven, he could some how visualize that mathematical pattern and structure and follow it’s lines, feeling the emotions of major triads (happy – consonance) and minor triads (sad – dissonance) without hearing it.
Consonance are a combination of sound sine waves that are in sync and sound pleasant versus dissonance that are a combination of sound sine waves that are out of sync and sound unpleasant and the contrast between the two create emotions. Wow!
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In both of these videos (Bach and Beethoven), we’re looking at mathematical ratios of frequencies in music. It’s just a matter of whether the frequencies are hundreds of times per second in the case of consonant note harmonies, or once every few seconds in the case of Bach’s harmonic patterns. I now feel like I should read a book about this.
I imagine it wouldn’t be too difficult to transcribe some Beatles songs the way they did with the Bach composition and run a computer analysis, something akin to a Fourier transform, to determine if there are any signs of these meta-harmonies. (Wow, I absolutely never thought I would have an occasion to invoke a topic from my old college math classes on this discussion board!)
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David, yes this brings back fond memories of my “Differential Equations” course in 1st year college! Seeing all this relationship between physics, math, and music, it is no surprise Albert Einstein, one of the greatest scientific minds in history, is also an accomplished violinist and music had a big factor in much of his scientific theories and discoveries. Check out this awesome article about Einstein and music. It’s an inspiring read for the weekend for any music lover.
The true picture is perhaps less colorful; Einstein was the product of a well-rounded education that, importantly, very much included the arts and humanities. It’s little known that Einstein was an accomplished violinist, and even less known that had he not pursued science, he said he would have been a musician:
I live my daydreams in music. I see my life in terms of music.
Looking at the role of music in Einstein’s thinking sheds some light on how he shaped his most profound scientific ideas. His example suggests that in being intimately involved with the scientific complexity of music, he was able to bring a uniquely aesthetic quality to his theories. He wanted his science to be unified, harmonious, expressed simply, and to convey a sense of beauty of form. He confessed to thinking about science in terms of images and intuitions, often drawn directly from his experiences as a musician, only later converting these into logic, words and mathematics.
Far more than a diversion or hobby, music was such a part of the man that it seems to have played a role in his scientific working processes. Einstein’s second wife Elsa told the story of him one day appearing totally lost in thought, wandering to the piano and playing for half an hour while intermittently jotting down notes. Disappearing into a room for two weeks (emerging for the odd piano session), he then surfaced with a working draft of the theory of general relativity. Of course, piano playing and the theory of general relativity are not related in any direct or tangible sense. On one level, the story suggests that for Einstein, piano playing had the same effect walking has for many people. Ambulatory thinking processes release creative juices. Beethoven knew it, as did apparently the ancient Greeks, not to mention many generations of writers.
But there were deeper levels to the science-music relationship in Einstein’s mind. There’s some evidence music played a role in the very shaping of his most important scientific discoveries.
The role of a well rounded education in elementary and high school is so important. In this article it also illustrates how if you take gravitational waves that can be measured from space, and convert it to sound waves, you can hear the big bang as sounding like a “pebble dropped in a bucket of water.
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That’s a great article, Jung! I can’t think of a single class I’ve ever taken in which the connection between math and music has been explored, and yet I see it all over the place in things I’ve read. Now I can add Einstein to Pythagoras and Kepler on my list of greats who have combined the two in their fundamental way of thinking about nature.
A couple of years ago I attended a talk in which a LIGO scientist summarized the lab’s recent results on gravitational waves, and played that “chirp” of the colliding black holes. It was a quite memorable moment associated with literally a whole new way to see the universe.
As part of my college major I took an introductory course in quantum mechanics, hoping to find out what inspired the whole idea of quantization in the first place, and I was surprised to learn that quantum energy states in an atom were mathematically identical to standing waves on a plucked string or in a column of air. Different combinations of standing waves are what give different musical instruments their distinct sounds. So there’s yet another fundamental aspect of nature with a connection to music!
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David, the mathematical equivalence of quantum energy states in an atom and standing waves from a plucked guitar string is fascinating! This whole fundamental connection between nature and music/math/physics is just fascinating for me the more it’s uncovered. I like the point this article makes about how the educational grouping of Science, Technology, Engineering, Mathematics (STEM) should include the Arts, STEAM as there is that linkage.
Music inspired and guided him; it stimulated parts of his brain that could not be accessed through sitting at his desk. It gave him a sense of patterns, feelings, hunches, intuitions – all manner of sensual information that could be described as ways of thinking that don’t involve words.
Some have suggested STEAM, so as to include the Arts in the grouping. Or STREAM, to include Reading and Writing. Wouldn’t it be great though if all human intellectual endeavours were simply treated equally?
Einstein used as many parts of his mind as he could to experience and interpret the world, to create knowledge.
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Lol…@ both Jung and David, in regards to how Mathematical stuff equates into music…,
Math and myself from Day one in Kindetgarten, to Grade 12, never got along, it was a constant struggle, still is, I don’t see eye to eye , er numbers with it, and therefore not fully understanding all this that you both are referring to and how it all correlates in music…I’m about visual, concrete, rhythm, not about technique, numbers, etc…lol…
Wish you could tell me in layman’s terms or offer visual reference as to what you’re talking about here, perhaps then I could get a, perhaps or not, a basic grasp of things you mention…lol
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Hi, Jacki.
Sorry, I was geeking out there a little. Here’s a pretty good and relatively mathless visual intro to standing waves, with application to music and a brief reference to quantum stuff:
https://www.youtube.com/watch?v=0Rfushlee0U
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Great video David, and explanation of standing waves.
Jacki. The closest tie between math and music is in the pattern. Music and math can both be represented as a pattern.
For me the way I envision music as a pattern is to think of music visually the way it appears on a music sheet, with the music notes, from low notes to high notes (C,D,E,F,G,A,B..), on a vertical access, and time or intervals on the horizontal access. As time progresses from left to right along the horizontal access, each music note plots on the vertical access as music notes or chords are played. So in effect music is represented as a pattern, just like music notes appear on the music staff as illustrated below.
With math, if you plot numbers on the vertical access, instead of music notes, representing any unit of measure you like such as temperature for example, and if you plot time on the horizontal access, it is not unlike music. So if you want to plot the temperature in Ottawa throughout the day this way, you get a pattern that looks like music!
Bach, Mozart, and Einstein envisioned math and music similarly as patterns. Mathematicians can graph math formulas for example to represent say an exponential virus growth visually as a pattern like how music can be represented on a music staff.
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Here is a piece of music (Scarborough Fair) plotted as a pattern.
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Lol @ both Dave and Jung, though both your visual references , somewhat helped, I’m still not fully able to grasp…andcI can’t read music barely, so that reference, kind of zoomed above my head, I know when a funny note thingy is low and high, that’s about my basic knowledge, I can sing somewhat and have done open jams/mics/karaoke, I just have no clue as to what key I’m singing in , I just know to how to sense/feel/hear a rhythm, tune, key, to then go with it from there, that is , I’m basically read music illiterate, rather tend to rely more on being a play by ear,more visual stimulation kind of technique, method. type musician person. I hear a song, I can sense the rhythm and pick up tambourine, harmonica to kind of play along, sing along with in tune to with what I’m hearing, kind of intuitively….sort of idea…do you understand, what I am trying to explain myself here with… kind of like my guitar/uke playing skills inability, where I explained best I could in another thread and David grasped what I was trying to say…lol
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Jacki, I think for most of the great musicians music is created and experienced intuitively by feelings too. The Beatles had no formal music training and yet created some of the greatest music by feel and intuition. Jimi Hendriks said he could not read music at all, he improvised. It’s just fascinating to see the natural linkage between math, physics, and music like it comes from the same place. It was the intuitive, sensual aspect of music that affected Einstein:
Music inspired and guided him; it stimulated parts of his brain that could not be accessed through sitting at his desk. It gave him a sense of patterns, feelings, hunches, intuitions – all manner of sensual information that could be described as ways of thinking that don’t involve words.
I love this part about Einstein and the piano. 🙂
Disappearing into a room for two weeks (emerging for the odd piano session), he then surfaced with a working draft of the theory of general relativity.
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Here is another fun and brilliant video that give insight into the Beatles and their music. If you got 20 minutes, it’s a well worth illuminating insight into the Beatles and their craft. It shows just how musically intuitive they were.
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Here is when music can be so beautiful.
Can you blame Paul Simon and Paul McCartney for being inspired by Bach! In a Rolling Stone Magazine interview, Kinks Ray Davies referred to a little Bach influence in “Sunny Afternoon”.
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In another interview with Kinks Ray Davies in 2018 in northjersey.com
Wanting to know what kind of music influenced him in the past and what he listens to nowadays, he responded,
“I listen to anything that has a bit of meaning and a bit of spirit and feeling.” He referenced Charlie Byrd, a guitar player from the 60s, who he characterized as buoyant, saying when he listened he would “expect something good to happen.” He added that some other favorites were Bach and Haydn as well as some of his contemporaries like Leo Kottke and The Band.
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A little music theory tidbit: All modern jazz to pop/rock music owes it’s existence to the medieval Mixolydian Mode (7th note in a major scale is flattened to give a hypnotic transcendental atmosphere). This is one of the important links that exist between old medieval music and modern music.
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