Music, Enrtropy, Neurons, and Information
“I would teach children music, physics, and philosophy; but most importantly music, for the patterns in music and all the arts, are the keys to learning”― Plato
Music is something that we listen to every day in many forms. Entropy and Neurons are yet to be understood by the people who work on them but they provide interesting insights about things around us. It is really interesting how we are moved by music and with that feeling, we can understand ourselves in a scientific way. To understand it we need to know something about each word in the topic and interpret it in our own way. This will be a long read but will be fascinating once you understand it in your own way.
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Music
Music can be academically defined as an arrangement of sounds. There are some technical terms that one should be familiar with. When the sound gives a pleasant and harmonious sensation it is called consonant, if the sound gives an inharmonious feeling then it is called as dissonant.
The sound of a trained singer singing a song, the sound of a temple or a church bell, when a student plays piano we get a consonant. When a normal person sings a song, the sound of hitting metal utensils, when a cat walks on a piano we get a dissonant. One can easily recognize this, whether he knows music or not. Sometimes in nature, we get these sounds like birds, cows, and fish make consonants (not always), whereas bugs, bees, and donkeys made dissonant.
From a musician's point of view, jass is mostly dissonant but gives a feel that depends on the player (not mocking jass, just a fact), metal and rock music is not pleasant but harmonic so it depends on the listener. Other than that all are consonant. Generally, consonants are predictable sounds.
Music is evolved through the ages among that classical music is the most ordered and has strict rules about music and the free-going type is jass, yet people like both the music. It is a question of why people like music? (Think it yourself)
Technically a piece of music has rhythm, harmony, and melody. We normally combine them to produce music. We can sense them easily.
The sense of rhythm
The best example of rhythm is our heartbeat or a ticking analog clock. It produces a sound in equal intervals of time or it is silent in a particular interval of time. 1,2,3,4:1,2,3,4;1,2,3,4;1,2,3,4... now if you count this pattern in your mind and repeat it the make a sound in everyone or in any pattern when which you wish you are producing rhythm ( technically a 4/4 rhythm pattern).
By nature, we have a sense of rhythm, we tap our legs, nod our heads or clap our hands while listening to a song which is nothing but our sense of rhythm. From nature, we can grasp the rhythm from The rustling of leaves, the sound of rain, the sound of water flowing, the sound of waves on the beach, the song of birds, etc.
The sense of harmony
In a very general meaning harmony is the existence of things together. So in music, it is the existence of different sounds together. The sets example is the "gooood mooorrrninggg" of kids in school. Is harmony sounds as a single sound but has various tones in it. Another example is the audience singing a song in a concert or a group of people in a choir. We as social beings sense and produce hormones in our daily life but we do know how.
The sense of melody
In general, a melody is a tone that produces a consonant. A bird singing is a melody, our random hummings are a melody. It has a certain pitch to be filled and follows a rhythm. The " Happy birthday song" is a good melody. So a melody is a set of notes which make a consonant.
The walking humans - music producers
As physicists approximate a cow as a cylinder (not a joke it is real check it here), we can approximate a walking human as a simple pendulum. As we walk we exhibit a harmonic motion i.e., an up-down motion, back-and-forth motion, extension, and compression.
All this is associated with a sound like a taping of feet, swinging of hands, and breathing. So a walking human can produce a piece of music.
When a group of people walk we can create a good random consonant. From this, we can obtain a predictable sound. By doing this we have different predictable sounds in harmony and when we can synchronize them we get spaces of silence that have two adaptations. we can filter our unwanted predictable sounds, and we can effectively find a tempo (time frame of a rhythm) and follow it and form a convincing melody or a beat.
So our natural activity can produce a piece of good music so people get inspiration from themself and from nature. Different cultures have different types of sounds and music but the feeling that they convey are universally understood? Which is again a question that we have to think about. I also have another question about this we humans do not need music to exist ( Like a human can exist without pizza) then why do we need music? (Think about these questions by yourself).
Basics of harmony
To understand the pattern of harmony in a physical and a mathematical way I encourage you to do a small activity. Make something as shown in the figure. Frequency ratios, Now take a model that was proposed by Pythagoras, in the following arrangement the white border is a slider so it can dived the string into two different parts and creates different sound when it is moved differently.
Now when the slider is kept in such a way that the ratio of their lengths or the frequency is a simple integer we will get a consonant (like 1:2, 1:2, 2:3, etc). Other frequencies like 1:13, 3:19, etc are normally dissonant. You can check it by yourself by making such an apparatus. These sets of notes are in different frequencies form chords and all the major and minor chords are composed of the simple frequency ratio.
The auditory system - The place where neurons play their game.
Once Sound reaches your ear it vibrates your eardrum which in turn vibrates the three bones that pass these vibrations along to your cochlea, inside the cochlea is the basilar membrane and which is a strip of tissue that runs along the length of the cochlea the basilar membrane is designed so that the stiffness and other properties vary along its length so different parts of it resonate at different frequencies near the base of the cochlea responds best to high frequencies and at the tip it responds best to low frequencies all along the basilar membrane are these sensors called hair cells because they're each in a different position on the membrane they each respond best to a different frequency so effectively the cochlea performs a Fourier transform it separates audio signals into different frequencies each connected to a neuron which sends a signal to the brain saying that it heard this frequency neurons communicate primarily through electrical signals.
When a neuron receives chemicals called neurotransmitters from a sensory cell or from another neuron those trigger ions which move positively charged potassium and sodium ions inside and outside of the neuron so there's a flow of current into the neuron at the same time all the charges that are accumulating on the inside and outside of the neuron are only separated by the thin cell membrane so this forms a capacitor on the edge of the neuron and the current source is charging up this capacitor (of course the cell membrane isn't perfect at holding back the ions so some of the calculus is going to leak through this means that the membrane acts as a resistor so now we've turned our neuron into an RC circuit) and we can analyze it just like we would in a physics class, the key value that we are interested in is the voltage across the membrane. The reason that we're interested in that is that once this reaches a certain threshold it will trigger voltage-gated ion channels to discharge the neuron and then it'll send neurotransmitters to the next neuron and repeat the whole process so here's the equation for our neuron the input current which again depends on the other neurons and sensory cells that our neuron is connected to equals the leakage current plus the charging and both of these depend on the voltage which is what we want to solve.
I don't think it's particularly enlightening (If it is enlightening do read about it) so instead of solving it let me walk you through what typically happens and I say typically because that noise that we included makes the solution slightly random the current signal coming from the hair cell is generally not high enough to trigger the sensory neurons on its own so it takes the addition of our noise to actually fire during the first cycle of the sound wave that we're listening to the neuron is charging up so the moment that it's most likely to fire first is at the peak of the sine wave when the current input is highest if it didn't happen to fire at that time then the next most likely cancer is going to be at the next Peak so if we make a probability distribution of the sensory neurons firing times it'll look something like this a high peak after one cycle of the sound wave and then they get smaller after that on round number three the input from a single sensory neuron is also generally not high enough to trigger it and because of the resistor or charges leaking across the cell membrane if there's no constant current input then it'll eventually discharge so in order for neuron number three to fire it needs to receive a signal from one neuron and then really soon after receive a signal from the other neuron this needs to happen before it has time to discharge so the more often the signals from neuron 1 and neuron 2 line up the more often neuron 3 will fire and send a signal to your brain we can use this to make a probability distribution of neuron number three's firing times but of course it depends on the relationship between the two frequencies that you're hearing.
Entropy and Information
Entropy and information are big words in the modern academic world because we don't understand it to a full extent but the basic definition and insight will provide us a good understanding of the thing that we are dealing with.
Entropy is the measure of disorder. A well-arranged room has lower entropy because the thing that room is already stable to our senses and we don't do anything about it. whereas a messy room has more entropy because things can be arranged in more ways, so the things in a messy room can be arranged in different ways, unlike a well-arranged room.
Information is knowledge of facts. Facts are something we know, so we can know something by seeing, hearing, feeling, reading, writing, practicing, etc. Now when we take the above room case we have information from both rooms, It is easy to get detailed information from a well-arranged room because we can easily navigate things and understand them. A messy room will have information but not in the way we like, normally in a very short time we will say a well-arranged room gives more information than a messy room. It is true and false depending upon some factors.
Music, Entropy, and Information
So here are some probability distributions for small integer chords you can see that they're pretty regular the signal that your brain gets is organized and predictable but here are some probability distributions for large integer chords as you can see they're much fuzzier it's not predictable when that neuron is going to fire we actually have a way of measuring this fuzziness it's called information entropy or Shannon entropy (after its inventor to introduce it let me show you this picture this is the Arecibo message).
In 1974 we sent this picture through radio waves into the cosmos I guess as an attempt to introduce ourselves to whatever aliens might find it but pretend that you're an alien and your job is to watch the data from a radio telescope and notify someone.
If you see a signal that looks like it's from Aliens most days you'll just see something like this random noise.
Then one day you see one of these signals gives you more information clearly. It is so organized that it must be an intelligent message, see you already have an intuition (Even if we don't know the meaning of the signal we can grasp this from the analogy of the messy room earlier.) For entropy, a signal that appears more organized is more likely to contain information a high entropy signal like this is probably just noise but a low entropy signal like this tells us something if you were just shown each of these signals then the low entropy one carries more information.
Now here's the counter-intuitive part let's say that you know that both of these signals are from Aliens they're both intentional, now which one gives you more information this one does the one with higher entropy see the low entropy organized signal follows simple rules you could recreate it by only knowing a few things but to recreate the high entropy signal you would need to know each bit so you actually gain more information by understanding the messy signal is ambiguous but decoding It ultimately gives you more information.
The entropy of neural signals reaching your brain is low for consonant low integer chords it's high for dissonant High integer chords and this makes sense in a lot of ways. I mean if you hear a C major chord on a piano then of course it was intentional it carries a simple message and it's unlikely to happen by chance somebody is probably reading music and playing it. On the other hand, if you hear three adjacent chromatic notes then it could just be that something fell on the piano on the surface you might not gain information from it but if somebody was reading music that directed them to do that then it would carry a profound amount of information because there are hundreds of bad chords and only a few good chords.
When it's less organized you have more to work with nevertheless our brain prefers the unambiguous case and that's why we like certain chords and we will easily have to connect to the musical and what feel it is delivering. Like a C major: Innocence, happiness with a spiritual feeling; Cm: Innocence, sadness, heartbroken and evokes yearning (Search them meaning in Google); D major: Triumphant and victorious. Feels like war marches or holiday songs; Dm: serious and melancholic. Brings on feelings of concern and contemplation; Em: Restless love, grief, and mournfulness; F chord: Optimism and the will to explode, etc.
When we hear a melody, we still need to think and figure out what the musician wants to say and that's the definition of high entropy. It is not a coincidence that according to our analysis of neural firing times, this is a high entropy interval. It is easy when we have low integer frequency chords that form consonants and are predictable & ambiguous to us.
When Claude Shannon introduced the concept of information entropy, he called it that way because the disorganization of information is clearly analogous to the disorganization of matter which we call entropy and thermodynamics and statistical mechanics but maybe there is another similarity between the two.
In matter entropy always increases on a global scale and this is just a result of statistics. If you drop food dye into the water there is only one state where all the dye molecules form a particular shape but there are trillions of states where the molecules look random so over time they'll tend to look random, This is the second law of Thermodynamics.
Maybe human culture follows a second law of information, I mean modern films, music, visual art, and literature all of it depend on ambiguities that are left up to us to understand them. A single spoken sentence can contain so many layers of information that are completely absent from something like a computer programming language even day-to-day functions like determining whether somebody is lying or if they understand you.
All (sound made by a human) is difficult to process because human speech has such high entropy but listening to music might be our way of training our brain for that. So, jazz music and indigenous drumming really aren't that different they both train us to process difficult information that might be the best benefit that music gives us. Of course, you can't listen to Hard music all the time because it might be white noise which has a very high entropy that we can not comprehend.
This is a connection to model theory (click here)
NOTE:
## Audio is made by John Paul J
- The rest of the audio is taken from "Sound Effect from <href="https://pixabay.com/?utm_source=linkattribution&utm_medium=referral&utm_campaign=music&utm_content=29388">Pixabay</a>"
- The pictures and equations are made by GIMP and "a paper" mobile application by John Paul J. The equations are not exact and are referred from the following.
- https://pubmed.ncbi.nlm.nih.gov/21981535/
- https://pubmed.ncbi.nlm.nih.gov/20481757/
- https://pubmed.ncbi.nlm.nih.gov/27134038/
Hope this article was useful and I hope you learned something from it.
If you have any theories or questions regarding this you are free to express them in comments or you can chat with me on my Instagram page https://www.instagram.com/phy.sci/?hl=en.
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IF ANY DOUBTS AND CLARIFICATION YOU CAN COMMENT HERE.IF ANY INFORMATION IS INACCURATE I AM READY TO CORRECT IT
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