As an engineer, a music lover – musician and a former philosophy graduate student I always wondered about the mathematical equations, formulas and ideas behind music, the philosophy of music and the interaction between the three. Sounds are basically frequencies, frequencies can be defined by numbers and can be explained by mathematics, while on the other hand the perfect amalgamation of sounds becomes music that creates emotions. Readers will find themselves at the crossroads where these three magical concepts meet each other.
The Interaction
Mathematics supplies formal models such as ratios, transforms, group operations, music supplies the perceptual and formal objects such as intervals, rhythm and form, and philosophy interrogates what those models imply about meaning, beauty and cognition. A tuning defect in mathematics can be discussed in terms of perceived consonance in music and then placed in an aesthetic value framework from a philosophical standpoint.
The relationship between mathematical reasoning and musical creativity, and the way humans grasp and appreciate both subjects, became a matter of interest for a number of academicians.
It has been observed that mathematics is the most abstract of the sciences and music the most abstract of the arts. Mathematics attempts to understand conceptual and logical truth and appreciates the intrinsic beauty of such. Music evokes mood and emotion by the audio medium of tones and rhythms without appealing to circumstantial means of eliciting such innate human reactions.
The Greek mathematician Pythagoras noted the integral relationships between frequencies of musical tones in a consonant interval; the 18th century musician J. S. Bach studied the mathematical problem of finding a practical way to tune keyboard instruments.
One inclined within one of these areas might fear the other, but there are people going back and forth between the right and left sides of the brain with no hesitation.
The physical basis of sound
Sound production — strings, air columns and electronic signals — is governed by physics that we model with math: frequencies, waveforms, overtones and Fourier decomposition explain why a note sounds the way it does. Fourier analysis and basic harmonic theory are the mathematical keys to acoustics and timbre.
I. Musical Theories of Pythagoras
Pythagoras did not compose music in the modern sense but created a foundational theory of music based on mathematics. His studies linked numerical ratios to musical intervals, giving rise to the concept of the “music of the spheres” and the tuning system known as Pythagorean tuning.
Mathematical ratios and musical harmony
Pythagoras discovered that musical harmony could be explained by simple whole-number ratios. According to a legend, he walked past a blacksmith’s shop and noticed that the different weights of the hammers hitting the anvil produced consonant and dissonant sounds.
While likely not historical, this story illustrates his discovery that musical intervals correspond to mathematical proportions. He demonstrated this principle using a monochord, a single-stringed instrument.
- Octave (2:1): Doubling the length of a string produces a pitch that is exactly one octave lower.
- Perfect Fifth (3:2): A string that is two-thirds its original length produces a note a perfect fifth higher.
- Perfect Fourth (4:3): A string that is three-quarters its original length produces a note a perfect fourth higher.
The music of the spheres
Pythagoras extrapolated his mathematical understanding of music to the entire cosmos. His philosophical concept, the musica universalis or “music of the spheres,” posited that the sun, moon, and planets all emit their own hum as they revolve.
He believed the universe was a mathematical and harmonious whole, and the celestial bodies’ movements, based on numerical ratios, created an inaudible but perfect and continuous symphony in divine harmony.
According to Aristotle, the Pythagoreans explained that humans don’t hear this cosmic music because we have heard it since birth, rendering it indistinguishable from silence.
Pythagorean tuning
We know Pythagoras from his famous mathematical theorem about the right angled triangle, but as a philosopher, he first discovered music intervals and also invented the monochord, a straight rod on which a string and a movable bridge could be used to demonstrate the relationship of musical intervals.
The Greek philosopher, initiate and teacher, stood at the point of the marriage of music, science, and mysticism. He was one of the first “scientists,” and as an initiate, he asked deep questions of the universe. He was known to be a person of great knowledge and psychic power. Due to his higher nature, legends grew up around him, such as an ability to travel to celestial realms and actually hear the music of the spheres.
Pythagorean principles are the basis of much of musical and mathematical study, and the strength and depth of his discoveries changed the way the world perceived itself, even up to our times. However, his influence goes beyond the world of science and mathematics; it penetrates into the mystical side of number and music.
Pythagoras was one of the first musicians to recognize the therapeutic power of music, viewing it as a way to influence and heal the mind and soul. His work with the mathematical properties and ratios of musical intervals convinced him that the music of the human organism would respond in various ways to these relationships. The Greek modes used at that time were distinguished primarily by their intervallic structures; each was thought to have a positive or negative effect on the human psyche. Consequently, certain rhythms, scales, and songs were used to heal the body and soothe the passions.
Legacy
While modern Western music uses a different tuning system (equal temperament) to resolve the issues with Pythagorean tuning, Pythagoras’s fundamental discovery of the mathematical basis of musical intervals was a landmark in Western thought. It fused mathematics, music, and philosophy, and his influence extended well into the Renaissance and beyond.
II. Music and Soul in Plato
Plato’s philosophy of music centers on its profound and direct influence on the soul, character, and political structure of the state. He believed music was a powerful educational tool that could either cultivate virtue or encourage vice, making its regulation vital for his ideal Republic.
Plato treats mousikē (music in the broad ancient sense: song, poetry, rhythm, and melody) as central to education and character-formation.
The phrase “to the brain and the blood and transmitted to the soul” is a concise, modern summary or interpretation of Plato’s view. It effectively captures the ancient Greek belief in a physical and emotional pathway for music’s influence. Music, consisting of rhythm and harmony, enters the body through the ears, which act as a gateway.
The Ancient Greeks believed the sound vibrations were processed by the mind and circulated throughout the body via the blood (or other vital forces), thus affecting every part of the human organism.
The final, and most crucial, effect is on the ‘inmost soul’, the non-rational, spirited, and appetitive parts of a person’s character. Plato states in the Republic:
“Rhythm and harmony find their way into the inmost soul and take strongest hold upon it, bringing with them and imparting grace, if one is rightly trained”
The Pythagorean discovery that simple numerical ratios produce pleasing intervals influenced Platonic ideas about mathematical order underlying reality and the “harmonies” of the world. Plato treats mathematical structure as revealing the form of cosmic order. He places the mathematical results into a broader metaphysical framework rather than the Pythagorean experimental or mystical program. Although some ethical and ritual ideas such as purification, the role of music for the soul, belief in transmigration, that appear in Plato reflect Pythagorean doctrines, Plato reworks them into his own philosophical system.
For Plato, music was inseparable from poetry (lyrics) and dance (movement); the words, melody, and rhythm all had to align to present a coherent, ethical message. He thought music isn’t merely entertainment; it’s a moral law and the cornerstone of education.
According to Plato, the ultimate goal of musical training is to establish harmony and order in the soul, preparing the individual for the later study of abstract philosophy and mathematics. By being habituated to beautiful, orderly, and moderate music from childhood, a person develops an inherent love of the beautiful and a dislike for the ugly, which extends to their moral judgment in all areas of life.
III. Theodor Adorno and His Ideas Upon Music
Theodor Adorno viewed music not just as an art form but as a reflection of societal structures, particularly under capitalism. He was deeply critical of mass-produced music, known as the “culture industry,” and championed avant-garde music for its potential to resist and critique social norms.
Adorno’s critique of the “culture industry” and popular music
For Adorno, the music produced by the culture industry, including popular genres like jazz and pop, was not authentic art but a commodified product designed for mass consumption.*
Adorno argued that popular music was built from simple, repeatable parts and followed predictable formulas. This sameness made it easy to consume but dulled critical thinking in the audience.
The illusion of variety was manufactured by altering superficial details, a process he called “pseudo-individualization”. This masked the underlying standardization and gave listeners a false sense of choice.
By offering easy, formulaic pleasure, popular music encourages passive listening rather than critical engagement. It functions as a tool for social control, keeping the masses docile and content with the status quo, no matter how bad their economic circumstances.
This process creates a psychological distance between the listener and authentic expression, deepening social alienation by turning art into just another product to be consumed.
The importance of avant-garde or “new music”
In contrast to the culture industry, Adorno praised new, avant-garde music, particularly the atonal and twelve-tone compositions of Arnold Schoenberg.
New music’s dissonance, complexity, and unconventional structures mirror the fragmented, anxious, and contradictory nature of modern life under capitalism. This serves as a form of social critique rather than a means of escape.
True art must maintain its independence from commercial and social pressures. This “aesthetic autonomy” allows it to challenge norms and foster critical awareness, which is the opposite of popular music’s function.
Unlike popular music, new music’s challenging nature demands active intellectual and emotional engagement from the listener. This process can lead to deeper reflection on society and the self.
His analysis of composers and styles
Adorno illustrated his theories by contrasting composers and styles.
Adorno saw Schoenberg’s move towards atonality and twelve-tone technique as a necessary, progressive break from the tonal tradition, accurately reflecting the anxieties of modern life.
He criticized Igor Stravinsky’s turn toward neoclassicism as a regressive step that adopted old forms in a meaningless, ritualistic way.
He viewed much of the commercialized jazz of his era as a standardized, repetitive product, dismissing its improvisation as “pseudo-individualization”.
Enduring relevance and criticism
While controversial and sometimes seen as elitist, Adorno’s work remains influential in musicology and cultural studies. His critique anticipates many modern issues, such as how algorithms and streaming platforms might further the commodification of music and shape listener tastes. However, modern critics argue he underestimated the complexity and critical potential of many popular and subcultural music forms.
* I do not fully agree with Adorno’s ideas today, which does not really make sense from a 21st century point of view, as the concept of ‘popular music’ changes in time.
Analytical Thinking
Our professors used to say studying engineering improves analytical thinking. The ability to think methodically, analyze and reasoning also helps to build a musical structure. Many great composers and musicians have technical background.
There are many commonalities between mathematics and music, which can also be a definition of analytical thinking. For instance, breaking complex structures into parts, can be described as melody, harmony, rhythm, texture and form in music. Understanding relationships and patterns, could be understanding intervals, chord progressions and rhythmic ratios. Applying rules, theories or logic can be defined as counterpoint, tonal harmony and algorithmic generation.
In music creation, this corresponds to being aware of how tension and release work, how listeners’ expectations form and are satisfied or violated and structural coherence across sections.
Most would argue, analytical thinking itself is not adequate for musical creativity and indeed there’s a spiritual and emotional aspect. Without being aware of the technical side, all these modal structures, chords, intervals, a talented singer can touch the human soul.
Modern studies show that music creation uses both analytical and intuitive systems in the brain. The prefrontal cortex, responsible for planning, analysis, working memory, activates during composition and improvisation, especially when a musician evaluates or refines ideas. The default mode network, associated with imagination, mind-wandering, is active during spontaneous creativity. When composing, musicians switch between these networks.
Creating a musical idea requires knowledge of harmonic or rhythmic possibilities which can spark new combinations while intuitive thinking helps to freely improvise and follow emotional impulse. While being able to analyze motifs, transform them logically and plan harmonic trajectory, a good musician can keep expressive coherence and feel how tension flows. While evaluating structure, pacing, voice leading and proportions, one must preserve spontaneity and human warmth.
The balance between two edges is significant. Too much analysis brings risk of sterility, the result will be music that’s correct but lifeless. If it’s too little, there will be chaos and incoherence. Plato’s ideal of harmony between reason and spirit still applies: a balanced composer integrates intellect (logos) and passion (thymos).
Modern Technology vs the Soul of Music
Today’s technology, the tools, variety of instruments, applications, gadgets, the abundance of free and affordable online training makes it easier to create music. On the other hand, it becomes more difficult to find and choose good music among all those various options.
The innovation of artificial intelligence had a huge impact on music creation. AI learns, listens, replicates, covers and creates music, which sometimes sounds unique, but mostly reminding of some tune you may already know.
So, here comes the question:
How does Artificial Intelligence tools for music creation handle the emotional part? Or is it also imitating the emotions that were already created a long time ago by real musicians?
The emotional part that’s passed from the musician to the audience, and the feelings during a live show keeps the music scene alive today, and something that AI cannot replicate, yet. Emotion in music is hard to codify, yet it’s exactly what makes it meaningful.
For AI, emotion isn’t felt, it’s represented or predicted. AI models learn statistical associations between musical features such as tempo, mode, harmony, melody shape, dynamics and rhythm, and human emotional labels such as being happy, sad, tense, relaxed, nostalgic, etc.
So instead of feeling joy or sorrow, the AI learns patterns that correlate with those feelings in humans. It’s trained on mood-labeled tracks and mimics the way certain musical cues statistically evoke emotions. Some models are trained on soundtrack datasets, so that it learns emotional tropes such as suspense represented by low drones or triumph by rising brass.
Despite all the innovations in tech, AI still struggles due to the lack of genuine feeling or embodiment. The system doesn’t experience tension, loss, joy; it imitates patterns humans associate with them.
Emotional meaning depends on culture, memory, and narrative context; AI lacks that personal embedding. Expressive nuance, small timing irregularities, microdynamics, articulation — still hard to generate convincingly, though models are improving. A symphony’s emotional journey still remains difficult for most generative models.
The innovation and improvements on artificial intelligence in this age is accelerating significantly and we have a lot to witness in the near future both in music and other forms of art. The day will come that modern AI will be trained to introduce “imperfections” and nuances to sound more human.
Music by Human Soul & Intelligence
We’re surrounded by more music than any human era before us, yet finding quality music with depth that’s genuine, lasting, emotionally and artistically rich, can feel harder than ever.
Anyone in search of ‘good’ music is after structural coherence, intentional harmony, rhythmic control and production quality. This matters as there’s skill and thoughtfulness behind the sound. The authentic sense that the artist reflects expressive honesty, vulnerability and conviction brings resonance and lasting impact on the audience. Distinct musical fingerprint with unique tone, harmonic language, rhythm and lyrics creates originality. Music that says something about life, society or the human condition embodied with cultural or philosophical depth has intellectual richness. Music that rewards repeated listening is a hallmark of quality craftsmanship.
So it’s all about personal aesthetic compass. Once you define these values, the noise around you becomes easier to filter.
The Future of Music Made with AI
The consensus among experts is that AI is not a replacement for human creativity but a powerful new tool that will fundamentally change the music industry:
Augmentation and Collaboration: The most impactful role for AI is as an enhancement tool for human composers and producers. It can quickly generate variations, create rapid mockups, and assist in creative tasks, speeding up the production process. Artists are already using AI to create “vocal twins” or generate quick instrumental tracks.
Personalization and Volume: AI is enabling the creation of vast amounts of highly personalized music. Tens of thousands of AI-generated songs are being uploaded daily to streaming platforms, creating a new, hyperscalable competitor in terms of sheer volume.
Ethical and Legal Frameworks: The future of AI music hinges on resolving copyright, licensing, and ethical concerns. Debates are ongoing about compensating artists whose work is used to train AI models and establishing legal frameworks for AI-generated content that may inadvertently copy existing copyrighted material. The focus is shifting toward creating a sustainable model for licensing and monetization.
The future of music will be a powerful mix of human creativity channeled through increasingly smart technology and we already started observing the signs.
Reading recommendations;
Theodor Adorno – Philosophy of New Music
Daniel J. Levitin – This is Your Brain On Music
Arthur I. Miller – The Artist in the Machine, The World of AI–Powered Creativity
* All photos and illustrations are created by various AI platforms.
