A letter from Albert Einstein to his daughter: on The Universal Force of Love
A Publication from the American Mathematical Society
“There is geometry in the humming of the strings, there is music in the spacing of the spheres.” — Pythagoras
|Counting, rhythm, scales, intervals, patterns, symbols, harmonies, time signatures, overtones, tone, pitch. The notations of composers and sounds made by musicians are connected to mathematics. The next time you hear or play classical, rock, folk, religious, ceremonial, jazz, opera, pop, or contemporary types of music, think of what mathematics and music have in common and how mathematics is used to create the music you enjoy.|
Music + Math: Symmetry.“From Pythagoras’ observations of the fundamental mathematical relationship between vibrating strings and harmony to the digitized musical world we enjoy today, The Majesty of Music and Mathematics with the Santa Fe Symphony and the Santa Fe Institute will explore the remarkable interweaving of the languages of music and mathematics.” View the entire Santa Fe Institute series, covering the tritone, harmonics, ratios and more.
“What could be a better medium to communicate math to the public than the universal language of music? Ever since Pythagoras used numerical terms to express intervals between notes and derived musical tones from geometrical patterns, mathematicians have linked music to numbers.” At the SIAM Annual Meeting in 2010, Tymoczko used graphics and sound to connect math to the music of Chopin, Mozart, and Schubert. Video by Adam Bauser, Bauser Media Group.
a mathematician who also is a concert pianist, describes how a mathematical breakthrough enabled Johann Sebastian Bach to write “The Well-Tempered Clavier” (1722). At the time, Cheng was a visiting senior lecturer in mathematics at the University of Chicago.
“ David Kung (St Mary’s College of Maryland) presents “Symphonic Equations: Waves and Tubes” — a miniexcursion into math and music, presented as a MAA Distinguished Lecture at the Carnegie Institution for Science.
Turning math into music. Sean Hardesty (Rice University) plays the opening of the Sibelius Violin Concerto and discusses the relationship between mathematics and music.
The world’s ugliest music: Scott Rickard at TEDxMIA. Scott Rickard has degrees in mathematics, computer science, and electrical engineering from M.I.T. and MA and PhD degrees in applied and computational mathematics from Princeton University. Rickard says that he is “passionate about mathematics, music and educating the next generation of scientists and mathematicians.”
Robert Schneider – Reverie in Prime Time Signatures (August 2013, Banff Centre). Robert Schneider (Apples in Stereo/Elephant 6) composed this theme for “MSI (Math Sciences Investigation): Anatomy of Integers and Permutations,” a play by mathematician Andrew Granville and screenwriter Jennifer Granville. “As the title indicates, the piece is written in prime-numbered time signatures; which is to say, there is a prime number of beats in each measure. The main theme plays in the time signature 7/4, which indicates 7 beats per measure, with an interlude that passes through the signatures 2/4, 3/4 and 5/4 as well. From the constraints imposed by these rhythmic patterns, melodies emerged naturally as I composed, special to each prime…”
Music and math: The genius of Beethoven – Natalya St. Clair TED Ed. Natalya St. Clair uses the Moonlight Sonata “to illustrate the way Beethoven was able to convey emotion and creativity using the certainty of mathematics.”
The Math Behind Music. Ethan Thompson and David Hamilton explain the math behind music in a fun, concise way in this finalist entry in the 2015 Math-O-Vision contest.
Listen Up (Podcasts)
- Marcus du Sautoy: music and symmetry. Marcus du Sautoy (Simonyi Professor for the Public Understanding of Science and a professor of mathematics at the University of Oxford) talks to a concert audience about the connections between music and mathematics.
- Putting Music on the Map. Listen to Dmitri Tymoczko (Princeton University) speak about using topology to represent musical chords as points in a space.
A Medley of More Mathematics and Music
- “No Static at All: Frequency modulation and music synthesis,” by David Austin
- “Time-frequency Analysis of Musical Rhythm,” by Xiaowen Cheng, Jarod V. Hart, and James S. Walker
- “Musical Actions of Dihedral Groups,” by Alissa S. Crans, Thomas M. Fiore, and Ramon Satyendra
- “Music: Broken Symmetry, Geometry, and Complexity” by Gary W. Don, Karyn K. Muir, Gordon B. Volk, James S. Walker
- “Was Something Wrong with Beethoven’s Metronome?” by Sture Forsén, Harry B. Gray, L. K. Olof Lindgren, and Shirley B. Gray
- “Math and the Musical Offering,” by Tony Phillips
- “The mathematics of piano tuning,” by Tony Phillips
- “The magical mathematics of music,” by Jeffrey Rosenthal
- “Can One Hear the Sound of a Theorem?,” by Rob Schneiderman
- “This Bird’s Songs Share Mathematical Hallmarks With Human Music,” by Helen Thompson
- Daniel’s Blog: Music and Math, by Daniel Tompkins
- “The Generalized Tonnetz,” by Dmitri Tymoczko
- “Neo-Riemannian theory,” Wikipedia
If you would like to recommend more websites on mathematics and music please let us know. Email the AMS Public Awareness Office.
Resources available by subscription or purchase
- Journal of Mathematics and Music: Mathematical and Computational Approaches to Music Theory, Analysis, Composition and Performance
- Mathematics and Music, by David Wright
- Many more books that can be found via a search on the web or your preferred online bookstore!
Also see: Society for Mathematics and Computation in Music. The Society was founded in 2006 as an International Forum for researchers and musicians working in the trans-disciplinary field at the intersection of music, mathematics and computation. The website inculdes information about joining and attending meetings, and online newsletters.
A lot has been said about Fibonacci but the Fibonacci sequence is quite simple to understand. You can find a clear outline of it on the following page.
Some very advanced financial trading software are using this sequence to outsmart the market and it works. Just put your mind on this sequence. It may generate miracles for you.
I found this guide quite interesting as it assesses the many ways one can reduce its CO2 footprint in various aspects of life. Perhaps very North American oriented but certainly worth to understand it and be able to apply in other regions and in our personal life.
The full guide is available at The 10 Step Guide.
Esta receita é ensinada por um dos mais esclarecidos médicos do país, o dr. Lair Ribeiro. Lair Ribeiro tem um invejável currículo e, hoje, ajuda em suas palestras a esclarecer as pessoas com informações sobre saúde que poucos têm coragem de dar.
Listen to “Living in the Heart Meditation” by Sri Chinmoy
If we can feel that
It is not our voice,
Not our fingers,
But some reality deep inside our heart
Which is expressing itself,
Then we will know that it is
The soul’s music.
The outer music
Comes from an outer instrument.
The inner music
Comes from the heart.
The name of this inner music
Music is the inner or universal language of God. I do not know French or German or Italian. But if music is played, immediately the heart of the music enters into my heart, or my heart enters into the music. At that time, we do not need outer communication; the inner communion of the heart is enough. My heart is communing with the heart of the music and in our communion we become inseparably one.
In the spiritual world, next to meditation is music, the breath of music. Meditation is silence, energising and fulfilling. Silence is the eloquent expression of the inexpressible. Aldous Huxley says: “After silence, that which comes nearest to expressing the inexpressible is music.”
Silence is the source of everything. It is the source of music and it is music itself. Silence is the deepest, most satisfying music of the Supreme.
Silence is like a stream that goes to one place and becomes a river, or to another place and becomes a brook, or to the sea where it is totally expanded.
Silence is the nest and music is the bird. The bird leaves the nest early in the morning and returns to the nest in the evening. Similarly, in the spiritual world, divine music comes from the inmost soul of silence.
Soulful music immediately awakens and inspires our hearts because it embodies the Absolute Supreme. Soulful music is the Light that wants to express itself in a divine way. Even as darkness wants to manifest its authority on earth, Light also wants to manifest its Reality and Divinity in a specific way. Light is the soul of everything. Light is the soul of music, Light is the soul of love and Light is the soul of all art. When Light divinely manifests itself in the form of music, it is the music of the soul.
Music means Self-expansion and oneness. The Self expands through music. The Self that expands is not the individual self but the unlimited Self. Music is the expansion of unlimited Reality.
We can use music to help us in our spiritual life provided we know that music and the spiritual life are like twin brothers; we cannot separate them. How can we separate two fingers, two eyes? They sit side by side. If one eye is not functioning well, then we feel that our vision is imperfect. Similarly, music and the spiritual life must go together; one complements the other. Music helps the spiritual seeker to go deep within to get the utmost satisfaction from life, from truth, from reality. The spiritual life, in turn, helps music to offer its capacity and its strength, which is the soul’s light, to the world at large.
When we listen to soulful music, or when we ourselves play soulful music, immediately our inner existence climbs up high, higher, highest. It climbs up and enters into something beyond. This Beyond is constantly trying to help us, guide us, mould us and shape us into our true transcendental image, our true divinity. When we hear soulful music, or when we play a soulful piece of music, we feel a kind of inner thrill in our entire existence, from the soles of our feet to the crown of our head. A river is flowing through us, a river of consciousness, and this consciousness is all the time illumined.
Next to deep prayer or meditation, music is of paramount importance. Meditation is like a direct route, or shortcut, to the goal. Music is a road that is absolutely clear: it may be a little longer, but it is quite clear of obstacles. If we can play soulful music or hear soulful music, the power of our meditation increases. Soulful music adds to our aspiration. Similarly, if a spiritual seeker wants to be a musician, even if he does not have a musical background, he will be able to be a good musician because prayer and meditation contain all capacities. You may never have studied music, but if you pray and meditate soulfully, then inside your prayer, inside your meditation, by the Grace of the Supreme, the power of music looms large. Then you can utilise this power in your own way.
Each time soulful music is played, we get inspiration and delight. In the twinkling of an eye, music can elevate our consciousness. But if we also pray and meditate, then we are undoubtedly more illumined and fulfilled than a music-lover who is not consciously leading a spiritual life. Each spiritual musician is consciously spreading God’s Light on earth. God is the cosmic Player, the eternal Player, and we are His instruments. It is the Supreme who makes the proper instrument. Then, it is He who makes the player play properly, and it is He who makes the musician.
Soulful and spiritual music really helps us; it feeds our inner life. Music has tremendous power. With fire we can burn ourselves, or we can cook and do many other good things. It is the same with music. Divine music immediately elevates our consciousness, whereas undivine music immediately lowers our consciousness and tries to destroy our sincere inner cry for a better spiritual life. The spiritual person will immediately be affected by this music. So music can change our consciousness provided it is the music that comes from the heart and enters into the heart. The music that touches the very depth of our heart can elevate our consciousness.
Our senses are restless. Therefore, our mind suffers. Our mind is doubtful. Therefore, our senses suffer. The mind has no capacity to bind or discipline the senses. Here music comes to the mind’s rescue. With the help of music, the mind binds and disciplines the senses and makes them into perfect instruments so they can be inundated with peace, light and bliss from above.
Again, when the mind is doubtful, when the mind drinks deep of doubt-poison, the senses have no capacity to inject faith into the mind. Here also music comes to the rescue. The senses take help from music to transform and illumine themselves. When the senses are calm and quiet, the doubtful mind is totally transformed and it becomes inseparably one with the heart, which is all receptivity. At that time our Inner Pilot—the Supreme Musician—can manifest Himself blessingfully, powerfully and measurelessly. As He is manifesting Himself in and through us, the divine music becomes part and parcel of our existence and we grow into perfect Perfection. In and through us the Supreme Musician creates a new world. We become the divine music, and a new vision of God’s transcendental Reality operates in and through us.
Can spiritual music be played during meditation?
Certainly, although it depends on the one who meditates. There are many seekers on earth who meditate extremely well, but who have not developed their musical sense. Their ears have not been trained, so we cannot expect them to change their nature overnight. They either lack the capacity of appreciation or they have some austere feeling about music. Psychic music is not very widely appreciated, and very few people appreciate the soul’s music. They feel it is like a stranger that is entering into their consciousness. But it is actually their eternal tenant, their soul, that is deep within them waiting to come to the fore.
If divine music is played during deep meditation, it enhances the meditation. It will immediately help in elevating the consciousness. If you are fond of music, then playing soulful songs or chants during your meditations at home will definitely help you.
Were we to play spiritual music on tape while we slept, would it benefit us in any way?
While you are sleeping if you play soulful music, your subtle vital, subtle physical and subtle mind will enjoy it. But your physical body may find it difficult to appreciate it, for it wants total silence. Although soulful music will add to pure silence, inner silence, the physical body wants a kind of silence which is totally devoid of outer sound.
If you play your tape very softly, it will definitely help and inspire the subtle physical and subtle vital which are not sleeping.
Many, many times when the physical sleeps, the subtle physical and the subtle vital do not sleep. They move around. They roam here and there. They visit their friends and enemies. My music is definitely a source of joy to them. So for the subtle physical, subtle vital and subtle mind, undoubtedly it is a help. But for the gross physical which is trying to sleep, it may be a hindrance, a disaster.
What is the supreme duty of an artist or musician?
The supreme duty of an artist or musician is to meditate before he creates something and, while creating, to be in a very contemplative, divine mood. Then, when the creation is completed, he will immediately offer his creation to the Supreme. No matter what others say about his creation, no matter what his feelings are about his own creation, as soon as his creation is completed, he will offer it to the Supreme for Him to use in His own way. This is the supreme duty of the spiritual musician or artist.
Is creativity another form of meditation?
It depends on what you are creating. If it is spiritual art or music, then certainly it is a form of meditation. But if you play undivine music or write unbearable books or keep your mind in the gutter while you are painting, this is not any kind of meditation. While you are creating, if your consciousness is in the lower vital world, it will not be a form of meditation. But if you are singing something soulful or if you are in a very high consciousness while you are creating, if you are giving yourself in a divine way to the object or subject that you are involved with, then definitely you are doing a form of meditation. You have to know what you are creating and where your consciousness is while you are doing it.
I am giving a lot of importance to aspiring through music.
There is nothing wrong if you feel aspiration in your music. But you have to know how many hours you can think of your music. If you spend five hours, six hours, seven hours a day on music, then you should spend one hour or two hours, let us say, on spirituality. Music is also a form of spirituality; I do not deny it. But the height that you will achieve from meditation either you may not get or cannot get from your music. Music is an added help.
If you can play spiritual music, soulful music, then you will have no problem in your life. But if you play only mundane music, then you may not be satisfied. You may be pleasing the outer world, but you are not pleasing your Inner Pilot in His own way. If you are not an aspiring seeker, that is fine. But if you are a sincere seeker, then you will feel miserable.
When I play music, I feel a tingling around my third eye.
That indicates an awakening. But this does not mean that your third eye is about to open. No. When you play most soulfully, an inner vision-light will come to the fore. Vision is within you, yet it is dormant. But now it wants to function properly; it does not want to sleep anymore. So inner vision is starting to operate. The vision of the third eye is trying to come to the fore, and that is why you are getting that sensation. It is a very good experience.
What is the soundless sound, and can it serve as a bridge between the manifest and the unmanifest worlds?
As it stands now the outer world is not at all aware of the inner world. So first the outer world has to be fully aware of the inner world, and then it has to listen to the blessingful dictates of the inner world. Then the soundless sound—which is now heard only by very, very few Truth-seekers and God-lovers—can be of divine service to mankind. It is an inner discovery. This discovery has to be brought to the fore, and for that the outer world has to be consciously awakened and devotedly accept the beauty and divinity of the inner world.
The soundless sound is something real, absolutely real. But we hear it only in our highest realm of consciousness, or when we dive deep within and reach the inmost recesses of our heart. The soundless sound is infinitely, infinitely more powerful than any man-made sound. But up to now, it has been operating only in the inner world. So those who have a free access to the inner world can hear this sound. Not only do they derive tangible benefit from this sound, but it helps the seekers and God-lovers immensely in their self-giving life to God the Creator and God the creation.
O music of love,
From you I learn
The secret of closeness.
O music of will,
From you I learn
The secret of future creation.
O music of silence,
From you I learn
The secret of universal oneness.
O music of surrender,
From you I learn
The secret of cosmic perfection.
How many songs have I sung?
How many more have I still to sing
Here on earth?
Within and without
I have been searching for myself
Through my songs.
With deep pangs my heart cries;
My self-form is not visible yet.
In the vast life-ocean,
I am floating all alone.
You are nothing but beauty, eternal beauty,
Wherever I turn my eyes.
Do You always drink the nectar
Of Your Self-Form
Residing in my eyes?
The waves of tune
And sweet and melodious songs
That create heart-elevating resonance,
O Beloved, do You hear them
By using my ears?