Kabbalah, Genetics and the Music of the Spheres

On the patterns hiding in the heart of biology, sound, and mysticism

By Stephen Wachtel and Jason Caplan

Introduction

Our study begins in 1285, the year Rabbi Abraham Abulafia completed the writing of his primary book, Ohr Ha-Sekhel (Light of the Intellect). This book was about Kabbalah, a mystical interpretation of the Creation narrative and of the Torah in general.

A principal advocate of Jewish mysticism, Abulafia was born in Saragossa, Moorish Spain (c.1240-c.1292). He was a devotee of the Sefer Yetzirah (Book of Creation), and he was the founder of Prophetic Kabbalah, which deals with the attainment of prophetic abilities through meditation, the visualization and chanting of divine names, and the rearrangements (permutations) of Hebrew letters in Hebrew words. Among his primary sources were the writings of Rabbi Moshe ben Maimon (Maimonides) and the writings of Rabbi Eleazar ben Judah ben Kalonymus.

Maimonides (1135–1204) was born in Cordova, Spain. He is a preeminent scholar and teacher among the Jewish people, notable for his works, Mishnah Torah (Reiteration of Torah) and Moreh ha-Nevuchim (Guide for the Perplexed). Besides serving as a rabbi, Maimonides was a philosopher in the Aristotelian sense, an astronomer, and a well-known physician. In 1168, he became the personal physician of Saladin, the Sultan of Egypt. French scholar Samuel ibn Tibbon, author of Sefer ha Mikhtav (The Letter Book), once asked to come visit, but Maimonides was so busy, he told Tibbon to stay home. Maimonides could only see him on Shabbat, and then only for a short time because most of the congregation lined up to seek his counsel after services.

Rabbi Eleazar (1176-1238) was born in Mainz, Germany. He was the head of the Chasidei Ashkenaz, a group of Jewish mystics living in 12th and 13th-century Germany. Among his multitude of works, R’ Eleazar wrote Sefer Ha-shem (Book of the Name) in which he outlined a system of permutations of Hebrew letters to facilitate imaginative meditation and prophecy, and thereby, a connection to God.

The philosophical works of Maimonides were not, and are not, easy to understand, and Kabbalah was always transmitted in secrecy. Yet Abulafia merged both traditions and made them accessible to everyone. It was the first time anyone ever taught Kabbalah in public.

Permutations in Kabbalah

The Torah teaches that God created the universe with Hebrew words, for example רוא יהי (Yehi ohr) meaning “Let there be light.” Abulafia and others therefore 3 viewed Hebrew letters as the building blocks of creation. Abulafia knew that barring repetition, any four letters can be arranged in twenty-four different ways.

This is expressed by the factorial: n! = n x (n – 1) x (n – 2) x 1 = 24, or 4! = 4 x 3 x 2 x 1 = 24. Examples are shown below for the English letters A-B-C-D and the corresponding Hebrew letters, ד-ג-ב-א (aleph, beit, gimmel, dalet).

These permutations illustrate the framework of Abulafia’s method. But the method is not limited to any number or sequence of letters. It can be applied to individual words, to groups of letters, or to the entire alphabet, to derive creative awareness and a link to the Divine Intellect. Consider these three-letter words taken from the word “Shalom.”

Abulafia might have construed these words as indicating that a person who emanates complete peace by meditating on His Name is like a precious jewel. Permutation of letters, especially letters from the names of God, was a common Kabbalistic practice. The method becomes increasingly complex as letters are added. Consider the name of God (Elohim), which occurs in the first 4 sentences of the Creation narrative (Genesis 1:1) and throughout Hebrew scripture. Barring repetition of a letter, this word has five letters, which can be arranged in 120 ways (5! = 5 x 4 x 3 x 2 x 1 = 120).

By emphasizing permutation of Hebrew letters in conformity with R’ Eleazar’s studies, Abulafia was able to encode complex schemes within groups of elementary symbols. He believed that the methods of R' Eleazar and the rationalist approaches of Maimonides pointed to the secrets of creation. We shall see that his permutations foreshadow analogous arrangements described more than 700 years later in music, genetics, and theoretical physics.

Abulafia believed that the intellectual traditions of Judaism have applications for all peoples. Like Maimonides, he met with Christian and Muslim mystics to share his ideas and maintain channels of communication between Jews and practitioners of other religious faiths. For Abulafia, enlightenment and the attainment of spiritual perfection were common human goals, not limited to a particular religious or national demographic. He saw the intellect (sekhel) as a gift to all peoples, a bond between God and human, enabling all peoples to recognize universal truths.

He described a connection between letters and musical notes. Regarding music on a stringed instrument, he wrote: “... The strings touched with the right hand or the left hand vibrate, and the experience is sweet to the ears . . . The joy is renewed through the pleasure of the changing melodies, and it is impossible to renew it except through the process of combinations of sounds. The combination of letters proceeds similarly. One touches the first string, that is, analogically, the first letter, and the right hand passes...to second, third, fourth, or fifth strings, and from the fifth it proceeds to the others. In this process of permutations, new melodies emerge and vibrate to the ears, and then touch the heart. This is how the technique of letter combination operates…” 1-3

The Universality of Music: Voyagers and Aliens

Abulafia was on to something. Music still plays a significant role in human culture. And scientists ask whether music may also be important in non-human cultures. In 1977, they launched two “Voyager" spacecraft to photograph the outer planets before continuing their travels into deep space. Each carries an identical golden record containing maps, images, voice messages, mathematics, and a mixed bag of twenty-seven musical pieces intended as a greeting to any alien life form they might encounter. The musical tracks consist of pieces from countries around the world — pieces as diverse as the first movement of Bach’s Brandenburg Concerto No.2 played by the Munich Bach Orchestra, Johnny B. Goode by Chuck Berry, and Raga Jaat Kahan Ho sung by Kesarbai Kerkar of India.

The piece that opens the Sounds of Earth section of the Golden Records is called the Music of the Spheres. Produced by composer Laurie Spiegel, this “computer music” is based on her impressions of the movements and speeds of planets Mercury, Venus, Earth, Mars, and Jupiter, according to the calculations of 17th-century astronomer Johannes Kepler. We’ll describe an earlier take on the Music of the Spheres below.

The Voyager spacecraft are still flying. At present, they’re more than 15 billion miles from Earth and still transmitting, though some of their systems are no longer functional.

Permutations in Modern Music

One of us (JC) designed the Universal Language Room, the central program of The Bridge Institute, dedicated to connecting people of different backgrounds through the medium of improvisational music. During his studies of musical improvisation, Jason discovered a system of permutations in modern music that duplicates the system of Abulafia. The lines were arranged to help musicians in improvisation.4 Any connection between these musical lines and Kabbalah is accidental. But these permutations are arranged in groups of four notes, and that led us to look more deeply into the connections between Kabbalistic permutations, music, and ultimately, the four-letter permutations of DNA.

The Four Letters of DNA

Both authors are musicians, and we often appear together on stage. One of us (SW) is a geneticist, and during our discussions of the four-letter permutations of Abulafia and the four-note musical permutations pictured above, the thought 6 immediately occurred that DNA is composed of four letters, and DNA letters can be translated into musical notes!

The initials DNA stand for deoxyribonucleic acid, which is composed of four chemical building blocks or bases — adenine, thymine, guanine, and cytosine. Scientists who study DNA like to call the bases by their initials: A - T - G - C. That’s why DNA can be portrayed as a long string of letters laid out end-to-end in seemingly random order, as in A-A-A-T-G-C-G-C-G-C-T-T-A-A and so on. But the order isn’t random at all, because the letters spell out the genetic code, which governs the destiny of every living thing, and indeed, every living cell. The DNA code contains all the information needed to make and maintain a living organism. The code determines whether the organism will be a cucumber or a cat, a whale or a snail, an oak tree or a human; if human, whether it will have brown skin or pink, blue eyes or green, whether it will be tall or small, healthy or sick, quickwitted or slow, male or female. All this with just four letters.

How is that possible? How can all the information needed for the life of an animal or plant be contained in an alphabet containing only four letters? The answer is, the DNA code governs the production of proteins — large chemical compounds with specific functions.

Just as DNA chains consist of four smaller units called bases, protein chains consist of twenty smaller units called amino acids. In every cell, the DNA code is translated into amino acid sequences. Each amino acid sequence determines the shape and function of a protein chain — where it fits, how it works, what it does.

There are various kinds of proteins. Examples are: antibodies, which protect us from bacteria and viruses; enzymes, which control chemical reactions in cells; hormones, which govern the activity of particular tissues; and building blocks, which form muscle and skin. For every protein chain, there is a corresponding sequence of DNA letters, called a gene. Gene length varies from about 200 bases to more than two million bases. The average human gene is about 3,000 bases long. The total number of human protein-coding genes is around 20,000-25,000.

Each DNA letter is important. Loss, gain, or substitution of a single letter or group of letters, called a mutation, can lead to a protein without function. This can cause severe disability (e.g., muscular dystrophy), cancer (e.g., childhood retinoblastoma), or even death (e.g., Tay Sachs disease).

Permutations of the Genetic Code

All life on Earth is governed by a genetic code that consists of three-letter DNA words called codons. Examples of codons are ATG, ATC, GAC, TCA, etc. With the 7 exceptions noted below, each codon specifies an amino acid. Given the four letters of the DNA alphabet and groups of three-letter words, there are sixty-four possible codons, including codons with repeated letters like ATA, CCA, or GGG. Four letters at each of three points in the codon is expressed mathematically as 4 x 4 x 4 = 64.

That means there are 64 different codons for twenty amino acids, or in other words, 64 three-letter arrangements of the four DNA letters. It also means more than one codon can specify an amino acid (actually, sixty-one of the codons specify amino acids; the other three are stop signals that mark the end of growing amino acid chains).

The letter permutations of genetics, like the letter permutations of Kabbalah and the tonal permutations of music, thereby involve the ordering of uncomplicated symbols that encode more complicated information.

Replication

In the early 1950’s geneticists discovered that DNA occurs in the form of a double helix — two chains of bases wrapped around each other in a spiral and connected to each other by weak chemical bonds.5

Image: Pixabay Images

It’s remarkable that A pairs with T, and G pairs with C within the double helix, because that suggests a way DNA can reproduce itself. In the language of biology, it can replicate. The helix unwinds, and the old chains serve as templates for the new ones.

In the diagram below, Section I shows paired sequences of DNA letters in a double helix. In Section II, the paired sequences are separated. In Section III, new bases are added, forming two copies of the original paired sequences.

To reiterate, A pairs with T and G pairs with C, and by that method, the genetic code is conserved in the two new double helices in Section III above. The newly made spirals (Section III) will have the same sequence of letters as the original double helix (Section I), ACC ATC AAA CCA CTT TTA...

That’s why we look like our parents. We inherited their genetic codes!

DNA Music

Here’s the connection to which we alluded above: Genetic sequences can be transcribed directly into musical scores by assigning one note to each DNA base. These sequences are melodic if somewhat repetitive (the presentation can be improved with the addition of rhythmic devices and echo chambers). But this music has a scale consisting of just four notes.

The connection between DNA and music goes well beyond that simple scheme. Susumu Ohno, a friend and colleague of one of us (SW), was a pioneering scientist whose work in the late 1980s led to a direct connection between genetic codes and musical notes. Among his original ideas was the notion that just as DNA can replicate, so too can individual genes within DNA chains and sequences of letters within genes.6 He called this repetitious recurrence.

Together with his wife, Ohno shocked the genetics community with a paper entitled: “The all-pervasive principle of repetitious recurrence governs not only coding sequence construction but also human endeavor in musical composition.” That was in 1986 — in a genetics journal!7 The Ohnos were saying that sequences of DNA letters “could be transformed into musical scores” and vice versa. This idea was based on the fact that certain sequences of letters within genes are repetitions of primordial sequences of letters found in ancestral genes. “For example,” wrote the Ohnos, “the adaptive immune system of (all) vertebrates has apparently evolved by plagiarizing one ancestral gene.” 7

We said above that a gene is a sequence of DNA letters that encodes an amino acid chain in a protein. In their paper, the Ohno’s found musical correlates in the DNA sequences of a human gene that encodes a protein called PGK (for phosphoglycerate kinase). PGK is an enzyme that helps produce energy. The Ohnos noted that enzymes like this have existed from a time shortly after the establishment of life on Earth. That’s why the amino acid sequence of the human PGK enzyme resembles the amino acid sequence of the related enzyme in baker’s yeast. And that’s why the two enzymes are almost identical in their three-dimensional forms, despite the vast genetic distance between humans and yeast.

Repetitious recurrence

So how do we make music from DNA sequences? Because there are eight notes in a musical scale and four bases in DNA, the Ohnos developed this “inviolate” format for converting genetic sequences to musical sequences.7

They noted that a “primordial building block” in the human gene that encodes PGK is the base sequence, A A G G C T G C T G. That sequence and a related sixletter sequence, A A G C T G, are found several times in the gene (the PGK base sequence was first described by geneticist Judith Singer-Sam and colleagues).

The development of the above scale and the strict logic behind it are beyond the scope of this article. But by using that scale, the Ohnos were able to assign alternative melodies to the A A G G C T G C T G sequence and a derivative, A A G C T G. They tested the different melodies and selected the most suitable ones. Then, they assigned what seemed to be an appropriate key and a time signature.

By using that method, they created a musical score based on the coding sequence for the PKG gene. Here is Figure 3 from their paper, showing the correlation of musical notes and DNA bases at the beginning of the human PKG coding sequence. The primordial and secondary DNA sequences are underlined by thick black bars. The three-letter groups above the genetic sequence are abbreviations of the corresponding amino acids.

The Ohnos went on to say that “repetitious recurrence is still the hallmark of musical composition.” They found another primordial building block sequence, C A A C C T C C C, and a secondary sequence, T A C G G T G, both from the mouse RNA polymerase gene, several times each, in Chopin’s Nocturne, Opus 55! The Ohnos concluded, “The resemblance between (DNA) coding base sequences and musical composition is indeed more than skin deep.” 7

Strings

Pythagoras of Samos (c.580 - c.495 BCE) is the Greek philosopher and mathematician best known for the theorem that bears his name. 1 - 2 - 3 - 4

Among his other ideas, Pythagoras taught that 1,2,3, and 4 are the most important numbers, because they add up to 10, the “perfect number” and the basis of all arithmetic and mathematics.

Pythagoras was among the first to make a connection between music and mathematics by noting that the frequency of vibrations on a stringed musical instrument depends on the length of the string. The longer the string, the fewer the vibrations when the string is plucked, and the deeper the resulting tone. This is obvious when comparing the sounds produced by a string bass, cello, and violin. Pythagoras observed that cutting the length of a musical string in half raises the tone by exactly one octave. He showed that various intervals (fourths, fifths, etc.) could be created by changing the lengths of strings in accordance with strict mathematical rules. Based on his studies, he taught that the universe is ordered by arithmetic and music — mathematical ratios and harmonies. 9

Pythagoras believed that the Earth is a sphere at the center of the universe. He also believed that the various celestial bodies orbiting the Earth produce musical tones according to their speed of movement and their distance from the Earth, and that together, the tones produce harmonics, which he called the “Music of the Spheres.” Surely the Kosmos of Pythagoras differs considerably from the cosmos we know today, yet the potential importance of music on a cosmic scale should not be underestimated.

Today, music is one way physicists reconcile Einstein’s General Theory of Relativity (concerned with gravity and massive structures like galaxies and black holes) with quantum physics (concerned with subatomic particles like electrons and protons). At face value, relativity and quantum physics are incompatible because relativistic gravity doesn’t fit into the mathematics of the quantum realm, but in the 1980s, physicists developed string theory, which unifies both.10,11

We know that matter is composed of atoms. Atoms consist of a nucleus containing neutrons and protons, with electrons orbiting around the nucleus like planets around a star. Neutrons and protons themselves consist of smaller particles called quarks, and electrons belong to a class of particles that includes muons and neutrinos. Physicists have described hundreds of different subatomic particles, but the great majority of these are unstable and very short-lived.

According to string theory, as defined by one of its proponents, Michio Kaku, Professor of Theoretical Physics at the City College of New York, all subatomic particles are infinitesimal one-dimensional strings arranged like tiny loops, vibrating in multidimensional space-time. “The subatomic particles that we see in nature... are nothing but musical notes on a tiny vibrating string.”10-12 In other words, the different particles are really strings vibrating in different ways.

“What is physics? Physics is nothing but the laws of harmony that you can write on vibrating strings. What is chemistry? Chemistry is nothing but the melodies that you can play on vibrating strings. What is the universe? The universe is a symphony of vibrating strings.” 10,12

Mathematics

Each of the fields we have reviewed rests on a foundation of mathematics. Consider the following:

Kabbalah: Hebrew letters are more than phonetic because each Hebrew letter is also a number. Aleph is the number 1, beit is 2, gimmel is 3 an so on. It follows that each word is also a number. The letters of the creation account thus provide a numerical code of creation, and this adds additional depth to the interpretation of Torah and Hebrew scripture in general.

Music: Mathematics and music are closely interlaced, with tonality, scales, chords, and rhythms based on numerical relationships. We said that Pythagoras showed how octaves and other intervals could be obtained by changing the length and thereby the frequency of a vibrating string according to strict mathematical rules. The same is true for wind instruments, in which the pitch of a note is determined by the length of a vibrating air column.

Genetics: Like any physical science, genetics relies on mathematics for statistical analysis of experimental data. Also, patterns of inheritance in general follow strict mathematical rules. Recently, physicists, mathematicians, and others in 13 the United States and England used number theory, the study of the attributes of whole numbers, to determine the likelihood that a particular point mutation, i.e., change of a single DNA letter, will affect a change in a physical trait of the affected organism.13

String theory: As a science within the field of theoretical physics, string theory is closely bound up with mathematics, relying on mathematical equations for expression and analysis of its concepts and proposals. The relation between physics and mathematics is long-standing, originating in part with Newton’s use of numbers and numerical equations to express his ideas. In fact, Newton invented calculus (at the age of twenty-four!) to simplify his study of gravity and motion.14

The close relationship between string theory and mathematics is based in part on the development of novel conjectures and structures that call for novel mathematics, such as differential topology, the study of forms that do not change even when deformed — items like a flat square, for instance, which can be shaped into a circle but not a hollow sphere.

Synopsis

In demonstrating that string length governs tonality in music, Pythagoras showed how mathematics and music are related, and it is not hard to see parallels with string theory, according to which subatomic particles are one-dimensional strings in hyperspace vibrating like musical strings on a guitar. The mode of vibration of these one-dimensional strings determines what kind of particles they are — photons, electrons, quarks, etc. — just as the mode of vibration of guitar strings, controlled by finger pressures, determines what kind of notes they produce.

An easy step forward to genetics: The DNA code, which controls the fate of all life on Earth, can be used to generate music, and indeed, primordial DNA sequences can be correlated with note sequences in musical compositions. DNA as music. Music as DNA. We have seen that genetic diversity is a direct result of permutations of the DNA code. We showed sixty-four possible arrangements of the three-letter words (codons) with a four-letter alphabet. That simple scheme is what makes us different from one another, from a chimpanzee, a dandelion, or a virus. The same scheme is found in the generation of three-letter groups (words) from the four-letter word “shalom,” םולש, described in the section above on Permutations in Kabbalah. What would Abulafia think of DNA permutations?

In conclusion, Abulafia finds links between musical tones and his alphabetical permutations, and we can see an interface between any two of the disciplines we have discussed. Letter sequences in Kabbalah can be likened to note sequences 14 in music, and both can be likened to base sequences in the DNA code. We have already noted shared aspects between vibrational modes in stringed instruments and string theory.

Regarding string theory, we note that this approach to reconciling Relativity and Quantum Physics suffers from a paucity of experimental evidence to confirm or falsify it (but see reference 15). In addition, string theory calls for supernumerary dimensions beyond the four space-time dimensions of Einstein’s relativity. We discuss it here for its potential cognates in music and genetics.

We have seen that string theory relates to Kabbalah and genetics through the common attribute of music. Thus, music may be viewed as a prime characteristic of Kabbalah, genetics, and string theory, whereas mathematics is a more basic characteristic underlying all four disciplines.

Mathematics provides numerical insights for interpreting scripture in Kabbalah. It is also central to the ordering of chords, intervals, and rhythms in music. Mathematical guidelines determine the nature of inheritance in genetics, and mathematical equations govern the behavior of vibrating strings in string theory. As to the significance of the shared attributes we have described, further research will determine whether these attributes are more widespread among information-bearing systems or only a haphazard observation, allowing the creation of papers like this one.

Stephen Shoel Wachtel, PhD is a Board Member of the Bridge Institute, an artist (www.shoelart.com) and a professional musician. He retired from the University of Tennessee Health Science Center as Professor of Obstetrics & Gynecology and Chief of Research for Reproductive Genetics. Stephen has 200 publications including four books and several papers each in Nature, Science and The New England Journal of Medicine.

Jason Caplan is the Founder and President of The Bridge Institute. In 2004, Jason began to create and implement The Universal Language Room (ULR). He has devoted his life to interpersonal communication and bridge-building through improvisational music. The Bridge Institute now supports musicians teaching the ULR concept in Uganda, Indonesia, Rajasthan, and Israel. Jason also leads his music group, Naqshon's Leap, a multi-faith music group in Memphis, TN. www.ulr1.com

References

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4. Bergonzi, Jerry. 1992. Melodic Structures Volume 1, Alfred Music.

5. Watson James D, Crick FHC. 1953. Molecular structure of nucleic acids: a structure for deoxyribose nucleic acid, Nature 171:737–738. 15

6. Ohno, Susumu. 1970. Evolution By Gene Duplication. Springer-Verlag.

7. Ohno, Susumu, Ohno, M. 1986. The all-pervasive principle of repetitious recurrence governs not only coding sequence construction but also human endeavor in musical composition. Immunogenetics 24:71-78.

8. Singer-Sam Judith, Simmer RL, Keith DH, Shively L, Teplitz M, Itakura K, Gartler SM, Riggs AD: 1983. Isolation of a cDNA clone for human X-linked 3-phosphoglycerate kinase by use of a mixture of synthetic oligodeoxyribonucleotides. Proceedings of the National Academy of Sciences (USA) 80:802-806.

9. Siegfried, Tom. 2023. Science News. https://www.sciencenews.org/article/ pythagoras-math-reality-music-spheres

10. Kaku, Michio. 2021. The God Equation: The Quest For A Theory Of Everything. Doubleday.

11. Greene, Brian. 2003. The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. Vintage Books.

12. Kaku, Michio. 2011. YouTube. The Universe Is a Symphony of Vibrating Strings | Big Think:

13. V. Mohanty, S.F. Greenbury, T. Sarkany , S. Narayanan , K. Dingle , S.E. Ahnert and A.A. Louis. 2023. Maximum mutational robustness in genotypephenotype maps follows a self-similar blancmange-like curve. J. Roy. Soc. Interface. https://royalsocietypublishing.org/doi/10.1098/rsif.2023.0169

14. Math and Science. 2017. How Isaac Newton Changed the World with the Invention of Calculus. https://www.mathtutordvd.com/public/How-Isaac-NewtonChanged-the-World-with-the-Invention-of-Calculus.cfm

15. Feldman, Andrey. 2025. Live Science. Physicists claim they've found the 'first observational evidence supporting string theory.’ https://www.yahoo.com/news/ physicists-claim-theyve-found-first-160000644.html?guccounter=1