The Sacred Geometry & Kabbalah of Music in the Gothic Cathedral of Lichfield, an Introduction to Unison
Now I’ve heard there was a secret chord. That David played, and it pleased the Lord … — Leonard Cohen, Hallelujah
Introduction
In this article, we explore the “geometric music” found in the architectural design of the Gothic cathedral, using Lichfield Cathedral as our ideal example. We will explain the meaning of the term “musical interval”, describe the various intervals and then focus on the interval of unison to show how it can be described in geometry and what this means from a spiritual perspective, in particular with the Kabbalah of Jewish mysticism.
How Geometry Corresponds With Music
“Music is the hidden arithmetical exercise of a mind unconscious that it is calculating.” — Gottfried Wilhelm Leibniz
Geometric proportions can be used to represent musical intervals through the use of ratios. In music theory, an interval is a difference in pitch between two notes. The frequency of a musical note determines its pitch, and the relationship between the frequencies of two notes can be expressed as a ratio.
Here’s a brief explanation of how some common musical intervals correspond to geometric proportions:
Unison (1:1)
In a (perfect) unison interval, the two notes have the same pitch, meaning their frequencies are identical. This corresponds to the simplest geometric proportion, a 1:1 ratio.
Octave (2:1)
An octave is an interval between two pitches where the higher note has a frequency that is twice the lower note. This relationship corresponds to a 2:1 ratio. In geometry, you can think of it as a line segment with a length twice that of another.
Perfect Fifth (3:2)
A perfect fifth is the interval between two pitches where the higher note has a frequency that is 1.5 times (3/2) the lower note. This corresponds to a 3:2 ratio. Geometrically, this can be represented by two line segments where one is 1.5 times longer than the other.
Perfect Fourth (4:3)
A perfect fourth is the interval between two pitches where the higher note has a frequency that is 4/3 times the lower note. This corresponds to a 4:3 ratio. In geometry, you can think of it as two line segments where one is 4/3 times longer than the other.
Major Third (5:4)
A major third is the interval between two pitches where the higher note has a frequency that is 5/4 times the lower note. This corresponds to a 5:4 ratio. Geometrically, this can be represented by two line segments where one is 5/4 times longer than the other.
Minor Third (6:5)
A minor third is the interval between two pitches where the higher note has a frequency that is 6/5 times the lower note. This corresponds to a 6:5 ratio. In geometry, you can think of it as two line segments where one is 6/5 times longer than the other.
The Geometry & Spirituality of the Perfect Unison in Gothic Architecture [Image for each in this section]
“There is geometry in the humming of the strings, there is music in the spacing of the spheres.” — Pythagoras.
In the harmonious realm of the spirit, the musical interval of unison resonates as a divine unity, a merging of individual frequencies into a single, pure tone that echoes the oneness of all creation. This celestial alignment of vibrations transcends the boundaries of the physical world, revealing the interconnectedness of our souls.
The sacred geometries that correspond to unison carry profound spiritual significance, embodying the eternal truth of unity and interconnectedness. They serve as visual representations of the cosmic order, reflecting the divine design that permeates the fabric of our existence.
Let’s also identify where these geometries can be found within the architecture of the gothic cathedral.
Congruent shapes
Two or more shapes are congruent if they have the same size and shape. This can be viewed as a geometric representation of unison, as the shapes are “in harmony” with each other, much like notes in unison.
Congruent shapes symbolize the principle of “As above, so below,” illustrating the idea that the microcosm reflects the macrocosm and vice versa. These shapes embody the essence of a desired balance and harmony between heaven and earth, mirroring the perfect alignment of musical notes in unison.
Rose windows — These large, circular stained-glass windows often feature repeating patterns of congruent shapes, such as petals, stars, or other geometric figures, that radiate out from the centre, symbolizing the divine light.
Rib vaults — Gothic cathedrals are known for their rib vaults, which are formed by the intersection of two or more sets of arched ribs. These ribs often create congruent shapes, such as squares or diamonds, in the ceiling design.
Parallel lines
Parallel lines are lines that never intersect, and they maintain a constant distance between them. They can be considered a geometric representation of unison since they share the same direction or “path.”
Parallel lines represent the spiritual paths that our souls journey upon, each following its own unique course yet existing in harmony with the others. They remind us that although we may be on separate paths, we are ultimately moving in the same direction, towards the same divine source.
Columns — In Gothic cathedrals, the tall, slender columns that support the structure create parallel lines reaching towards the heavens, emphasizing the verticality and spiritual aspiration of the building. They also complement their opposite columns in supporting higher structures, emphasising that any spiritual pursuit of heaven requires a complimentary grounding in the real world.
Buttresses — Flying buttresses are a key feature of Gothic architecture, transferring the weight of the building to external supports. These structures often display parallel lines as they extend outward, illustrating the harmony and balance in the cathedral’s design and furthermore exemplifying the need for any spiritual journey to be as much grounded in earth as it is in its desire to reach for the heavens.
Tessellations
Tessellations are patterns formed by repeating a single shape without any gaps or overlaps. In this case, the same shape (or pitch) is repeated continuously, similar to the concept of unison in music.
Tessellations convey the concept of infinite expansion and repetition, akin to the eternal cycle of birth, death, and rebirth. In this sacred pattern, the unison of a single shape echoes the eternal song of the universe, expressing the interconnectedness of all life.
Floor tiles — Many Gothic cathedrals have intricate floor tile patterns that feature tessellations. These geometric patterns form a continuous and harmonious design that covers the sacred ground within the cathedral.
Friezes — Some Gothic cathedrals have decorative friezes that incorporate repeating patterns of tessellations, often with religious or symbolic motifs, adding to the ornamental and spiritual richness of the building.
Reflection symmetry
A figure has reflection symmetry if it can be folded along a line (the line of symmetry) so that the two halves match exactly. This correspondence between the two halves can be thought of as a geometric unison, as they share the same properties.
Reflection symmetry speaks to the spiritual truth of duality, the existence of light and dark, and the balance that lies within. As the halves of a symmetrical figure merge in perfect unison, they remind us of the importance of embracing both aspects of our nature, spiritual and human, to achieve spiritual harmony.
Portal tympana — Above the main entrance of a Gothic cathedral, the tympanum (a semi-circular or triangular space) often features a symmetrical scene, such as the Last Judgment, reflecting the duality of salvation and damnation.
Tracery — The delicate stonework in Gothic windows, known as tracery, often exhibits reflection symmetry. This can be seen in the symmetrical arrangement of shapes, such as circles, trefoils, and quatrefoils, that adorn the windows.
Translations
A translation is a geometric transformation that moves every point of a shape by the same distance and direction. Translated shapes can represent unison, as they maintain their original size and shape while being shifted to a different position.
Translations symbolize the spiritual journey each soul undertakes, moving through various stages of existence while maintaining its unique essence. These transformations echo the unison of music as our individual vibrations merge into the divine resonance that connects us all.
Gargoyles and grotesques — These ornamental sculptures are often found adorning the exteriors of Gothic cathedrals. They are sometimes arranged in a series of translations, with each figure repeating at regular intervals along the building’s edges.
Fretwork — Fretwork is a decorative technique that involves carving intricate, interlaced patterns into wood or stone. In Gothic cathedrals, fretwork can be found adorning screens, choir stalls, and other architectural elements, often featuring translated patterns that repeat in an orderly and harmonious manner.
An Introduction to the Relationship of These Geometries and Music with Kabbalah and Sefer Yetzirah
"The first foundation: Aleph, Mem, Shin; an eternal source, without limit or end, sealed with His ring." — Sefer Yetzirah
The Sefer Yetzirah (Book of Formation) is a foundational text of the Kabbalah and the oldest book known to Judaism. It delves into the mysteries of creation, exploring the relationship between God, the universe, and the Hebrew alphabet. You will recall from earlier articles that we hypothesised that the Paleo-Hebrew Aleph may be found as the foundational letter of Lichfield Cathedral.
In simple terms, Aleph (א) is the first letter of the Hebrew alphabet, symbolizing the primordial beginning and unity. In Kabbalistic thought, Aleph represents the unity of God and the source of all creation. It is associated with the sephirah of Keter (Crown), the highest emanation in the Tree of Life. Keter represents the divine will and the origin of all the other sephirot, which are channels through which God’s energy flows into the world. The letter Aleph is also often used to connect the sephirot of Chesed (Mercy) and Gevurah (Severity). The connections between the sephirot are called “paths” or “channels.” These paths represent the flow of divine energy or the interactions between the different sephirot. In total, there are 22 paths that link the 10 sephirot on the Tree of Life, each associated with one of the 22 letters of the Hebrew alphabet. These paths symbolize the dynamic relationships and processes through which the sephirot influence and interact with one another, allowing for the flow of divine energy throughout the entire structure. We earlier reviewed the symbolic representation of the soul in the floor plan of Lichfield, which using the simple geometry of the golden spiral, also drew out the Paleo-Hebrew letter Beth.
While it does not explicitly discuss geometric and musical ratios, there are principles in the text that can be related to these concepts.
Sephirot
“The Lord of all is one, and His name is one, and all things are dependent on His oneness.” — Sefer Yetzirah
These Sephirot can be seen as corresponding to a geometric structure, often represented as the Tree of Life, where each Sephirah is connected to others through pathways. This interconnectedness can be thought of as a network of relationships, similar to the way that musical intervals are connected through ratios.
22 Hebrew Letters
“The 22 letters are the foundation of all that exists, and by means of them the universe was created and all things in it.” — Sefer Yetzirah
The Sefer Yetzirah posits that God used the 22 Hebrew letters as the building blocks of creation. These letters can be associated with different aspects of the universe, including spatial dimensions, time, and the soul. In a sense, the letters represent different frequencies or vibrations, similar to how musical notes have unique frequencies. When combined in various ways, these letters form the basis of creation, just as different musical notes and intervals create harmonies and melodies.
Combinations of Letters
“Twenty-two foundation letters: He carved them, he hewed them, he combined them, he weighed them, he interchanged them, with them he formed the universe and everything in it.” — Sefer Yetzirah
The Sefer Yetzirah describes how God combined the Hebrew letters in various ways to create the universe. This process can be compared to the mathematical combinations of ratios in music and geometry. Different combinations of letters result in different aspects of creation, just as different ratios create distinct musical intervals and geometric proportions.
The Three Elements or “Mothers” of Aleph, Shin and Mem
“There is nothing above Him and nothing below Him, for He is the highest of all and the lowest of all.” — Sefer Yetzirah
In the Sefer Yetzirah, the three elements of fire, water, and air represent different aspects of creation, associated with the three “mother” letters of the Hebrew alphabet. These elements can be thought of as the fundamental building blocks of existence, comparable to the simple ratios that underlie musical intervals and geometric proportions.
While the Sefer Yetzirah does not explicitly discuss the correspondence between music and geometry, the principles within the text can be related to the idea of fundamental structures and relationships underlying creation. Both music and geometry can be seen as expressions of the harmony and order that pervade the universe, and their shared mathematical basis can be understood as a reflection of the divine structure of creation.
Keter, Chockmah, Binah & The Tree of Life
Recall that in Kabbalah, the Tree of Life represents a map of the divine structure and the process by which the universe came into being. The sephirot are the ten emanations through which God interacts with the world. While there are many symbolic interpretations and associations made between the sephirot and various aspects of human knowledge, it is hard to find any direct references that compare the sephirot of Keter, Chokhmah, and Binah to the musical interval of unison and the remaining sephirot to the musical octave.
In his 1972 book Tree of Life, Z’ev ben Shimon Halevi wrote about the Octave and the Tree of Life. The Octave, or the Law of Seven, is shown descending down the tree from Keter to Malkhut following the traditional lightning flash path, which zig-zags down the tree. This brings in some new ways of understanding both the octave and the tree.
Kabbalistic teachings often use symbolism and metaphorical language to explore the connections between the divine and the mundane, and the sephirot are associated with various qualities, numbers, and symbols. It is possible to draw an analogy between the concept of unison in music and the sephirot, particularly the supernal triad of Keter, Chokhmah, and Binah, which represent the highest levels of divine emanation and unity before the multiplicity found in the lower sephirot.
The sephirot can be seen as a progression, with Keter representing the ultimate unity and source of all creation, Chokhmah representing the divine wisdom that emanates from Keter, and Binah representing the understanding and receptivity necessary to receive that wisdom. In this sense, the supernal triad could be metaphorically compared to the unison in music, where multiple sounds or voices come together as one.
As for the remaining sephirot, they could be compared to the musical octave in that they represent the various stages of divine emanation and manifestation, similar to the way an octave contains different pitches yet still shares a fundamental harmonic relationship.
Practical Applications of the Music & Geometry of Unison in the Real World
“Music in the soul can be heard by the universe.” — Lao Tzu
Relationships & Communication
Think about the relationships in your life. What are the most important relationships, such as family, friends and key business colleagues? How much in unison are you with them? What is it about those you are more in unison with that defines the best qualities of those relationships? How did you achieve this, and what are you doing to maintain this? Is there anything about the way you communicate and relate to these people that aids your relationship? How does this make you feel? In contrast, which relationships are most difficult, and which people are most far from unison with? What is it that has led to this position and caused it to continue? Is there anything about the way you communicate and relate to these people that have led to this relationship? How does this make you feel? Would it be true to say that your spirituality is defined by the quality of your relationships?
Music
Considering the concept of unison in music intervals, first think of composed tunes that seem to make use of repeated unison intervals in their melody (a classic simple example is adjacent notes in “Twinkle twinkle little star”) and what this says about the composer's intentions to convey spiritual meaning. Do these songs evoke anything in you, such as memories or feelings? While unison is not a particularly common interval in melodies, it is often used in harmony, rhythm, and accompaniment to create a sense of unity and cohesion.
Here is a list of well-known popular songs that use the unison interval in their melodies or harmony in a prominent way:
“We Will Rock You” by Queen — The iconic stomping and clapping rhythm is a clear example of unison in music.
“Eleanor Rigby” by The Beatles — The string section in this song is played in unison, creating a distinct and memorable sound.
“Seven Nation Army” by The White Stripes — The main guitar riff is played in unison with the bass, making it a powerful and recognizable melody.
“Come Together” by The Beatles — The guitar, bass, and drums all play in unison during the intro.
“O Fortuna” from Carmina Burana by Carl Orff — This famous choral piece features sections where the choir sings in unison.
“Poker Face” by Lady Gaga — The synth melody that runs throughout the song is played in unison, giving it a catchy and memorable hook.
“Baba O’Riley” by The Who — The opening synthesizer line is played in unison with the piano, creating a driving and memorable sound.
Here is a list of spiritual songs that use the musical principle of unison that you may be familiar with:
“Hallelujah” by Leonard Cohen — Although not strictly a religious song, this piece has become popular in spiritual contexts, and the chorus is often sung in unison.
“Amazing Grace” — This popular hymn is often sung in unison, creating a powerful and communal atmosphere.
“Ave Maria” — Both the Schubert and Bach-Gounod versions of this iconic piece feature sections where the melody is sung or played in unison.
“Kumbaya” — A traditional spiritual song, “Kumbaya” is often performed with everyone singing the melody in unison.
“Om Namah Shivaya” — This Hindu mantra is typically chanted in unison during meditation or prayer.
“Go Down, Moses” — This African American spiritual song is often sung in unison, with the melody being repeated by a leader and the congregation.
“Hare Krishna” (Maha Mantra) — This mantra, originating from the Vaishnavism tradition, is often chanted or sung in unison during group meditations or spiritual gatherings.
“O Come, All Ye Faithful” — This classic Christmas hymn features unison singing, particularly in the refrain, “O come let us adore Him.”
“Shalom Aleichem” — This traditional Jewish song is often sung in unison during Shabbat services or at home before the Friday night meal.
“Wade in the Water” — Another African American spiritual, this song is often sung in unison, with a strong emphasis on the melody.
Sacred Buildings
Then look for these geometries, as described above, in a Gothic cathedral near to where you live, or indeed any sacred building that belongs to any faith, as you will certainly find them there. Like a detective, see how many you can find, including ones we have not described here. Think about the spiritual meanings underlying these designs and the feelings they invoke in you.
Dr Nick Stafford
Eye of Heaven — Lichfield Cathedral, a Theory of Everything
“Sometimes too hot the eye of heaven shines.” — Sonnet 18, William Shakespeare
Footnotes
All photographs of Lichfield Cathedral by the author
Musical intervals geometric rations image with thanks to: https://www.sacred-geometry.es/?q=en/content/proportion-musical-scales
AI using Chat GPT was used to research aspects of this article
