The System of 1->3->7->12 (Pt.1): Kabbalah and Western Tonal Theory



Part 0: 10 Seferiot of Nothingness



Kabbalah been very foundational to my creation of music. I discovered it through a Tool album which someone pointed out had many similarities with the Tree of Life in Kabbalah. They never specifically said they thought about that, but posted the fans analysis in a newsletter saying it was very interesting. At the time I discovered this, I had been DJing for a little while, was hesitant to make my own music, as I feared I would be to critical of myself. But by looking at this Number based system of explaining greater philosophical ideas, and the possibility that awareness of it could be brought through music gave me the confidence and drive to start creating music myself.  But in the same way Tool never confirmed they even used Kabbalah to inspire the album, they just found it interesting that someone related it, I feel the same way about approaching the topic, in general but specifically in music.

I wanna make it clear I’m not saying there’s anything there, I have studied this quite a lot and still and not very convinced it has much basis in reality besides being a metaphor for something we couldn’t even begin to fully describe the nature of. Yet sometimes these mathematical metaphors can engulf a person in both emotion awareness, and mental clarity and bring and add meaning to life. Just as music is a mathematical system that can express deeper meaning, I think we can look to mathematical systems as a method of perceiving and interpreting philosophical and spiritual ideas, and Kabbalah’s Tree of Life is my first and so far favorite diagram and method of expressing this. And so in the nature of it being the thing that made me realize the beauty and importance of creating music, I feel almost inclined to explore the comparison between it and the theoretical systems I’ve learned in studying music.

Fundamentally I see one big comparison between kabbalah and Western music theory, that being a exponentially expanding system with its fundamental points being 1,3,7,12

In this being the first time I’ve ever tried to compare kabbalah and music outside of my own thoughts, I was and still am hesitant at even attempting the task, as it would take multiple lifetimes to fully comprehend either kabbalah or Western tonal theory; let alone both to the extent you could compare them. I have just the slightest glimpse of understanding of either of the two, yet the more I study one, the more I understand and see connections with the other. I feel a sort of intuitive implication that they share some patterns, yet I’m increasingly aware of how large both the topics are and how much I know nothing in comparison to what is to be known. But just as the 10 Sefirots were created from nothingness, maybe I might be able to create something from the nothingness of where my knowledge is currently. No matter if it has any basis in reality or not, it’ll be something created, something to build off of and take from, and to me that better than not having it at all. Because multiplying by zero gets you nowhere, but before 1 what do you count?




Pt. 1: Fundamental



The fundamental is the essence of the sound. It is a sort of point of oscillation of the sound, like a Key that a song might be in. all the melodies, chords or anything in tonal music revolve around this fundamental. Technically, it can be said all harmonic progressions are just embellishments of I. Another quality of the fundamental is it is fundamentally indescribable, like if I hit a drum once and ask you the tempo, you wouldn’t be able to describe it to me. In kabbalah it is compared to breath, and i would also add a heartbeat. These are the personal source of sound, the heart being the rhythm and the voice being tone. They are always with us, and project the essence of music (tone/timbre & rhythm) outward in basically all that we do.




Pt 2: Triadic Split


A triangle is one point opposite two other points who sit side by side. In Kabbalah the triad is Aleph, Mem, and Shin. Mem hums, Shin hisses, and Aleph is the breath that decides between them. It is said Aleph is breath from breath (direct connection to fundamental) Mem is water from breath of Aleph, but in a more tangible form than air, yet you still can’t touch water, only feel it as it caress your hand. Shin is fire from water, and as well you cannot touch Shin, just as if you get to close to fire it will burn you, but you still feel it with intense sting as you grow closer. And when you reach shin in the purest form, you burn and become the air again.

Mathematically, three points can be looked at as one point opposite 2, whose three lines are dependent on one another in a exponential power of 2 (a2+b2=c2)



Pt. 3: Musical Applications



Triadic split is the start of harmony. The first harmonic partial that’s not the same as the fundamental is the third, which is the fifth or V chord(aka the chord built upon the 5th note of the scale), which is the second layer of embellishments, I->V->I.

To compare the phenomenon of sound and music to the three mothers in Kabbalah,  I’ll start with Aleph. It seems the breath from breath is the objective sound itself, a breath in air vibrations caused by a breathing being.

Air vibrations or sound, specifically ones represented in an electronic format, could be described as revolving around or caressing a unitypoint (absolute zero, silence) and scratching two opposite poles of extension (-1 & +1)  

Aleph could be thought of as the waveform itself, or the manner in which the air is vibrating.

Mem is said to hum, which is a closed mouth singing of the the fundamental and lower harmonic series. Is it a more constant sound (it is sounds more pleasing). Consonance is the basis of harmony In music, and tends to be more organized in structure (harmony tends to start and end on I for example) in my experience consonant sounds create more of a caressing feeling, or they please me like a massaging touch, relieving me of tension or stress. In an abstract sense, I believe this relief to be one of the foundation driving forces of music, as I think one of the biggest motivations of music’s creation is to sooth or settle something in the world, even if that’s just the world not having that piece of music in it. I might describe this an intent in music, and that intent to be a line in the triangle between Aleph and Mem.

Shin is said to hiss, which is a sound with lots of noise, or a sound with all possible harmonics. As a human, a hum is a sound you might make out of simple joy alone, or feeling of union with another, while a hiss is a sound of judgment or separation between you and another. (You hum with your friends, and hiss toward your enemies) In music, I would describe Shin as dissonance or a sound that is less pleasing to the ear, which to me feels like a scratching sensation as opposed to the massaging or caressing one of consonance. I see its relationship with the objective sound to be that of reaction. If the intent is the chariot running to the listener, then the reaction is it returning to the Creator. Finally the relationship between the two subjective concepts of Mem and Shin to me would be the perceptive experience, or the experience of the listener. Although it is composed of the connection between two subjective points of consonance and dissonance, I think their connection, or line between them itself can possibly be said to also be objective as well; especially due to the line’s direct juxtaposition to the objective point of Aleph. This could possibly allude to why the second harmonic partial is an equal proportion to the fundamental, as you need a air vibration and perceiver before it is technically sound or music.

It seems as if there is a flow from Aleph, to Mem, to Shin, back to Aleph, although in the nature of duality I think the reverse process seems possible, but I will need to explore it deeper. Another thing I’m still developing is the idea that when 3 circles are placed over each other vertically, 5 middle ranges are formed, but I will get to this later.


Pt. 4: 7 doubles, 7 scale degrees, 7 church modes


(A B C D E F G)


A scale degree describes which note in the scale is being played, the 7 modes are the scales formed by shifting the patterns of intervals (black and white piano keys) through the scale degrees.

This is the point where I feel I still have to learn so much before I can better grasp this concept of 7, because obviously in the fractaling nature if these systems, 7 will provide so many more possibilities. Yet I did notice some interesting patterns when I compared it to the geometric diagram I drew which I found as an alternative view of the tree of life

*All of this explanation assumes the context of a major key,  and will expand with further exploration of the subject of the 7.

I placed the dominant (5) subdominant (4) & leading tone (7) or V, IV, and vii chords to mimic the foundational chords of tonal Harmony. IV and V in the places of Mem and Shin. This represents the fact that the 4th is produced by inverting the 5th, and that movement between IV V chords is common. 7 is at the top as the leading tone, or note that wanted to go back to 1 really badly. It reflects Aleph, as it leads back to one, as Aleph leads back to the breath or foundation. I’d like to note the common relationship between V and vii, and the common relationship of breath between Aleph and Mem, as I think there is something interesting here to be explored.

And as the 2nd note is the inversion of the 7th note, I put the supertonic function opposite the leading tone. In Tonal Harmony the ii, III, and iv chords are less common, so they are spatially subjected in the diagram. Noting the reflection of ii/2 and vii/7 I repeated this process and put the III and iv functions opposite each other, oppose the ii. The line that is formed encompasses the 3, 6, &, 7 scale degrees, which are the defining modal scale degrees.

In the center of all of these is tonic, which is the revolving harmonic and scalar function…all things return to 1/I


Want more???

Continue to Pt. 2


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