Mystical diagrams and geometry

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Nahumatarah
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Mystical diagrams and geometry

Post by Nahumatarah »

"Plato said god geometrizes continually"

- Plutarch (Convivialium disputationum, liber 8,2).

"God arithmetizes".

- Carl Friedrich Gauss

I was revisiting “Kirjoituksia Magiasta” (“Demon’s Cube and Other Writings on Magic”) by frater Nefastos while taking a break from work today, and started thinking about different sorts of “mystical diagrams” then a chain of thoughts led me to pondering geometrics. I would be interested to hear your ideas, and experiences about practical magical applications to meditation diagrams, such as the yantras or mandalas or any sort of “mystical diagrams”.

Tattva vision, the basic exercise of "scrying in the spirit vision" used in the Golden Dawn system. is one practical exercise than comes to mind when thinking diagrams or simple geometric representations. Similar tools to tattva cards are for example the Zener cards designed by perceptual psychologist Karl Zener to conduct experiments for extrasensory perception. I constructed a set of tattva cards (a simple set, only the symbols in isolation on a black background) a couple of years back when I was studying the Golden Dawn tradition, but they saw little use from me. My visualization is pretty strong stemming probably from a lot of imaginative play from when I was a child, but I'm interested to hear has anyone here done any experiment with these sorts of tools especially relating to their claimed aid for astral clairvoyance, scrying or ESP?

Personally, I just love Islamic ornamental art. There seems to be something about minimalistic, symmetric patterns in both visual and audio arts that call me like a moth to a flame. Im absolutely horrible at drawing with free hand but I have learned to enjoy creating pieces with a help of a ruler and a compass. I know there are already discussion about the magical side of creating visual arts, but relating to patterns and geometry does drawing images or creating mandalas of some sort have significance in your work?

David Brewster, the inventor of the modern kaleidoscope created his invention to be "for the purposes of rational amusement" and of great value in "all the ornamental arts", but from time to time, I have been thinking about testing if these sort of optical devices could have any application in scrying or other occult work. Does anyone have any ideas where to go from here regarding such devices? Back in the day when I used to do psychedelics (I'm sober, and boring these days) I spent long hours gazing through my kaleidoscope while high on lysergic acid diethylamide. There were some moments and experiences there pertaining to the spiritual, but I can't trust these experiences since there were perception altering substances and other distractions involved. I even drew plans back then for devising a helmet with a kaleidoscope attached to it like binoculars, with electric motors rotating the cell, to allow for hands free experience. When I showed these plans to a friend who is an electronics engineer he remarked that “you are truly autistic in the worst possible ways”. I think maybe kaleidoscopes could be used in a similar way to crystal spheres.

Also enjoy this virtual tour of the W.B Yeats exhibition of National Library of Ireland. They have on display his personal handmade set of tattva cards, among other occult curiosities.

https://my.matterport.com/show/?m=CfD9eU6iPhf&mls=1
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Re: Mystical diagrams and geometry

Post by Nefastos »

I include a part of fra Benemal's post from another recent conversation, for it seems to fit here well:
Benemal wrote: Wed Nov 10, 2021 2:33 amFor example, I saw mathematics as colors and shapes, and always got it all correct, A+. Some form of synesthesia, I guess. I suspect I know the reason for it, but for now I'll leave that out of public discussion.

I'm very visual, but I consume words a lot. When reading a book, about anything, I see it all, so it's not really letters, that's why I'm not good at writing. I can write a bit, because I've read so many books. If I read about a city 2500 years ago, I see it, and can construct a detailed 3d model, where events take place. That's a very psychedelic experience of time-space dissociation. In dreams, it's sometimes so powerful, that the "real world" feels like a black and white photo, of a farmer with a donkey, in Poland 1920.

Synesthesia as oneness of experience and being is, after all, how the world is, and our perceptions are partly specialized (by evolution) and partly culture-trained to notice just very definite dimensions of that world. It's similar than the so-called triple or threefold world: as a matter of fact, these "bodily," "emotional" and "intellectual" (and their higher octave âtma-buddhi-manas) are not ultimately different things, but the one same thing, seen in different ways. Attempt to separate these principles absolutely is a mistake, although a form of heuristic separation is needed in order to live and operate. In his final unity in nirvâna, yogi is the great synesthetic, seeing the whole being in a one infinitely nuanced and yet understandable aura of being: the ultimate principle (usually called "God," but why not Svabhavat instead).

In those moments of higher vision I have had in waking, I have seen (felt) the higher, "real" world as an incredibly sophisticated vastness of fully living and conscious universe of geometric shapes. "Geometric shapes" might sound very kâma manasic, engineer-like world, but the actual realization is opposite to this. On the contrary, the depth of these geometric shapes is so immense and so spiritual, that everything that happens in any scale of time or detail is fully supported by those shapes and the "great plan" that is their movement. For being above time themselves, they are the extreme immanense in everything, even though they seem transcended from out limited point of view. (We might compare this – in the other end of the spectrum of manifestation – to the presence of atoms. One can ask, has anyone actually seen an atom? No; but on the other hand, no one has ever seen anything else but atoms. The similar is true to the grand geometries of archetypal world.)

It is also an interesting intuition that the mind simultaneously feels that these spiritual worlds are everywhere, but they are at the same time "above." When I became a Satanist, I started to cultivate the practice where I sought to feel the stars not only above me in the heaven, but also under me, on the other side of the planet. For the stars (symbols and manifestations of the ultimate geometries) are de facto everywhere, in every direction at once. Yet it is psychologically telling that it is harder for us to see those that are below us, because there is something so dense (our own planet = our own personality) between them and the individual eye.
Faust: "Lo contempla. / Ei muove in tortuosa spire / e s'avvicina lento alla nostra volta. / Oh! se non erro, / orme di foco imprime al suol!"
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Re: Mystical diagrams and geometry

Post by Nahumatarah »

Great pointers. Thank you brother. I guess We could have had this conversation in the arts or philosophy section too so I ask for forgiveness for not being able to formulate my ideas in a more exact manner.

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Re: Mystical diagrams and geometry

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Has anybody thought of why is it that the overtone series, that can be found from mathematics, nature and music has that "reciprocal or mirror side", and why is it that we as humans cannot find that "mirror side" from physical nature without human inventions, like piano or other instrument?

Overtone series from C (which note C in Blavatsky's texts was said to be the foundation of the tones on our physical level) goes as follows:

1. Partial 2. 3. 4. 5. 6. 7.
C C G C E G Bb

8. 9. 10. 11. 12. 13. 14. 15.
C D E F# G Ab Bb B

16.
C


The "reciprocal or mirror" series would then be to reversed direction in our 12- tone musical scale as it follows:

1. Partial 2. 3. 4. 5. 6. 7.
C C F C Ab F D

8. 9. 10. 11. 12. 13. 14. 15.
C Bb Ab Gb F E D Db

16.
C

We will find for example that the 7 first partials of the overtone series make up a C7 chord, that is a major chord owning "positive or luminous or happy" sound.

If we take the 7 first partials of our "reciprocal or mirror" series, we find that they make up an Fm6 chord that is a minor chord owning then the "dark or melancholic" sound.

It was also said by Blavatsky that F is the "center note of the nature".

In the overtone series we see that the second partial C emanates G. In the same way it makes me think if this F note, that is not at all found from the overtone series no matter how far we go with the partials, as a possible creator for the C note.

In sanskrit solfege C is named "Sa" , F is "Ma" and G is "Pa".

This makes my thinking associate overtone series as a sort of Brahman and "father" As it makes me associate reciprocal series as a sort of Parabrahman and "mother".

My thinking went this way as I was thinking generally about Plato's world of ideas and its reflection as our emanated world.

In this sense our overtonal series would seem to be in its self sort of reciprocal side of the "overtone series of ideas".
So this makes me think if our earthly reciprocal side that we humans have found from our musical instruments and inventions could be our mirror image of the mirror image of ideas.

Is my logic completely at the woods or can you find reason within this?
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Re: Mystical diagrams and geometry

Post by Kavi »

Nahumatarah wrote: Mon Nov 08, 2021 2:21 pm
Personally, I just love Islamic ornamental art. There seems to be something about minimalistic, symmetric patterns in both visual and audio arts that call me like a moth to a flame. Im absolutely horrible at drawing with free hand but I have learned to enjoy creating pieces with a help of a ruler and a compass. I know there are already discussion about the magical side of creating visual arts, but relating to patterns and geometry does drawing images or creating mandalas of some sort have significance in your work?
It's good to keep in mind also that those artists who made their art to be known in these parts of the world, had dozens of hours of practice with help of a ruler, dots and other rules etc.
Even the audio arts that seems to be free of any rhythm has it within, even excelling in exact symmetry.

I'd like to inverse the mundane thinking upside-down - forms and geometrical shapes are revealed for the artist while engaging with them. I think this is quite obvious interpretation if one is thinking within Platonic framework? There is also "a danger" to make the essential assumptions based on this, but I think it has quite healthy mentality - to carve the sculpture from day to day and engage in this process for its own worthiness - for Truth and so on.
Utthavat wrote: Fri Nov 26, 2021 3:25 pm Has anybody thought of why is it that the overtone series, that can be found from mathematics, nature and music has that "reciprocal or mirror side", and why is it that we as humans cannot find that "mirror side" from physical nature without human inventions, like piano or other instrument?


I am not very familiar with overtone series. My guessing would be that most instruments have limitations and therefore they might reveal something on this phenomena?
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Re: Mystical diagrams and geometry

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Utthavat wrote: Fri Nov 26, 2021 3:25 pm Has anybody thought of why is it that the overtone series, that can be found from mathematics, nature and music has that "reciprocal or mirror side", and why is it that we as humans cannot find that "mirror side" from physical nature without human inventions, like piano or other instrument?
I'm not sure I understand the question properly. What do you mean by "it has a mirror side" if it can't be found in nature? Can't we just invert any given series? I mean, the laconic answer to why it can't be found would be that it just doesn't exist. What made you think the undertone series (isn't that what it's called?) would be significant in the first place?
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Re: Mystical diagrams and geometry

Post by Kavi »

Utthavat wrote: Fri Nov 26, 2021 3:25 pm
We will find for example that the 7 first partials of the overtone series make up a C7 chord, that is a major chord owning "positive or luminous or happy" sound.
If we take the 7 first partials of our "reciprocal or mirror" series, we find that they make up an Fm6 chord that is a minor chord owning then the "dark or melancholic" sound.
It was also said by Blavatsky that F is the "center note of the nature".

In the overtone series we see that the second partial C emanates G. In the same way it makes me think if this F note, that is not at all found from the overtone series no matter how far we go with the partials, as a possible creator for the C note.
https://hellomusictheory.com/learn/negative-harmony/
Look up to negative harmony:
To create a Negative, or “opposite”, interval of C-G, we need to start at C and go down a Perfect 5th, or down 7 semitones.
This gets us to F, and therefore the inversion of C-G is F-C, because they have the same interval distance between them.

A Major 3rd above C would be 4 semitones up, which gets us to E.
Therefore a Maj 3rd below C would be 4 semitones below, or an Ab.
I don't know is your example of Fm6 chord actually exactly like how jazz musicians might improvise over C7 chord. (might be the same "negative harmony" although I never heard the name until very recently)


Blavatskyian music topics seem to reiterate ideas of Plato and Pythagoras? I have tried to understand these kind of ideas for longer time, but as long as theory is held separate from practice "kama manas" empties paradoxically the form out of meaning.
I tried to dive through Secret Doctrine, but I couldn't make sense of the musical phenomenas.
What is the meaning of "center note of the nature" she refers in Voice of Silence?

I guess tuning to Pythagorean tuning one should tune according to perfect fifth and fourth. Do 'til Fa - Fa 'til Do, from Do 'til Sol, from Sol to Re... Re - La... and so on. etc.
Fifth, which is Fifth but also Fourth depending if one approaches it from above or below. (Circle of Fifths?)

Put in historical perspective I could see that Theosophical movement being very influential in some of the classical musicians' thinking and works of art.
Two names comes to my mind first, Scriabin and Debussy. (Stravinsky was not that strictly influenced by Theosophical Society?)
This then gave arise to new visions how composers and musicians could explore harmony in music, like in Jazz.

******

Maybe exposure to certain ideas gave also easy associations to different origin myths. Like interpreting Father and Mother, or light and dark.
Or like I would think in this framework Mother being conceived but while something in incubation cosmic doubt came and twins ( Note G and F) were born.
Then these twins are trying to get hold on the special place of note C.
But I don't know...
My attempt has been for the most part trying to explore music in practice, because forming these systems seem to entrap and veil the life it tries to explain in the first place.
Men who are in love I asked about your face and ruby lips.
They pronounced them to be Khizr and living water – this is true.
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Re: Mystical diagrams and geometry

Post by Utthavat »

Kavi wrote: Sun Nov 28, 2021 9:56 pm
Utthavat wrote: Fri Nov 26, 2021 3:25 pm
We will find for example that the 7 first partials of the overtone series make up a C7 chord, that is a major chord owning "positive or luminous or happy" sound.
If we take the 7 first partials of our "reciprocal or mirror" series, we find that they make up an Fm6 chord that is a minor chord owning then the "dark or melancholic" sound.
It was also said by Blavatsky that F is the "center note of the nature".

In the overtone series we see that the second partial C emanates G. In the same way it makes me think if this F note, that is not at all found from the overtone series no matter how far we go with the partials, as a possible creator for the C note.
https://hellomusictheory.com/learn/negative-harmony/
Look up to negative harmony:
To create a Negative, or “opposite”, interval of C-G, we need to start at C and go down a Perfect 5th, or down 7 semitones.
This gets us to F, and therefore the inversion of C-G is F-C, because they have the same interval distance between them.

A Major 3rd above C would be 4 semitones up, which gets us to E.
Therefore a Maj 3rd below C would be 4 semitones below, or an Ab.
That site has a fine introduction to negative harmony. I've used negative harmony as a tool in composing music, but my knowledge of the concept does have a lot of blanks.
I'll aim to dig in to it in more depth. But for starters, I could recognize that the way the diatonic seventh chords (called seventh chords, because they have the triad chord + the seventh tone of the scale counted from the root of the specific chord, like G7, as it has G, B, D + F) from the key of C major / A natural minor which are Cmaj7, Dm7, Em7, Fmaj7, G7, Am7, Bm7b5, invert to the chords of Eb major / C natural minor accordingly:
(I degree in C) Cmaj7 to (iii degree in Eb) Gm7
(ii degree in C) Dm7 to (ii degree in Eb) Fm7
(iii degree in C) Em7 to (I degree in Eb) Ebmaj7
(IV degree in C) Fmaj7 to (iiv degree in Eb) Dm7b5
(V degree in C) G7 to (vi degree in Eb) Cm7
(vi degree in C) Am7 to (V degree in Eb) Bb7
(vii degree in C) Bm7b5 to (IV degree in Eb) Abmaj7

So we can see that C can be seen to switch its polarity in this procedure as does F as Cmaj7 becomes Cm7 and Fmaj7 becomes Fm7.

Good that you mentioned the impovisation part because the 7 first partials of the overtone series, the C7 chord, and the 7 first partials of the reciprocal series, the Fm6 chord, when combined as Fm6+C7 give us the tones of F melodic minor scale or often called ''jazz minor'': (F, G, Ab, Bb, C, D, E) and they work well for improvising over both Fm6 and C7.

Blavatskyian music topics seem to reiterate ideas of Plato and Pythagoras? I have tried to understand these kind of ideas for longer time, but as long as theory is held separate from practice "kama manas" empties paradoxically the form out of meaning.
I tried to dive through Secret Doctrine, but I couldn't make sense of the musical phenomenas.
What is the meaning of "center note of the nature" she refers in Voice of Silence?
In secret doctrine Blavatsky seems to actually regard Plato and Pythagoras as Adepts, so in that light I wouldn't be suprised if the teachings of these all stemmed from the same root.
I would be very interested in hearing more esoteric interpretation of this ''center note of the nature". could that center note itself be the "Voice of Silence"?

I've also been trying to understand these concepts for a while, my motivations been to understand these relationships to broaden my musical output in practice, but also to get more familiar with numbers, ratios and relationships for the sake of understanding the laws which operate them.

It seems to me that the little out-of-tune music that our modern culture has in its 12-tone equal temperament somehow still resides in the lap of mathematically more accurate just intonations like Pythagorean tuning. I'll aim to dig into this concept later but there is another interesting question about tunings on my mind regarding tunings.

Our modern day (accepted) frequency for the A note is 440 Hz. However, I've heard some talk about frequency of 432 Hz being richer and fuller in sound.
Recently I came across a book written by Erkki Lehtiranta called: ""Astrologia ja hyvinvointi" (roughly translated to Astrology and well-being), and in this book Lehtiranta connects each of the zodiac signs to one of the 12 tones of our equal temperament. He regards the note A to 432 Hz and connects it to the sign of Capricorn, from which we can find interesting associations to Baphomet and Abraxas. number 432 (and number 9 that is the sum of its components 4 + 3 + 2) seem to connect for example to the vedic time cycles as 4 320 000 000 solar years are understood as 1 day of Brahma, and 432 000 solar years is the length of Kali Yoga.

Number 9 seems to have interesting qualities in the multiplication table as every time we can trace the numbers of every multiplicaton back to the 9, like 432, or like 189 as in 1 + 8 + 9 = 18 = 1 + 8 = 9. 432 is also a point where the worlds of 2 and 3 or 8 and 9 meet in the multiplication tables.

Here is the chart from the book:
20211119_130934.jpg
20211119_130934.jpg (1.64 MiB) Viewed 84 times
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Re: Mystical diagrams and geometry

Post by Utthavat »

Utthavat wrote: Mon Nov 29, 2021 6:18 pm I could recognize that the way the diatonic seventh chords (called seventh chords, because they have the triad chord + the seventh tone of the scale counted from the root of the specific chord, like G7, as it has G, B, D + F) from the key of C major / A natural minor which are Cmaj7, Dm7, Em7, Fmaj7, G7, Am7, Bm7b5, invert to the chords of Eb major / C natural minor accordingly:
(I degree in C) Cmaj7 to (iii degree in Eb) Gm7
(ii degree in C) Dm7 to (ii degree in Eb) Fm7
(iii degree in C) Em7 to (I degree in Eb) Ebmaj7
(IV degree in C) Fmaj7 to (iiv degree in Eb) Dm7b5
(V degree in C) G7 to (vi degree in Eb) Cm7
(vi degree in C) Am7 to (V degree in Eb) Bb7
(vii degree in C) Bm7b5 to (IV degree in Eb) Abmaj7
Made a small mistake there in my way of seeing the first step to negative harmony of C major. This way might be different from the way it was done on the website Kavi mentioned, at first look there seemed to be some differences. Here is this correctly:

(I degree in C) Cmaj7 to (iii degree in Eb) Gm7
(ii degree in C) Dm7 to (ii degree in Eb) Fm7
(iii degree in C) Em7 to (I degree in Eb) Ebmaj7
(IV degree in C) Fmaj7 to (vii degree in Eb) Dm7b5
(V degree in C) G7 to (vi degree in Eb) Cm7
(vi degree in C) Am7 to (V degree in Eb) Bb7
(vii degree in C) Bm7b5 to (IV degree in Eb) Abmaj7

Insanus wrote: Sat Nov 27, 2021 8:26 pm by Insanus » Sat Nov 27, 2021 9:26 pm

Utthavat wrote: ↑Fri Nov 26, 2021 4:25 pm
Has anybody thought of why is it that the overtone series, that can be found from mathematics, nature and music has that "reciprocal or mirror side", and why is it that we as humans cannot find that "mirror side" from physical nature without human inventions, like piano or other instrument?
I'm not sure I understand the question properly. What do you mean by "it has a mirror side" if it can't be found in nature? Can't we just invert any given series? I mean, the laconic answer to why it can't be found would be that it just doesn't exist. What made you think the undertone series (isn't that what it's called?) would be significant in the first place?
I had understood that the overtone series can be found from nature without human inventions but that its negative side at least in direct mirror form not, Although we can find its important implications in the world of our musical universe for example.
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Re: Mystical diagrams and geometry

Post by Kavi »

Utthavat wrote: Tue Nov 30, 2021 12:47 am Made a small mistake there in my way of seeing the first step to negative harmony of C major. This way might be different from the way it was done on the website Kavi mentioned, at first look there seemed to be some differences. Here is this correctly:

(I degree in C) Cmaj7 to (iii degree in Eb) Gm7
(ii degree in C) Dm7 to (ii degree in Eb) Fm7
(iii degree in C) Em7 to (I degree in Eb) Ebmaj7
(IV degree in C) Fmaj7 to (vii degree in Eb) Dm7b5
(V degree in C) G7 to (vi degree in Eb) Cm7
(vi degree in C) Am7 to (V degree in Eb) Bb7
(vii degree in C) Bm7b5 to (IV degree in Eb) Abmaj7
I have always been interested to know how does John Coltrane's Giant Steps chords work, maybe this sidetracks from your point of view but in this chart you refer to Eb.
I think there is quite "esoteric chart" based on that chord progression.
https://en.wikipedia.org/wiki/Coltrane_changes

I heard that tuning to 442hz or 440Hz has more to do with pragmatic solutions due to concert hall. When things get standardized, they usually spread this influence over to other instruments or cultures. Just as 12 equal temperament is basis on many digital workstations, other cultures have to work on that premise too. Although there has been recent development in making software that enable one to work in more traditional settings too.
But I am sure that some instruments might sound much better when the instrument is tuned either lower or higher.

I'd assume that in the old - "troubadour times" what mattered most was that key of the songs were not too high or too low to sing.
Men who are in love I asked about your face and ruby lips.
They pronounced them to be Khizr and living water – this is true.
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