Experimental Mathematics: Finding Number Patterns

[Musicinventor]

Can a sequence describe everything there is to know about numbers?

I find it fascinating how music can describe a number sequence! If I compose a short melody based on a sequence I actually end up with four different but organically related; the original, the original retrograde, and both of those inverted. Sometimes you only get two… Adding to that are the permutations of the melody itself! I always have this internal sensing that music is describing an "other dimensional quality" of the numbers but I can never quite wrap my brain around that. If you like the this book you should get your hands on The Schillinger System of Musical Composition. The material is a life time of knowledge and study.

Many, many patterns spring from the inevitable number 1...

When I do my Fibonacci trees and get down to the lowest pairs of numbers I notice the only thing left are strings of 1’s, i.e. 2 and 3 : 1+1 and 1+1+1 As for the ones; fractals? osit…

 

[Natus Videre]

The following excerpt inspired me to delve into music theory in order to understand the resonance found in prime numbers:

Session 7 November 1998

Q: Okay, let’s move on.
(A) You mentioned the term ‘pyramidal’ and I thought about putting prime numbers along a pyramid, around, higher and higher, but then, today, we discovered that Ulam was putting prime numbers along a spiral and there were funny patterns arising. So, I thought that maybe we should do something similar, but three dimensional rather than two. Is this the right track?
A: In prime numbers, you will find resonance.

Q: Resonance in prime numbers? Can you please elaborate a little bit on that?
A: Elaboration is not needed because the answers are there for you already in the texts, as with so much else. One needs only listen to the “music to your ears.”

Q: Why didn’t you answer my question about putting prime numbers around a pyramid?
A: Mathematics converts to sound in geometric measurements. Why do you think the pyramid became a pyramid?

Q: (A) It became a pyramid because it is a simple shape to build.

(L) Did it become a pyramid because a sound shaped it? Determined its shape?
A: Closer.

Q: (L) And, what was the origin of this sound?
A: Those who heard it knew.

Q: (L) Who were those who heard it?
A: Those who knew how to convert math to sound. Why would the mystics reside there? Yahoo!

Q: (A) Somehow I have problems with following your clues, and I really don’t know what is my problem...
A: The problem is impatience with the digestion phase.

Q: (A) How long can a digestion phase last? We don’t have much time!
A: However long it takes. And who says you do not have much “time?” Answer, mi Arkady, answer!!

Q: (A) Well, I agree that I am impatient. But, the point is that I feel that if I would have a little bit more of a clue, I could do much more, and for now...
A: Our words sing to you. Let them ring.

Q: (A) What is the difference between singing and ringing?
(L) I don’t think that’s the point.
(A) Ring is to awake? Probably. You mean I am not taking your words seriously enough?
A: No. We meant to let it sink in rejoice. Exult!

Q: (L) Would it help...
A: Listen to Ludwig’s 9th. Combine with the prime numbers, and what do you have?

Q: (L) Hmmm... musical notation that relates to prime numbers?
A: Why not bring the ninth in here now for inspiration?!? [We put the ninth on and crank up the volume so that it can be heard.]

Q: (L) Okay, now we can hear it, but not too loudly.
A: That is good.

Q: (L) Now my question is: if you translate numbers into musical sequence or notation, does this accomplish the deed?
A: You are certainly on your way!

Q: (A) What can I do as a mathematician, or what SHOULD I do?
A: Let the pathway lead you. It has not yet failed Lolly. [Laughter at the use of Laura’s nickname.] So you insinuate failure for yourself? Tsk tsk, my boy. Faith in this enterprise takes one places. Look where it has taken you so far!!

So I started looking for prime numbers in Ludwig's 9th and was amazed by what I found, but I lacked the necessary musical foundation to complete the task. Maybe it's time to give it another shot...

Beethoven 9 - Chicago Symphony Orchestra - Riccardo Muti​

I also stumbled upon Leonard Bernstein, the famous conductor, who described Ludwig's note selection as being "phoned in from God."

Timestamp: [7:05]
Maximilian Schell: What makes it interesting?
Leonard Bernstein: It's the form. Well, form is a mold that can be made to be a very uninteresting factor, but in Beethoven's case, the form is all because it is a case of what note succeeds every other note, and in Beethoven's case, it is always the right next note as though he had some private telephone wire to heaven which told him what the next note had to be. No composer ever had that even Mozart so that's a great where everything is so unpredictable and yet so right. It all checks. It all works out. You can rely on it, you know the next note has to be the next note and the only next note. That makes his form perfect. How he had this nobody knows because he struggled, he scratched out, he never left his rooms [...]

Leonard Bernstein Discussing Beethoven's 6th and 7th Symphony​

Structure, organization, arrangement—the necessary conditions for life.

 

[Musicinventor]

So I started looking for prime numbers in Ludwig's 9th and was amazed by what I found, but I lacked the necessary musical foundation to complete the task. Maybe it's time to give it another shot...

I’ve studied Beethoven, string quartet’s, piano sonatas, and a few symphonies, back in the late 80’s at Berklee but never heard or thought of any use of such things except in Bach and Bartok. Our analysis showed the golden ratio used by Bach at areas of climax; Bartok in form and areas of climax. You have my interest stoked!! I need to get a score of 9 and would LOVE to hear what you found! I’m going to start digging into the Bach fugues to see what can be found…

While in bed this morning I asked the universe/4Dsto/cass for some guidance on the issue. All I kept seeing was the 89 from the post above. Then I saw; 8+9=17 7+1=8, 8x9=72 7+2=9. Not sure what it means but… will definitely be doing some experimental composing today!

Thank you Natus!

 

[Musicinventor]

Jeepers! I almost forgot about this…

The C Major scale two octaves; C D E F G A B C D E F G A B C
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Fibonacci series; 1 2 3 5 8 13 Related scale; C D E G C A permutate the A; C D E G A C = Major Pentatonic scale.

Time for breakfast!

 

[Musicinventor]

Here is my preliminary analysis of the overall form of Beethovens 9th symphony. Each movement needs to be broken down further to extrapolate their form, except mvt. 2 which is basically constructed as shown in my example. I will look at it closer though to determine if any number sequences show up, along with the rest. As I do each movement I’ll post the results!

 

[Musicinventor]

Updated attachment.

 

[Natus Videre]

The C Major scale two octaves; C D E F G A B C D E F G A B C
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Fibonacci series; 1 2 3 5 8 13 Related scale; C D E G C A permutate the A; C D E G A C = Major Pentatonic scale.

Yes, the famous N-tonic scales!
A few years ago, I found a pretty cool app called the Harmonagon to visually explore chords, scales, and sequences.

The Harmonagon™ is a web app that uses simple geometric shapes to teach music to anyone, anywhere, for free.

Here is my preliminary analysis of the overall form of Beethovens 9th symphony. Each movement needs to be broken down further to extrapolate their form, except mvt. 2 which is basically constructed as shown in my example. I will look at it closer though to determine if any number sequences show up, along with the rest. As I do each movement I’ll post the results!

Thanks for your initiative! I think you have already found more patterns than I did!
When I was analyzing some parts of Ludwig's 9th, I was simply looking for the prime numbers 1,2,3, and having in mind the following excerpt which marked me profoundly.

Q: How do we find out who are the prime numbers? Do we plot...
A: Who are the first 3?

Q: Father, Son and Holy Ghost?
A: Numbers!!!

Q: (A) 1 2 3 are the first three prime numbers...
A: Yes, thank you Arkadiusz!!!! Laura is dancing around in wonderland, meanwhile all of creation, of existence, is contained in 1, 2, 3!!! Look for this when you are trying to find the keys to the hidden secrets of all existence... They dwell within. 11, 22, 33, 1/2, 1/3, 1, 2, 3, 121, 11, 111, 222, 333, and so on! Get it?!?!

Q: When you say that the secrets of all existence dwell within 1 2 3 or variations thereof, what kind of secrets are we talking about here?
A: All.

Q: Well, name two at the top of the list just so I know where we are going here?
A: You can do that!

Q: Are we talking about secrets of physics?
A: Yes.

Q: Are we talking about secrets as in encoded words?
A: Yes.

Q: Are we talking about the Fibonacci series?
A: Yes.

Q: (A) Continuous fractions?
A: Yes.

Q: (A) That means all...
A: Yes.

Visually, it's quite striking if we try to fill in the primes (at least, how I see it ):
1, 222 (3), 222222 (33), 222222 (33)
1212, 121212121212, 121212121212, 1(1212121212)1

 

[Musicinventor]

Howdy Natus!

A few years ago, I found a pretty cool app called the Harmonagon to visually explore chords, scales, and sequences

I’m wondering if the video is connected with a book I purchased a few years back, skimmed through, but haven’t fully read yet. The title is The Geometry of Music by Dimitri Tymoczko. He has a website created as a companion to the text.

 

[Wandering Star]

When reading your posts, I remembered a movie where the actor Keanu Reeves achieves cold fusion with sound.

Likewise, I just watched the series "The man who fell to earth", where they achieve cold fusion by harmonizing the wave through a musical score.

 

[Wandering Star]

And I'm thinking that there are many examples of this in the movies.

For example, also in the "Alien Covenant" movie, the "engineers" use a short tonal sequence playing a flute, which boots up and stabilizes the spaceship's systems.

In the movie it looks like just a boot code, but I think it's something more.

 

[Musicinventor]

In the movie it looks like just a boot code, but I think it's something more.

I’ve often wondered about a ‘secret code’ kinda thing as well. Different combinations of pitches, harmonic progression, and rhythm combined. As an example, using chordal structures alone, there are 96 different structures, each applicable to the twelve chromatic pitches. That gives 96x12=1152 leading to the number of combinations 1x2x3xn… x1152=? I’m not sure if there’s a faster way to calculate the total as I’m not that advanced in math…

 

[Musicinventor]

What a coincidence! I just found this latest post in the thread; Session 10 December 2022…

In essence all languages, once converted from semantics to a geometric cloud of relationships, form a very similar shape. Words and concepts that relate to one another are similar. So if you can understand that shape, and overlay it against any other known language, you can sort of have AI develop an understanding of a new language without having an actual translation reference.

Things that make you go hmmm…

 

[Natus Videre]

Things that make you go hmmm…

Well, there is one language from which every other is derived...

Q: (L) Okay, crop circles are a language, so to speak. Are they in some way related to mathematics?

A: Mathematics is the one and only true universal language.

...and if this language can explain itself, then there is hope, because, as you see, when an organism who is an expression of this language becomes sufficiently complex, it starts asking existential questions: who am I? who are you? why are we here? is this real?

This brings us to the topic of building blocks. There must some irreducible units that can be used to assemble more complex structures. If primes numbers (especially 1,2,3) offer a starting point, what can we do with them? First, we need a way to compose them... we need mathematical operators!

Among other things, humanity has discovered addition, subtraction, multiplication, division—all of which can accomplish useful work.

Q: (SV) I have a book on the Brotherhood... I get all kinds of things in the mail... one is from a guy who is supposed to be an extraterrestrial... I'll have to bring it... (L) What could we use to represent 7th density as a mathematical symbol?
A: Try this: [draws figure eight on side in ellipse]

Q: (L) When you get to the point of the Big Bang, or mass disbursement, what mathematical symbol would represent that? Plus, minus, multiply or divide?
A: NAB

Q: (L) Do you mean? None of the above?
A: Close.

Q: (L) What mathematical operation would represent this?
A: You have not yet discovered.

Understanding the universe then becomes a matter of discovery. Our assumptions must match reality in order for our knowledge to be crystallized. If a foundational piece is missing, progress is affected.

Q: (A) Is entropy the key concept that must be included into the unified field theory in order to include other densities into the equations?

A: Need to back up and reflect before proceeding. There is still a "missing link" that is earlier in the process. Any mathematics problem will collapse if there is a missing link.

Q: (L) Well if he goes back and finds that missing link, will he then need to include entropy into the equation? Into the theory in order to include other densities?

A: Must find link before answer is given, otherwise it is useless information.

The puzzle needs to be assembled from all sides. There is no shortcut or free lunch.

Q: (L) In what sense would the fruit of the tree of life be limiting?
A: Believing that one source contains all knowledge is contradicting reality.

Q: (L) What was the flaming sword barring re-entry to Eden?
A: Do you not understand?

Q: (L) No I do not understand.
A: Review. If the concept was the eating of the fruit of the tree of knowledge provides all knowledge, then one is being deceived, because no one particular source can provide all knowledge. Therefore, when one believes in the deception, one has now trapped oneself within parameters. And, forevermore, the human race, will be poisoned by the very same problem which is reflected in several different ways: one is always seeking the truth through one pathway instead of seeking it through a myriad of pathways; and also believing in simplistic answers to very complex issues and questions.

 

[Natus Videre]

While searching for prime patterns on YouTube, I found this 10-second 'video':

Video Description: Two sets of parabolas are filtering prime numbers.

I have reproduced a portion of the diagram here and labeled the numbers (up to 5) that are represented by each parabola. Even numbers have a 'triangular' top while odd numbers have a 'flat' top. Notice how there is a lot of regularity: the lines pass perfectly through very specific grid points and each parabola is symmetric along the x-axis. If you consider each horizontal grid line, the labelled points are spaced equally, and as you move up the y-axis, their spacing increases by one each time.


Things start to get very interesting when we label the horizontal distance between each point of a parabola.


We can arrange the segments of each parabola to form a mysterious triangle!

If we sum the rows of the triangle, we obtain the sequence 0,2,4,8,12,18,24,32,...
The sequence A007590 - OEIS corresponds to a(n) = floor(n^2/2), which is also the average of a pair of successive triangular numbers!

 

[Natus Videre]

Q: Would you say that the writings of Albert Pike might be interesting to decode?
A: Yes.

Q: (L) Is there any particular number sequence that could be used?
A: 353535...

Q: (L) Is this also a genetic code?
A: Much is missing between "point A and point B."

Q: (L) You mean by jumping from documents to DNA?
A: Yes.

Q: (L) Does that sound right? (TB) It worked. I guess. I'd never thought about it that way. (L) Okay, now about the Pig God: what is it about pigs that makes them ideal as a symbol for the manifestation of God energy, or even as a vehicle?
A: Genetically manipulated RU 353535.
Q: (L) What does that code relate to?
A: Race underpinning tribal code structure.
Q: (L) Are you suggesting that some codon of human DNA that relates to a "tribal code structure" was spliced into an animal?
A: Close.
Q: (L) Why an animal and not a human being? Is it because the STS energy is so contractile that a pig is an appropriate receptacle?
A: Yes.
Q: (L) That's bizarre. Moving along. What sort of 4th density weapons was copper used for?
A: Mostly conduction of EM energies.

35/99 = 0.353535...