From: MetPhys@aol.com
----- Original Message -----
The numbers around the central 13-1 of the middle 7th column are:
5-12-6
<< Not how I imagined it at all!! >>
Look at it this way if you will. You are thinking in 9 units. 8 units are an octave scale with a 9th note between 2 groups of 4 notes. Isn't 13 notes the same thing as 9 notes?
9 notes are really an octave
MetPhys@aol.com
<< I am just having a go at doing a 20 by 13 grid and including the chromatic notes. In Equal temperament there are 13 chromatics (although 1 and 13 are the same, meaning that to extend the octave we must think in 12 and not 13). There are others that insist on there being 18 chromatics in the octave.
C Db D Eb E F Gb G Ab A Bb B C
This is 12 chromatics and the 13th being the 0ctave of the first. Yet the sharp notes are missing. Ab and G# are not the same notes, unless one think Equal Temperament.
C C#/Db D D#/Eb E F F#/Gb G G#/Ab A A#/Bb B C
So, 17 different tones, the 18th being the octave of the first.
The table I want to produce will only use the flats, although these will represent the sharps too. >>
<< Luigi >>
From: luigi.di-martino@ntlworld.com
From: MetPhys@aol.com
99JJJ Electrons and Mythologies
Luigi,
99.62.2 Tzolkin, Symmetrically Numbered and Musically Noted (jpg) (Luigi)
OK this 20x13 Tzolkin Grid is the way I imagine it, with a few problems,
Problem #1:
Problem #2:
260 / 13 notes is an even 20
Aside from this, if you work on this arrangement of the Tzolkin, you should find, or be very close to finding symmetric, mirror-like musical patterns within it.
MetPhys@aol.com
From: luigi.di-martino@ntlworld.com
----- Original Message -----
<< Electrons and Mythologies >>
<< Luigi,
99.62.2 Tzolkin, Symmetrically Numbered and Musically Noted (jpg) (Luigi)
Problem #1:
The two C's are the axis point. This grid is no different to the Mode Box in effect:
C Db Eb F G Ab Bb C/C D E F G A B C
The note pairs around the axis are:
C/C
It has been seen how the tri-tone replicates the results of the root axis. The grid starts with the two C notes in the middle (1^13, 2^1), is replicated by the tritone (Gb) and moves across a 45 deg. angle and repeats the process until the other side of the grid.
The B and the Db are the next pairs that perform a similar journey across the grid. B goes to its tri-tone (F), goes across a 45 deg. angle and moves on. In reply Db begins at the opposite end, finds its tri-tone (G) and flips across the 45 deg. angle. B and Db are note partners around C Major. Also as B goes to F and Db goes to G there is another note pair around the C axis emerge, the F and G being either side of the C axis.
The rest of the grid is similar, note/tri-tone partner/45 deg./mirror note partner responds in similar manner/ second mirror note pair created (F and G being secondary relationship and note pair around C).
All the characteristic swap over points are evident in this grid as is
evident in the mode boxes and just mirroring in general.
<< Problem #2:
260 / 13 notes is an even 20
Aside from this, if you work on this arrangement of the Tzolkin, you should find, or be very close to finding symmetric, mirror-like musical patterns within it.
MetPhys@aol.com >>
From: luigi.di-martino@ntlworld.com
If you imagine a windmill with its big wheel rotating you will get an idea of what the swap over at the tri-tone position is.
C Db Eb F G Ab Bb C/C D E F G A B C
Starting at the centre there is -TONE ,TONE , SEMI-TONE. This is the only formula needed. Here is the one traveling to the left:
C (t) Bb (t) Ab (s) G
The invisible tri-tone flips this formula over:
F (t) Eb (t) Db (s) C
At the same time the formula is applied rightwards from the centre:
C (t) D (t) E (s) F
Then the invisible tri-tone there (Gb/F#) flips over the formula:
G (t) A (t) B (s) C
Luigi
From: MetPhys@aol.com
Hi Luigi,
I've already put years of thought into the toroidal form of the Tzolkin and the two counter-directional stylized sine curves upon its grid surface representing light permutations.
The 45 deg. pattern of music that you have discovered recently, is brand new and I spent several days and nights imagining in my mind, the toroidal form of the Tzolkin and the path of your musical progression. Simply folding the Tzolkins left and right edges together, we have a cylinder with your musical pattern beginning at the South Pole of this cylinder and it spirals or corkscrews uniformly up to the North Pole, without any changes in the amplitude of the spiral because of the uniform cylinder surface.
To get to the correct shape of the spiral we will have to compress the ends of this cylinder to points so that the whole cylinder becomes a sphere. Now upon this sphere is your musical 45 deg. double band spiral from the South Pole, beginning in a tight spiral and moving "up" and becoming ever larger in amplitude, to a maximum at the equator and becoming ever smaller in amplitude (tighter) as it approaches the North Pole. This should be the path of your double band of musical tones and it seems to make 1 1/2 turns on the visible outer surface.
Whether these double rows are traveling opposed to each other, or each two tones in one row are opposed, or that each two tones in each row are opposed to two tones in the adjacent row, or that all tones are progressing in the same general direction or in any other unknown combination or configuration, is open to questions.
MetPhys@aol.com
From: luigi.di-martino@ntlworld.com
Hi Robert
I have no real claims about the possible meaning of the Tzolkin. It is too fresh a concept for me to really get any positive meanings from it. However it has answered for me why a 1 -13 progression is needed. Basically it seems to show the axis point at C. Or maybe not. Perhaps the same result is there with a 1-12 grid. One simply takes the lone C as axis.
The only thread I looked for was the relationship between the visible and invisible axis points, one at the root and one at the tri-tone. So to see these two relationships behaving in the way they do through the grid, and the note partners emerging either side just like when C Major is mirrored, I am awed in a way.
My mind has told me from the beginning that in the scales was a marriage point between both the male/female forces. I knew this before it was manifest in the mode box.
So if this grid actually is anything to do with music progressions then there is a secret flow in there that marries the male/female. It may be to do with the fact that another force is evident when the visible and invisible aspects are merged.
In every other mirror experiment there is always a swapping over across the axis point every move along the flow of energies. I see that is true for the info in the grid at the moment. Yet it seems just as likely that it all springs from the 11^1, or perhaps there is a hidden tri-tone axis between 10^13 and 11^1.
Either way I don't have an opinion as to the meaning of the grid, only an observation. With your extensive research into this area I hope it was a helpful. And of course you are welcome to get me to do any other musical experiment you think would be worth doing on the grid.
I noticed, that where Gary saw the word KEY in the grid, that the notes are Bb E B. There is also a possibility of sequencing the chromatics following the 'tri-tone then 5th' movement:
C Gb Db G D G# Eb A E Bb F B F#
Luigi
From: MetPhys@aol.com
Hello again Luigi,
Hope you are doing fine.
1. In column 1, beginning with tone A, each tone A from left to right, along the 45 deg. band across the Tzolkin, progresses by 3 units. Example: 1^10 A, 4^10 A, 7^10 A, 10^10 A, 13^10 A, 16^10 A, 19^10 A.
2. Each similar tone in column 1, from left to right, along the 45 deg. band, progresses by 3 units, in the same manner as tone A.
I still don't quite understand your comments such as
<< The B and the Db are the next pairs that perform a similar journey
across the grid. B goes to its tri-tone (F), goes across a 45 deg. angle
and moves on. In reply Db begins at the opposite end, finds its tri-tone
(G) and flips across the 45 deg. angle. B and Db are note partners
around C Major. Also as B goes to F and Db goes to G there is another
note pair around the C axis emerge, the F and G being either side of the
C axis. >>
But don't try to explain it to me at this time. I still won't get it. I tried for hours to find B, Db, "the C axis", "B goes to G", "tri-tone F" etc.
MetPhys@aol.com
From: hoopoe@popd.ix.netcom.com
I used the tzolkin as a 'matrix' to compose a piece once , that was awhile ago, I'll look around and see if i can find my notes (pun intended) but I'll check your link and catch up on what going on, thanks for the invite. below I've re-ordered the 'code', see if that works for you, i think it explains it?
lets see, sorry about the spacing thing, i was wondering if it might do that, i was trying to show the 'cross-notes' or the notes each scale has in common with the other as a link function within this pattern; how the these scales can fit in a very symmetrical way to make one huge symmetrical 'scale' (sounds good too) that encompass's the cycle of 5ths literally and by implication in smaller segments and using 3 (trinity) different intervals within a scale structure instead of the usual 2 (tone-semitone) of the diatonic system.
also since luigi seems to be on about the major diatonic stuff and relative modes, i thought I'd thrown in 2 cents about the harmonic minor series.
the harmonic minor series doesn't show its symmetry the same way as the diatonic series.
so how about this:
T=tone
TS¿STS¿STS¿ST-(S-¿ -would continues sequence) 13 interval symmetry.
obviously you could start the sequence with whatever note you like.
example with notes filled in:
F-T- G -S- Ab -¿ -B-S- C-T- D-S- Eb-¿- F#-S- G-T- A-S- Bb-¿- C#-S -D-T- E- ...(S-F-¿-G#...etc. would continues the series.)
three unisons F G D wthin a 14 note structure.
notice F to D in the 'scale' is part of the C harmonic minor scale.
C to Bb is part of the G harmonic minor scale
G (the 2nd G in the sequence) to F (last note) is part of the D harmonic minor scale.
the C G D are the fundamentals of the 'scale segments', in this case the Harmonic minor scale so:
F G Ab B C D Eb is 'over' C (fundamental of the C harmonic minor scale) from the 4th scale step
C D Eb F# G A Bb is 'over' G (fundamental of the G harmonic minor scale) from the 4th scale step
G A Bb C# D E F is 'over' G (fundamental of the D harmonic minor scale) from the 4th scale step
you can also use other fundamentals from those respective scales (example G, D, A , the 5th scale step) but they would always move in a cycle of 5ths direction.
notice how the scales overlap each other using 3 notes as 'links' (C, D, Eb between CHM & GHM, and G, A, Bb between GHM & D HM also if you continue this symmetry you will eventual traverse the cycle of 5ths of the HM scales. and you can play it backwards to traverse the cycle of 4ths.
so like:
allow it to be non-tempered.
_T
From: luigi.di-martino@ntlworld.com
Tried a Google search for group 3 squares but found nothing.
What I did find was something I know I should be trying to understand. There is something to do with crystals I need to find out but I first need to learn how to understand stuff like at this link. There is some thought provoking symmetry combinations on this page.
http://www.geom.umn.edu/docs/reference/CRC-formulas/node12.html
----- Original Message -----
Luigi, Do you know what the heck a group 3 square is?
Harveys plan:
According to each windings ability, there is a need to procure the highest adjacent portion of a solitary winding, with reverence to the potential differences on that adjacent pathway. This simplest Group 1 Square is the first 3 dimensional bifilar winding. Such a winding is logically built from the inside out. The purpose of these windings will be to lower a coils resonant frequency by encompassing the largest possible internal capacity. The group 3 squares will be necessary for binary application. I will be working out a document on this monumental possibility. HDN
My question to Harvey:
Is a group 3 square the same as a order 3 magic square?
Harveys answer to my question: The Binary Resonant System: Re: Question..3 dim.
My answer:
Thank you Sir,
Your answer to my 3 dimensional bifilar windings question is appreciated. I'm going to show this answer to a musically minded friend to see if he can expand on your idea then will return the answer to you if he can make some analogy.
MetPhys@aol.com
From: MetPhys@aol.com
Hello Luigi,
In a message dated 7/17/2 3:56:40 PM, luigi.di-martino@ntlworld.com writes:
<< www.geom.umn.edu/docs/reference/CRC-formulas/node12.html >>
I've seen plenty of pages and books about crystal symmetries like this and the authors have never been able to connect their complicated data of crystals to the Tzolkin or anything else. What I did connect over 26 yrs was extracted into the website. I did find a great book by Vogt (Reality Revealed), which I have and its info is in the biblio.html file, about crystals and the connections to the Cheops pyramid side angle etc, the specific types and angles and why they come together. One crystal shape was especially interesting and that was the octahedron, which Vogt said was the shape surrounding the universe. That was why it seemed, the Cheops pyramid operated as it does. It's a copy of universe, and any machine that copies the universe in whole or in part, operates just like the universe. This is why machines based upon Scared Science, sacred Platonic shapes, and the matrix of the Tzolkin and I-Ching, are the best possibilities. We are trying to find the musical sounds and patterns of the Tzolkin, at this time.
MetPhys@aol.com
© Copyright. Robert Grace. 2002
To: luigi.di-martino@ntlworld.com
Subject: Numbers Around the Center 13-1 of the Tzolkin Grid (MetPhys)
Date: 07/12/02
From: MetPhys@aol.com
To: luigi.di-martino@ntlworld.com
Sent: Friday, July 12, 2002 11:10 AM
Subject: Re: MetPhys- Numbers Around the Center
6-13-7
7- 1- 8
8- 2- 9
13 notes are an octave with all the sharps and flats included?
To: MetPhys@aol.com
Subject: Tzolkin, Symmetrically Numbered and Musically Noted (jpg) (Luigi)
Date: 07/11/02
To: luigi.di-martino@ntlworld.com
Subject: Musical Problems, Tzolkin 20x13 Grid (jpg) (MetPhys)
Date: 07/14/02
Do the 2 repeating C notes imply 2 missing Csharps?
Will this cause future problems?
We need to find the correct number of notes to fit the Tzolkin.
The present series of notes may be the correct one.
We have many temperaments to choose from and many notes in each scale.
260 / 52 notes is an even 5
260 / 12, 17, 18, 19, 34 (phi based) or 54 notes does not come out even.
To: MetPhys@aol.com
Subject: Tzolkin Music Grid (Luigi)
Date: 07/15/02
From: MetPhys@aol.com
To: luigi.di-martino@ntlworld.com
Sent: Sunday, July 14, 2002 10:10 PM
Subject: MetPhys- Musical Problems, Tzolkin 20x13 Grid (jpg)
OK this 20x13 Tzolkin Grid is the way I imagine it, with a few problems,
Do the 2 repeating C notes imply 2 missing Csharps?
Will this cause future problems? >>
D/Bb
E/Ab etc
We need to find the correct number of notes to fit the Tzolkin.
The present series of notes may be the correct one.
We have many temperaments to choose from and many notes in each scale.
260 / 52 notes is an even 5
260 / 12, 17, 18, 19, 34 (phi based) or 54 notes does not come out even.
To: MetPhys@aol.com
Subject: Tzolkin Music Grid (Luigi)
Date: 07/15/02
To: luigi.di-martino@ntlworld.com
Subject: Tzolkin Music Grid (MetPhys)
Date: 07/16/02
To: MetPhys@aol.com
Subject: Tzolkin Music Grid (Luigi)
Date: 07/16/02
To: luigi.di-martino@ntlworld.com
Subject: Tzolkin Music Grid (MetPhys)
Date: 07/16/02
I've been studying your Tzolkin Music Grid (99.62.4) and have noticed a few things you might be interested in.
To: MetPhys@aol.com
Subject: Turkish Maquam System and more info (hoopoe)
Date: 07/17/02
S=semi-tone
¿= b3rd interval
To: MetPhys@aol.com
Subject: Crystal Symmetry (Luigi)
Date: 07/17/02
From: MetPhys@aol.com
To: luigi.di-martino@ntlworld.com
Sent: Friday, July 12, 2002 11:11 PM
Subject: MetPhys- "The Binary Resonant System: Re: Question..3 dim."
3 dimensional bifilar windings.
Posted by HDN on 1/17/2002, 10:49 am
165.121.206.253
To: luigi.di-martino@ntlworld.com
Subject: Crystal Symmetry (MetPhys)
Date: 07/17/02
