From: MetPhys@aol.com
Rediscovering Gravity and Force by Paily
Luigi,
If you would like to keep John Paily's ratios in mind, this is his page.
You and Paily use similar language and seem to use similar music ratios and concepts so I thought you might understand what he is talking about when it comes to gravity.
I want to discuss his ratios and compare them to what you know because I have always been interested in gravity and its musical harmonics and we never know what we will learn when comparing the works of two intelligent people.
MetPhys@aol.com
From: luigi.di-martino@ntlworld.com
Hi
Thanks for the cool link which is just the sort of reading I need. The diagrams don't seem to want to show , which is a real pity. All I get is big areas of white screen. So I just been reading little bits. I can see that there are correlations already!
I sent you something about the elements chart the other day. This showed how the overtones and undertones spring forth from an axis point. It showed that, as G was born (dominant) in the overtones, the F was born in the undertones. From the axis point the G is 3:4 and the F is 4:3. I described these points as the beginning of the duality. Well maybe that's a bit far stretched. What may be closer to the truth is that they are first 'gate' points, the beginning of the sharp/expansion and flat/contraction journey. And as John says they are like two arms that wind onwards and eventually come back to the same point. The actual non-involved aspect to this creation resides between the F and G, and it is the 4.5 position. That could be likened to the balanced point, whereas around that non-involved centre is the heartbeat action of Nature expressed as points of ratio around the 4.5. It is funny that someone finds the true 'uninvolved' axis by beginning at the 'involved' axis (C). Perhaps that has to be our starting point because we are creatures of duality looking for our still Neutral centre. Plus the uninvolved is related to the number 9 (4.5 at either side of mirror =9), whereas the C is related to the number 1, a beginning for another one of them cycles I am desperate to get off!
The Lambdoma chart will clarify some of these ratios and put the mirror scales into clearer perspective too.
Luigi
From: hoopoe@popd.ix.netcom.com
Hello Met-
Sorry its taken me a second to get back to you; nyc really keeps one hustling.
I decided just to private email you this info which would be the turkish maquam system of music. again thanks for the exchanges I hope you can make some good use of this info, maybe you already 'know' about it.
I'm still a bit confused as to how to approach the example you gave me and just how Pond is viewing this info, but I'm very interested in the science of sound, resonance, and vibration, and I have noticed from your web site you have major 'math skills' and have explored this through many facets.
So here it is:
Comma = 23 cents
2 series.
Starting at C a line below the staff we have:
Series 1) C G D A E B F (raised 5 commas) C (raised 5 commas) A (lowered 4 commas)E (lowered 4 commas) B (lowered 4 commas) F (raised 1 comma)
Series 2) C F Bb Eb G# C# F# B (lowered 1 comma) E (lowered 1 comma) A (lowered 1 comma) D (lowered 1 comma) G (lowered 1 comma) C (lowered 1 comma).
You will notice every note in series 1 has its "Siamese twin" only one comma lower in series 2; so basically we have a 12 note systems with 2 'versions' of each note, one slightly higher then the other.
This is the work of H. Sadettin Arel (1880-1955) and Dr. Suphi Ezgi (1869-1962).
I've studied Arabic/Turkish classical and folk musics for the last 6 years. also West African rhythms and musics (I spent 3 months in west Africa studying and playing/performing). I play reeds (saxophones) flutes (specializing in the ney), oud, guitar, djembé, and mbira. I've recorded and played with Ronald Shannon Jackson's Decoding Society, tenor players Dewey Redman, Pharaoh Sanders, and morrocan sintirist Hassan Hakmoun, I've studied with Bassam Saba (principal ney player for Marcel Khalifi and Simon Shaheen), Tidjiani Bangoura, and Abdul Aziz Touré.
I've also read the book by cousto and keely's stuff, also childress's anti-gravity & the world grid, also as I mentioned to you once before on a thread I've read most of R.A. Schwaller de Lubicz's stuff including the whole of The temple of Man which I am re-reading/studying; I'm afraid I'm not up to par in the 'math' department, but I do find his whole 'number' approach much more exciting and interesting then how I remember being 'taught math' in school and I am trying to get more into this 'head'. Again I would think you would find his work interesting and possibly useful in some way with your endeavors, maybe he's 'old news' as I'm not up on whatever the current 'cutting edge' is in this 'field'. Intuitively I feel that the 'science' of music is practically the 'science' of phi, 'generation' and basically life and love. In my compositions and improvisations I am very focused on all of this and I really enjoy the affinities I'm finding through it.
_T
From: luigi.di-martino@ntlworld.com
Hi
I do love these coincidences that are happening! I just handed in a paper on Berber Music (from Morocco) where I had to find out about their scales and practices. I look forward to hearing some of Mr Tuttle's insights. I notice straight away that the two series are all the note pairs. If you run the two series in parallel it shows the same note partners as those around the C axis.
I know why everyone likes to start from the note C and not A! It is because C, as a Major scale, has no sharps or flats in its Key Signature. Yet what I don't know is why the F note of this first series shouldn't be F# instead.
<< Series 1) C G D A E B F (raised 5 commas) C (raised 5 commas) A (lowered 4 commas)E (lowered 4 commas) B (lowered 4 commas) F (raised 1 comma)
Series 2) C F Bb Eb G# C# F# B (lowered 1 comma) E (lowered 1 comma) A (lowered 1 comma) D (lowered 1 comma) G (lowered 1 comma) C (lowered 1 comma). >>
The note partners running parallel are:
C/C
All of them correspond except from the F onwards. So is the first series about diatonic movements? I don't think so because it looks as though the first series is attempting a circle of 5ths whilst the second series is moving in an anti-clockwise manner and creating a circle of 4ths at the same time.
It could be that the first series starts as a circle of 5ths and then, in order to remain a diatonic sequence, drops the F# and replaces it with an F. It would be nice to see that chart that's for sure.
Talking of charts you may like to check out the Cosmology section on Dale's site (section 4). You'll see the Mode Boxes there drawn in a circular fashion with a very interesting result (talking of the phi spiral).
Luigi
From: hoopoe@popd.ix.netcom.com
Met-
Thanks for the quick reply. Yes I read this link before.
Some thoughts:
Some thing I notice is statements like this: "from a vibrational sense, theDorian is where Light and Dark meet and become balanced." and
" It is a gateway in fact for the 'marriage' of the male/female." etc. I have no real reference point for judging what they ultimately refer to, although I respect that everyone has there own "speak" so to speak...um no pun intended, really and I'm sure I do too... and I can see he knows his subject well and I feel the enthusiasm and openness.
I understand the symmetrical nature of the dorian mode. I'm note sure if I'm making a correct correlation here, but to me I 'intuitively' think and feel this as a 'closed circuit' : a circle not a spiral. Within 'music' this phenomenon is not as 'all encompassing' as again say the cycle of 5ths. It would seem to be a 'node' type 'station' in my minds eye.
I believe his 4.5 reference is basically the tri-tone (yes the infamous 'devils' interval) which divides the octave in 'two'. What happens when we cycle this 'interval' in 5th/4th's with non-temperment from a fundamental, then do the same from a another fundamental a major 9th above, or lets say a non-tempered 5th above, or 1 comma below, or maybe using the Maj/minor intervals of a Major chord, what kind of 'mapping' do these relationships produce? Does this sound interesting to you? Sorry, no pun intended.
"There is a Triangle of Frequencies found in the Major scale when it is
'mirrored' (the formula is reversed starting from the same root note). This triangle includes the three Dorian Modes -222. "
What ends up happening here is we have 2 major scales a major third apart; C major played from C and Ab major played from the M3rd or phrygian mode. A complete cycle of major 3rds is always 3; here it would be Ab C E ..Ab etc. The 'resonance' of this structure is best 'heard' in my opinion in the wholetone scale of which there are 2. Notice the addition E is the Major 3rd in the C scale. How about we cycle this in non-tempered 5ths/4ths, then do the same here as my suggestion above with the tritone?
I'm not sure what he means by the "three dorian modes" unless he is referring to the 3 modes built from the cycle of thirds I've explained above. But I wouldn't think of them as 'dorian'.
Sorry this is all I can share at the moment I'm running out of time. I hope its a good thing, and I apologize in advance if I'm completely misunderstanding anything here or being redundant.
You can forward my emails to luigi and I hope its a positive or at least
unbothersome contribution.
Thanks again.
_T
From: luigi.di-martino@ntlworld.com
Hi
Here is the link:
You may like to know that this diagram was the result of my posting the 'alternative' explanation of Keys to Dale, where the Dorian is seen to produce the sharps and flats needed for the 12 Major keys in symmetry. Phi Spiral?
Dale used my explanation of the Dorians in order to include it in his own explanation of the law of One.
Luigi
----- Original Message -----
Oh yes!! Send the link to Dales site that has your Mode Box in a circle.
Robert
From: luigi.di-martino@ntlworld.com
Thanks for these notes. Some of the suggestions I must say I would not have the know how to take on but I would be really interested to see any results one would produce. Some of the things I say sound a bit, well you know, I know exactly what you mean! Yet it's all there but one must scrape away at the sand before coming to an educated decision as to what it is they see. If this structure were not consistently perfectly symmetrical I doubt if I would want to put myself here at the moment!
<< What ends up happening here is we have 2 major scales a major third apart; C major played from C and Ab major played from the M3rd or phrygian mode. A complete cycle of major 3rds is always 3; here it would be Ab C E ...Ab etc. The 'resonance' of this structure is best 'heard' in my opinion in the wholetone scale of which there are 2. Notice the addition E is the Major 3rd in the C scale. How about we cycle this in non-tempered 5ths/4ths, then do the same here as my suggestion above with the tritone? >>
It was awesome in my eyes to see the seed of three in the mirror! No Major scale is alone bless it! It has a 'mirror thread' triangle existing there. The witness to this triangular set up is in the Mode Boxes and even the overtones series. Threeness is in the scales. Even when only two are visible the third is playing a hidden role (usually at the b5 interval). It was precisely the fact that this tritone was called the intervalis diablos that perhaps people forgot to research it. Jazz musicians seem to thrive on the rule of the b5 substitution.
This whole tone scale I call the Circle of Tones. I don't like calling it the WTS because it reminds people of a six note scale. The circle of tones is the six major keys that are exposed in the Mode Box. They are not a tone apart at that stage, they are in the form of two triangles. Again 'triangle' is used for the word triad. Yes the triad is C Ab E, all movements of Minor 6ths (and not major 3rds). Yet these are three Major keys and not notes so I just got into the habit of calling them the Triangle of Keys. Because they have this 45 degree angle and 666 connotation and can resemble two stars of David (this is because the major scales break down to 4 possible triangles) I like the word triangle that's all! Plus the scales have three points , so again triangle is implied.
It took about seven years of research on and off to finally realize that one triangle was female and the other male. The female was not so much made that way by any relationship within the outer layer of the mode box, but underneath the skin where the nuts and bolts are it plays this Dorian role with the first triangle which is male. I expect a lot of people will think I'm pretty cuckoo but I think only this symmetrical structure exists! It really isn't of anyone's finding as it simply is there. It is there even if one use the harmonic series and not scales.
The more experiments threw up the same structure the more I wanted to know why it was there. It was because of the 9 number sequences.
If you can bear another diagram this is like a psychedelic effect the number 9 has on the Mode Box.
It creates a leaf effect. The conflict is one of 9:8. The 8 steps of the major scale completes its cycle before the 9 number sequence cycle. This spillage of One tone is why it is a 45 degree progression across the mode box. Each strand of the leaf is only one Mode going on forever in both directions. For example, there will be a string of Phrygian Modes on one of the arms stretching out at 45 degree, whilst on the other side of the mirror will be a string of Ionian Modes. It is interesting that 9:8 is also the ratio for a Tone (equal temperament ).
Anyway yapped on enough. Hope you like the picture!!:-))
Luigi
From: luigi.di-martino@ntlworld.com
Hi Robert
I know I write a lot but I wanted to show you this. As the whole tone scale has been mentioned there is a very subtle axis interplay within it. This diagram is taken from a Microsoft Word document and I have had to take three snapshots of it.
The F and B points prove to be the Lydian/Locrian Points which prove to be the tri-tone that lives within the scale of C. This is not the same as the tri-tone between C and F#. F# does not belong in the key of C, Only at one point between all the notes in C Major is a tri-tone created and that is between F and B (or B and F). The most awesome thing , in my eyes , happens when the F and the B are inserted into the Whole Tone Scale. The reason it is awesome is that the Whole Tone scale (or the Circle of Modes) is about the invisible tri-tone relationship. So to be able to imprint the visible and invisible this way is quite astonishing.
The diagram shows how F fits into this WTS and becomes axis point. It won't happen with any other note. Then the B fits into the other possible WTS. This is those two flows I told you about. When the WTS and Major scale are run parallel it shows where they part ways:
C D E F G A B C
At F there is a departure of ways (but the thread is not broken because of the symmetrical link). It is at B that the original flow is reestablished. So the flow meets one of the circle of tones. It is conjecture to say one flows anti-clockwise to the other.
F and B are found to be catalysts in quite a few experiments. One is to go through the circle of 5ths but to take both sides of the mode box into account. So one starts with a chord like Cmaj7 for the 1, then moves to the mirror side for the 4 chord (DbMaj7). Then a step to the next line and beginning on the right find the 7 chord, then go to the left for the 3 chord, etc all the way round the circle. One needs to go through the circle of 5ths twice. The whole thing gets repeated on the next position of the Major scale, the D note. This translates as Dmin7 for the 1 chord and the whole process continues. The dual chord sequences are always a tri-tone apart. Plus it is only when the cycles are run from F and B that perfect symmetry exists between all the chord changes.
Unless you tell me otherwise I'll send you the second and third diagram from this document.
Luigi
From: luigi.di-martino@ntlworld.com
Summation Tones, Fibonacci numbers and the augmented triangles:
C 1 + C 2 = G 3
After the summation tones of G E C there is a continual flow of the augmented triad. The notes are approximate. The first augmented triad produced within the summation tones is A F C#. Then Bb F# D,B G Eb, C Ab E etc.
What has happened I think is that there is a polarization to this Minor 6th interval, or perhaps that 2:3 equation. The fact that the Fibonacci numbers flow along with this may be the reason this happens. Isn't there a polarization to PHI within the numbers ? Only the first move from G to E is that of a Major 6th. After that there is a constant leaning toward the Minor sixth.
Luigi
From: MetPhys@aol.com
Luigi,
Cellular Automata is a discovery that points to a universe that acts like a computer algorithm or a simulation. It is said in cellular automata that, "If it cannot be modeled on a computer, it isn't physics".
I noticed a similarity in the quote below, and your Diagram of the Mode Box Leaf Effect (GIF)
I see a possible direct analogy of the "rules", below, and the leaf effect "cells" of your Mode Box. In other words, I would expect to eventually see that each note representing each "cell" of your Mode Box, behaves under those cellular automata rules.
Can you see it? If so, please feel free to elaborate the possible correspondence, musically.
************
From Wolfram:
" I (page author) haven't read the book itself, but I've read a lot of descriptions, excerpts, and reviews, *and* I did a lot of experimentation/reading on cellular automata (this is what Wolfram is exploring) back around 1980 when Conway's "Life" automata was all the rage.
Short form: If you divide a space (planar, 3D, or otherwise) into an
array of "tiles" (e.g. the squares on a checkerboard), and choose a set
of possible states for each tile (e.g. on/off, black/white, 1/2/3/4,
etc.) there are a huge number of possible "settings" for the space as a
whole -- practically an infinite number.
Now if you pick a "rule" that all tiles obey which determine under what
conditions a tile will change from one state to another every "clock
tick", you have a "cellular automata". Each tile acts as an independent
"cell", which is "automated" by the universal rule. Traditionally, a
rule can consider only the current state of the cell in question, and
the states of the cells immediately surrounding it (i.e., touching it).
Conway, back in the late 70's, discovered that if you use a checkerboard tiling, two cell states ("live"/"dead"), and a very simple rule:
Death If an occupied cell has 0, 1, 4, 5, 6, 7, or 8 occupied neighbors, the organism dies (0, 1 neighbors: of loneliness; 4 thru 8: of overcrowding).
Survival If an occupied cell has two or three neighbors, the organism survives to the next generation.
Birth If an unoccupied cell has three occupied neighbors, it becomes occupied. Then the results are very "lifelike" in behavior. And pretty much impossible to predict. It's also possible to construct "machines" that consist of many tiles working together to form stable patterns and/or actions.
For a marvelous visual demonstration of
Conway's rule in action "
MetPhys@aol.com
From: luigi.di-martino@ntlworld.com
Hi Robert,
Well I'm having a good peek! Both systems could be born from the inherent symmetry point of view. 9 steps versus the 8 in a musical octave is what creates the steady shifting of one tone at a time . I see a lot of correspondence in that Java animation on the web page. It's all a bit freaky if you ask me! These cells are like vibrations coming together are they not?
Survival If an occupied cell has two or three neighbors, the organism survives to the next generation.
Perhaps this is to do with Octave Slicing. Together with the one occupied cell there are either 3 or 4 cells. Cutting the octave into 3 produces three Major 3rds, or the Augmented triad. Cutting the Octave in 4 produces Minor 3rds, or the Diminished 7th chord. Both these chords are perfectly symmetrical.
C Ab E (C) Ab E C
C Eb F# A (C) Eb F# A C
The diminished chord even shows why the 4.5 position (F#) is another axis point.
Cutting the octave in three or four would make a bit of sense because it would only introduce one movement and then allowing symmetry to double, treble and quadruple it.
The question arises in my mind why not cut the octave into six or seven or even twelve? Surely that would produce life too. Yet these other combinations don't have the power of 3rds perhaps, which seem to be such building blocks.
Nature wills creation based more on harmony than overcrowded dissonance. Take London for example, I wish somebody would! Harmonic strands of 3rds (6th implied) injecting life at that 45 degree angle perhaps.
Anyway just downloaded one of those cell automation programs to play with!
Luigi
From: luigi.di-martino@ntlworld.com
Hi
That last diagram on the Marko Rodin page reminds me of this one I drew for the Circle of Tones. As stated, I call them this but sometimes I slip and call them the Whole Tone Scale Structure but what they are, are the six keys that are on the mirror side of the C Major Scale Mode Box.
Also what Gurdjieff says about the 3(mi) and 4(fah) and 7(teh) 1(doh) can have a bigger explanation. These two points are where the Circle of Tones switch.
I have had a growing suspicion that the whole puzzle is centred around the note F. On the piano it is shown as a white key. It is the odd white key out, because all the other keys (except C major) are 'sharp' keys, whereas F is a 'flat' key. What this means is that the Major scales commencing from D E G A and B all contain sharps in their key signatures. F major contains one flat. So if anything the F should be a black note! Either way it is 'swap over' point. The first circle of tones is
C D E F# G# A#
Between E and F there has been a swap for the black notes and travelling to the other circle of tones:
Db Eb F G A B
Each circle of tones has half the white notes and half the black notes. This 'excess' structure is caused by the nine number sequences and I believe it is Nature's way of maintaining the law of One. The differing systems are never seperated. They are held in 'recognition' by the movement of numbers over the movement of scale steps. If you can imagine that character from Star Trek who's name is Gordie, the one who wears those special glasses. If Gordie represented the nine number sequences it would mean that when he looks at a Mode Box he sees the Circle of Tones moving as two flows and a swap over point between them at Mi-fah and Teh-doh. We, on the other hand see the mode box as a collection of vibrations grouping up into Major/Minor pairs.
So, these two points of the scale formula exactly correspond to the results of continual mirroring of Major scales and Modes etc. They (do) not so much visit other octave families as they do provide the access to the flows that tie numbers and scale formulas together. If one look at the left hand side of a Mode Box they will see six major keys (counting F# and Gb as one). So every point of the Major scale has been made an access point to another Major scale family. The first Mode, C Ionian, mirrors to C Phrygian. That is a Mode from another Major scale family. Then we find E Phrygian mirroring to E Ionian, another Major scale. F Lydian is seen to mirror to F Locrian. This mirror mode comes from Gb Major. As you can see all these six Major scales are umbilically linked to C Major, and they become like a circle of Tones (or any other name one wish to concoct!). They are also flowing at 45 degree angles across the left hand side of the mode box. The first list is
Ab C E - Bb - D F# A#
A different axis point is opened up between both triangles (at Bb). This actually opens up another formula. It is in finding this formula and applying it in order to find the other axis points that opens up the journey toward the XXXX signs, which represent the triangles travelling in and out of the mirror point. As stated it is the number 9 that is catalyst and I don't mind backtracking in order to prove this is so.
Luigi
----- Original Message -----
Perhaps Gurdjieff has some insight into cutting the octave?
Robert >>
From: MetPhys@aol.com
Luigi,
I noticed Dale Pond added one extra Ionian scale to one of your Diagrams (fig. 21.1), on the SVP Link (Section 99.59.6)
Do you feel like telling us neophytes why Pond expanded your 7 scale progression to an 8 scale progression with two Ionian scales?
MetPhys@aol.com
From: luigi.di-martino@ntlworld.com
Hi
LOL, it's alright for you but I had to look up the word neophyte!
Not sure how to answer this. Basically somebody wrote in on the forum and talked about monks levitating stones and the use of the Dorian Mode. So I wrote in and told everyone about one of the Dorian Mode's 'secret' functions! So it was seen that the Dorian possessed a strange system where it would bear the sharps and flats for the key signatures. This is more or less the explanation I sent in Section 99.57.7.
No one had really paid much attention to my speil until then and Dale liked the sound of the Dorian having this symmetrical system. Before I knew it I was honored with a couple of diagrams on his site!
The centre of the mode box on his site is basically C Ionian and D Dorian. Then around that are the six Mirror Modes. The other Ionian happens to be the Mode that E Phrygian mirrors to (from the right hand side). So all the mirror modes are there arranged in expansion and contraction, plus C Major and D Dorian.
This is also the type of thing done with the circular chart of the Modes.
Perhaps I should explain the key signatures a little better so one can see how uncanny the Dorian Mode's relation to them is?
****************
As you must be suspecting the Dorian also provides the link between one side of the mirror and the other. It is the only right hand side modes that survives the journey!
****************
This is some of the reading just under the diagram of the modes on Dale's site:
<< In musical note terms we could equate the Passive Neutral to the note "C". In musical key terms we could call the Active Neutral Key of C. All the other keys or modes are born from within the character of the note of "C", including the Key of C; the effect of "C". I submit the Key of "C" is the male (alpha) and Key of "D" is the female (beta). >>
It isn't my business to correct anybody because the absolute certainty is not with me. Yet I do feel Dale hurriedly tried to incorporate the new vision of the Dorian into some understandable context to do with the Law of One. It isn't the key of D which is female, it is the Mode of D Dorian which is the second mode of the C Major scale. This second Mode is where the number 9 falls and so it endows the collection of vibrations there with birth potential. Here is C Major and it's mirror:
C Db Eb F G Ab Bb (C) D E F G A B C
It's a shame showing it like this without any helpful arrows and stuff. The arrangement of notes here can also be seen as starting points for those note's Key signatures. For example, C has no sharps or flats in it's key signature. If you look at the right hand side you will see no alterations in the C scale. The next note, Db has five flats in its key signature:
Db Eb F Gb Ab Bb C Db
The note in symmetrical reflection to Db is the note B, which has five sharps in it's key signature:
B C# D# E F# G# A# B
This is true for all the symmetrical note partners. D has two sharps in its key signature and Bb has two flats, or Ab has four flats and E has four sharps.
This can be seen as a "male' arrangement, in that it is a picture of Major scales about to be born. The C Major scale has adopted another function perhaps. It certainly shows all 12 Major scale roots born in symmetry, key signatures matching movement for movement.
The Dorian is the provider of the individual sharps and flats needed to build each of these Major scales. As mentioned, it starts with F and G. G has one sharp in its key signature, that of F#. F has one flat, that of Bb. These two notes live around the D Dorian axis. The next keys that are born will have the first sharp and flat by default and will also gain another one of each (this is the circle of 5ths). The keys in question will be Bb and D, one with two flats and one with two sharps. The new flat is Eb and the new sharp is C#. Not only has the Dorian provided these in symmetrical pairing but the process has also swapped over the mirror point, so that the sharp is generated on the side of the mirror where the flat had been generated before and likewise for the flat. After this comes the invisible symmetrical pairs, after the note G#. So once the tri-tone is crossed there is also a change from visible pairs to invisible pairs.
Luigi
From: luigi.di-martino@ntlworld.com
Hi Robert
Here's that Lambdoma chart. If you need it to look different let me know. I thought that maybe a link to it underneath the other Lambdoma diagram would help people's eyesight a little when trying to determine the notes.The notes of C Major and it's mirror partner correspond with this table. There's some ratios that don't add up in this chart, like at the 13:5 and 5:13. The notes are F and G, which are mirror partners. Yet the G should be G# in the overtone series of E. One can see at the higher overtones how the notes are really approximations. Also there has been no use of sharps in the chart. It was easier to read using only the flat sign. So notes like Gb are also F#, for example.
Luigi
From: marydrabble@hotmail.com
Hi Robert,
I'm afraid I'm unable to fully articulate what it all means beyond what's already been explained to me. I'm trying to cram up on as much history and geometry as is possible at the moment.
From what I can gather, the key is to line up the staff in the paintings to a line going through the Wood pentagram; i.e. the cross line, not the
points. The guys who discovered this thought it originally only related to
Rennes, but were amazed when they found it also aligned with certain points at Giza. What caught my eye was the position of the hands from Poussin's Arcadia painting, one covering the small pyramid, Menkaure, and one pointing to the Temple of Aida (?). But the major discovery appears to be the fact that the paintings, and subsequent pentagram placement, were hinting at the town of La Borde De L'Auguste in France, which nobody had ever considered before.
As far as what's to be found at both locations ... I'm unsure. Some say that if there was ever any material treasure connected to Rennes, then it's long gone. I heard mention that the Giza reference might point to hidden
manuscriptsÉ Or even the secret to life itself !!!
You might find the following site informative though...
Lovely chatting with you the other day : )
Take care, Mary
From: MetPhys@aol.com
Hi Luigi,
This excerpt may explain a little more about the role of 2/3 in Newtons prism experiments. It goes on to define a 34 note scale based upon the Golden Mean (phi). What do you think?
pdf doc:
AESTHETICS, DYNAMICS, AND MUSICAL SCALES:
A GOLDEN CONNECTION
<< The golden scales.
The construction of a musical scale is then a problem involving approximating irrational numbers by rationals. The mathematical technique to obtain the best such approximations is well known, and consists of writing the irrational number as a continued fraction (Hardy & Wright, 1975).
The golden mean has the continued-fraction expansion
"Unreadable Golden Mean progression"
and the best rational approximations to (phi) are given by the convergents of this infinite continued fraction, arrived at by cutting it off at different levels in the expansion: 1/1, 1/2, 2/3, 3/5, 5/8, 8/13, and so on; the convergents of the golden mean are ratios of successive Fibonacci numbers. The essence of a musical scale is the discretization of the octave. The octave interval is such that the sensations produced by two notes separated by an octave are very similar, and harmonious when sounded simultaneously. This is independent of cultural roots or specific musical training, and is a shared characteristic that seems to be
linked to human physiology.
As the octave is an interval defined by the first and second convergents 1/1 and 1/2 of the golden number, we can attempt to construct a scale by continuing the series, adding the succeeding convergent of the golden mean 2/3. The choice of a note x in the octave interval (1/2, 1) satisfies the minimal condition to have a proportion: we have three elements(1/2, x, 1) that define two ratios, a=1/(2x) and b=x. However, the introduction of this rational number, 2/3, breaks the symmetry of the interval because there are now two ratios defined, a=(1/2)/(2/3)=3/4 and b=(2/3)/1=2/3.
This is to say that there is a hidden solution that corresponds to the permutation of the intervals. If we equate the two ratios, a=b, this gives for x the geometric mean of 1/2 and: x= sqrt1/2. For the geometric mean the two ratios are equal; for the rational 2/3 there is one interval greater than the other and the permutation corresponds to the exchange of these. If we include this hidden solution, 3/4, we reestablish the symmetry as if a mirror were placed at the geometric mean (see Fig. 3).
This palindromic character for a musical scale was first proposed by Newton in his notebooks written between 1664 and 1666. Newton pursued this idea further and presented in Opticks (Newton, 1952) the visible optical spectrum divided into ratios corresponding to those of a musical scale, with the divisions in the form of a palindrome. >>
MetPhys@aol.com
From: MetPhys@aol.com
Dutch Crop Circle Archive Aug 1991, Milk Hill.
Luigi and Gary,
Luigi, if you don't mind, can you give us an interpretation of the mirror words associated with this glyph, in musical terms, and I will post it?
Gary do you have any Alphanumeric analysis of this glyph? If not can you give an Alphanumeric interpretation of the phrases and I will post it.
MetPhys@aol.com
From: luigi.di-martino@ntlworld.com
Hi
Very interesting. One could see their own interpretation no problem in this. Perhaps it's a perfect mirror that brings meaning to everyone's work all in their own private ways. Here's a funny one I found. I will post a more serious one when I can find the right way of putting it.
One word says "C N(ine) U C 11 0" - See 9 and you will see two circles of tones (also tying in with the number 11)! Also Circle of Tones and Circle of Stones imply Stonehenge. Is there an underground Stonehenge where colored crystals are stored which actually hold the key to creating histories?!
Plus the first phrase " U see C Use 7 undertones in 11"! The 11 is the Tri-tone in the harmonic series.
Luigi
From: luigi.di-martino@ntlworld.com
Hi
I can see maybe that there is a centre point connection and the three 11's could point to the Lydian/Locrian tri-tone position ( a 7/4 mirror mode relationship). Or perhaps they may even imply 222. Don't know if this is allowed but I applied the law of octaves to the alphabet. I noticed there were two C's together. That made me think of octaves, so I split the alphabet into 'octave' type groups:
A =1 B = 2 D = 4 H = 8 P = 16
I noticed that one of the letters missing was the U. This interestingly enough is worth 21, which is what G and N equal.
U = G + N = 21
C is also F L X. 3 + 6 + 12 +24 = 45
I is also R. 9 + 18 = 27
21 + 45 = 66
93 appears within the totals when the letters are given there ANV.
11- 21 3 3 21 7(?) 21 -11- 9 3 14 21 3 -11
If there are three 11's above then these add up to 33, which is the ANV of PHI. The 93 can spell out IC. My preference is for it to mean
ONE CHRIST = 111
CHRIST = 3 8 18 9 19 20. There is a hidden 189 in there also.
Luigi
From: MetPhys@aol.com
Luigi quote:
"It all makes sense now - double light, PHI and the 54. The loop does it's visible then disappears like in a tunnel, winds round and comes back out into the visible again."
Luigi, you seem to be talking about a shape that you haven't yet named. You also say that a "loop does its visible" then "disappears like in a tunnel" then "winds round" then "comes back out into the visible again".
So you imply:
1. A loop of something. Is it light?
Are we talking about musical light, upon a surface that is called a torus?
MetPhys@aol.com
From: luigi.di-martino@ntlworld.com
Hi
That reference is about the Dorian Mode's way of distributing sharps/Expansion and flat/contraction to the keys as they evolve through the cycle of 5ths. On the way to the Tri-tone position of G# the sharp/flat pairs are being created on the visible notes of the Dorian. After the Tri-tone has been traversed the sharp/flat combinations are found on the 'in between' positions of the Dorian. I equate this as a swapping over of sides, or as dissappearing into some 'tunnel' (the 4.5 gateway?). This then makes sense of the two Circles of Tones that flow through the Major scale. They are dislodged at the semi-tone positions. The semi-tone positions switch flows of these two Circles of Tones. The sensitive areas are around F and B, which happens to be the Tri-tone interval within the C Major scale.
I constantly have to read the notes I have gathered during the years to make any sense of this in my own mind. I don't know if it sounds anything but cuckoo without the supporting material. There are many other visible/in between (and I love calling it invisible) relationships that can be unearthed by consolidating one step and building another step on top. The whole flow of keys when true symmetry is applied is a dance between these two states.
The way the relationships switch over at the tri-tone can be highlighted in the diagram attached.
rennes3_small.jpg
The poles live in the centre. There comes a time that they are reached and the second cycle of 5ths is generated. B# and Dbb become the new poles and the scales continue to evolve in a circle of 5ths. The difference between this cycle of 5ths and the previous is that Comma. The poles always live in the centre. F#/Gb lived at the centre of C Major. B# and Dbb live at the centre of F#/Gb Major. This continues until 167 Keys have been reached.
In the diagram the numbers above each note represents how many sharps or flats are contained in that note's Key Signature. Here is a quick list:
F and G major = 1 flat/1 sharp
I don't know enough about light to make claims concerning it. However the circle of 5ths evolves according to PHI, but it also evolves according to the symmetrical system within the Dorian Mode. So perhaps it does have an obvious relationship ( Yeah man I'm Light and I'm here one moment and I'm on the other side the next").
The biggest defining feature of all this music and number speil is the 'swapping over' effect. That is all that is seen when mirroring is used. The number sequences swap over, the Fibonnacci numbers as well and the music note pairs.
Luigi
----- Original Message -----
Luigi quote:
"It all makes sense now - double light, PHI and the 54. The loop does it's visible then disappears like in a tunnel, winds round and comes back out into the visible again."
From: luigi.di-martino@ntlworld.com
Hi Robert
I hope this diagram helps.
The numbers above the notes signify how many sharps or flats are in that note's key signature. The first line is C Major mirrored, and the line below is the Dorian mode mirrored. There is also a way of compressing both sides of the mirror into one as shown in the next two lines.
F Major is the first Key to contain a flat as is G Major the first key to contain a sharp. These are found in symmetry around the D Dorian Mode. Therefore the B note gets a flat sign against it as the F note gets a sharp sign. This is the first movement on either side of the mirror.
The second movement in the evolution of keys is from F to Bb on one side of the mirror and from G to D the other. Bb Major contains Eb as the new accented note as D Major contains C# as it's accented note. This pattern repeats itself until the keys with six sharps and the key with six flats are reached. These two keys are F# and Gb Major respectively. These keys have to be found within the very center of the Ionian and Phrygian Modes of C above, at the Tri-tone position.
This then turns the note C into Cb on the mirror side (Cb is an enharmonic of B), and the note E into E# ( enharmonic of F ) on the other side (because F# Major contains an E# and Gb Major contains a Cb)
The only notes in isolation are F and B, which in effect have been represented by their enharmonic cousins previously. It would be possible to superimpose all the information from the mirror side onto its partner side. It would look messy but here is what it would look like. The first scale is C major beginning at the note B and ending on the note D one octave and a minor third above. The second scale is D Dorian beginning at C and ending on E one octave and a Major third above.
As you can see this diagram does indeed link the place of rest with the note E, or maybe more precisely Fb. Or just as like ley in the opposite direction to B#. And so perfect symmetry is seen to appear around the F and B notes.
Although the note B begins the first of the above scales this is only because it is easier to see the over structural elements. We are still dealing with the key of C Major C - C and it's second Mode D - D. The journey begins in the middle at F within the C major scale. This is linked tio the note B in the Dorian Mode which becomes a flat. Likewise the note G in the C Major scale is linked to the note F in the Dorian Mode which becomes a sharp. It is no different to the previous diagram in this respect. In the center is the F#/Gb. F# links with E and turns it into a sharp. Gb links with C and turns it into a flat.
I know this may sound very confusing. What may alleviate the confusion is knowing the twelve Major keys and how many flats and sharps they have in their key signatures. The circle of 5ths explains it.
C = 0
Luigi
----- Original Message -----
Luigi quote:
"It all makes sense now - double light, PHI and the 54. The loop does it's visible then disappears like in a tunnel, winds round and comes back out into the visible again."
From: luigi.di-martino@ntlworld.com
Hi Robert
Check out this diagram of numbers being divided by 7.
This fraction shows quite a few things. Movements in threes and inversions, for example.
Then compare the equation with the doubling of a number sequence as mentioned by Rodin (99.58.3)
1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5
Both are doing the same thing. Here is the fraction obtained when dividing by 7. It will be repeated in order to show the sytem at work:
1/7 = 0.142857142857
You can see by the diagram that 1 and 8 are not only +1 and -1, or number sequence partners of the Vedic Square, but they are also the musical inversions. The movements go in threes. 4 and 5 again are Vedic Square sequence partners but also musical inversions, the same being true for 2 and 7.
Yet an inversion is supposed to work both ways, so that as well as 1 and 8 there is also an 8 and 1. This is what happens when the fraction is repeated. So in all there is, 1+8 - 4+5 - 2+7 - 8+1 - 5+4 - 7+2. And if the fraction were repeated again it would revert back to the first set of pairs.
This is also true for the sequence 1 2 4 8 7 5. As you will also know this is quite a prolific sequence most when numbers into infinity are either continually doubled or continually halved.
1 2 4 8 7 5 1 2 4 8 7 5
Repeating the number shows the same arrangement as with the previous example on the division by 7. The inversions appear when the numbers are taken to moving in threes.
Luigi
Addenda:
The 1 and 8 stay the same in both approaches, like anchor points (or octaves). The movaeable numbers are the inner 2 and 4 and the 5 and 7.
1 2/4 8 5/7
The inner numbers can swivel and this just shows that it happens everywhere if wants to look for it. What does the swiveling in music is usually the tri-tone axis point. It swivels F and G either side of the mirror , for example.
----- Original Message -----
Luigi quote:
"It all makes sense now - double light, PHI and the 54. The loop does it's visible then disappears like in a tunnel, winds round and comes back out into the visible again."
© Copyright. Robert Grace. 2002
To: luigi.di-martino@ntlworld.com
Subject: Luigi's Ratios and Paily's Gravity Ratios (MetPhys)
Date: 06/14/02
To: MetPhys@aol.com
Subject: Luigi's Ratios and Paily's Gravity Ratios (luigi)
Date: 06/14/02
To: MetPhys@aol.com
Subject: Turkish Maquam System (hoopoe)
Date: 06/14/02
To: MetPhys@aol.com
Subject: Turkish Maquam System (luigi)
Date: 06/14/02
G/F
D/Bb
A/Eb
E/Ab
B/C#
F/F# etc
To: MetPhys@aol.com
Subject: Turkish Maquam System (hoopoe)
Date: 06/14/02
To: MetPhys@aol.com
Subject: Major/minor Diagram at SVP (luigi)
Date: 06/14/02
From: MetPhys@aol.com
To: luigi.di-martino@ntlworld.com
Sent: Friday, June 14, 2002 9:46 PM
Subject: Re: Re: 2 Met- Fwd: Major/minor Diagram at SVP
To: MetPhys@aol.com
Subject: Turkish Maquam System (luigi)
Date: 06/14/02
To: MetPhys@aol.com
Subject: Turkish Maquam System (luigi)
Date: 06/14/02
C D E F# G# A# C
To: MetPhys@aol.com
Subject: Finding the triangles in summation tones / Fibonacci (luigi)
Date: 06/15/02
C 2 + G 3 = E 5
G 3 + E 5 = C 8
E 5 + C 8 = A 13 (nearly A)
C 8 + A 13 = F 21 (nearly F)
A 13 + F 21 = C# 34
F 21 +C# 34 = Bb 55
C#34 + Bb 55 = F# 89
Bb 55 + F# 89 = D 144
F#89 + D 144 = B 233
D 144 + B 233 = G 377
B 233 + G 377 = Eb 610
G 377 + Eb 610 =C 987
Eb 610 + C 987 = Ab 1597
C 987 + Ab 1597 = E 2584
Ab 1597 + E 2584 = C 4181
E 2584 + C 4181 = A 6765
To: luigi.di-martino@ntlworld.com
Subject: Cellular Automata and the Mode Box Leaf Effect (MetPhys)
Date: 06/15/02
To: MetPhys@aol.com
Subject: Cellular Automata and the Mode Box Leaf Effect (luigi)
Date: 06/15/02
To: MetPhys@aol.com
Subject: Cutting the Octave and Gurdjieff (luigi)
Date: 06/16/02
From: MetPhys@aol.com
To: luigi.di-martino@ntlworld.com
Sent: Sunday, June 16, 2002 1:20 AM
Subject: MetPhys- Cutting the Octave and Gurdjieff
To: luigi.di-martino@ntlworld.com
Subject: Ponds Extra Ionian Scale (MetPhys)
Date: 06/17/02
To: MetPhys@aol.com
Subject: Ponds Extra Ionian Scale (luigi)
Date: 06/17/02
To: MetPhys@aol.com
Subject: Lambdoma Chart (luigi)
Date: 06/17/02
To: MetPhys@aol.com
Subject: Poussin/Giza/Pentagram (Mary)
Date: 06/17/02
Rennes Mystery Solved
To: luigi.di-martino@ntlworld.com
Subject: Illuminations of the 2/3 Exponent (MetPhys)
Date: 06/19/02
Julyan H. E. Cartwright, Diego L. Gonz«alez, Oreste Piro, & Domenico Stanzia
To: luigi.di-martino@ntlworld.com, CodeUFO@aol.com
Subject: 1991 Milk Hill Glyph Interpretations (MetPhys)
Date: 06/19/02
To: MetPhys@aol.com, CodeUFO@aol.com
Subject: 1991 Milk Hill Glyph Interpretations (luigi)
Date: 06/19/02
To: MetPhys@aol.com, CodeUFO@aol.com
Subject: 1991 Milk Hill Glyph Interpretations (luigi)
Date: 06/19/02
C = 3 F = 6 L = 12 X = 24
E = 5 J = 10 T = 20
G = 7 N = 14
I = 9 R = 18
21+ 45+ 27 =93
To: luigi.di-martino@ntlworld.com
Subject: Question 4- Is the Path of Musical Light a Torus? (MetPhys)
Date: 06/29/02
2. Is the loop actually two in opposite direction?
3. The loop does its visible. Does this imply an outside?
4. The loop disappears like in a tunnel. Does this imply an inside?
5. The loop winds around and comes back out into the visible again.
To: MetPhys@aol.com
Subject: Question 4- Is the Path of Musical Light a Torus? (luigi)
Date: 06/29/02
C and F# Mirrored
CandFmirrored.gif
Bb and D major = 2 flat/2 sharp
Eb and A Major = 3 flat/3sharp
Ab and E Major = 4 flat/4 sharp
Db and B maor = 5 flat/5 sharp
etc:
From: MetPhys@aol.com
To: luigi.di-martino@ntlworld.com
Sent: Saturday, June 29, 2002 12:25 PM
Subject: MetPhys- Question 4- Is the Path of Musical Light a Torus?
To: MetPhys@aol.com
Subject: Question 4- Is the Path of Musical Light a Torus? (luigi)
Date: 06/29/02
G = 1 sharp
D = 2 sharps
A = 3 sharps
E = 4 sharps
B = 5 sharps
F#/Gb 6 sharps/6 flats
Db= 5 flats
Ab = 4 flats
Eb = 3 flats
Bb = 2 flats
F = 1 flat
C = 0
From: MetPhys@aol.com
To: luigi.di-martino@ntlworld.com
Sent: Saturday, June 29, 2002 12:25 PM
Subject: MetPhys- Question 4- Is the Path of Musical Light a Torus?
To: MetPhys@aol.com
Subject: Question 4- Is the Path of Musical Light a Torus? (luigi)
Date: 06/30/02
From: MetPhys@aol.com
To: luigi.di-martino@ntlworld.com
Sent: Saturday, June 29, 2002 12:25 PM
Subject: MetPhys- Question 4- Is the Path of Musical Light a Torus?
