Characteristic Number Binders are Plus One. The word “pastries” suggests many kinds of baked products made from ingredients such as flour, sugar, milk, butter, shortening, baking powder, and eggs. Flour and eggs are binders that keep the ingredients together. Number squares also have binders. They are called characteristic numbers. Any two opposite numbers on the perimeter of such a square have a plus one effect on the total. Without these number binders, the number square could not exist. The 8 x 8 number square has 64 “houses”. Multiple perimeters around the center all share the +1 property. On the 8 x 8, the center consists of the four numbers: 37, 28, and 36, 29. Note some of the following 65 sequences. They are all characteristic number binders.
The center is also becomes a perimeter. For, 37 + 28 = 65. Or, 36 + 29 = 65.
Here are some other means of arriving at plus “1” totals of 65: Look at the yellow diagonal. 64 + 1 = 65. Or. 55 + 10 = 65. Again, 46 + 19 = 65.
Look at the brownish-orange diagonal, 57 + 8 = 65. Or 50 + 15 = 65.
Civilizations Everywhere Used 6 and 5 for units of building measure.
6/5 = 1.2 An Egyptian remen is 1.2165 feet.
6 x 5/6 + 5 = 2.727272…A megalithic yard is 2.72 feet.
6 x 6 x 6/5 x 5 x 5 = 1.728. The larger Egyptian cubit is 1.728 feet.
6²/5² = 1.44. One hundred and forty four is a Fibonacci number and a dozen dozens.
6 x 6 x 6 x 6 / 5 x 5 x 5 x 5 = 2.0736. Approximates the Palestinian cubit of 2.107 feet.
(6 to the 6th power) / (5 to the sixth power) = 2.979… By number this isis close to the three foot English yard.
Very important for Central America and the Mexican Pyramid of the Sun: The key unit of measure was the “hunab.” (See Peter Tompkins Mysteries of the Mexican Pyramids). The hunab is 3.41 feet. Again, the invaluable fives and sixes: (5 x 5 x 5) + (6 x 6 x 6) = 341. I took this information from my previous blog called “Measure Proves a Pre-Genesis Citadel in Mexico.” Click on the internal links below for more information
Look at the checkered 8 x 8 number square above. Any two opposite numbers going around the concentric perimeters total 65. The total is always the total number of squares plus one. It can be expressed by characteristic total = n² + 1. John Michell explains how the Great Pyramid of Egypt was based on this number square.
Characteristic Number Binders are the Plus One Part
The question becomes what did the plus “1” represent in antiquity? It represented the unity of all things with the Creator. Thus each ancient number square, through its characteristic number, touches the plus one concept. The one becomes: The “Ultimate“, the summum bonum, the “Absolute Infinite“, the “Transcendent“, or Existence or Being itself. We are about to have another Golden Age. Understanding number squares is one way to illuminate the path.
Characteristic Number Hides a Secret Code. Civilization has lost its touch with the past. A lost Golden Age was all about number squares. Two opposite numbers always totaled the same number. Our featured number square will be the 3 x 3. Its characteristic number is 10. Any two opposite numbers total 10. These include 9 + 1; 4 + 6; 3 + 7; and 2 + 8. First, where did I first learn about number squares? From the writings of British author, John Michell. Many of my blog are about the 3 x 3 number square. Below is an internal link to one of them. I However, I was able to take John Michell’s work a step further. This is because of an American Indian spirit guide from the Lennie Lenape. It all happened on Oquaga Lake (See picture below).
View the square 2 numbers at the time by opposites. Whereas two numbers that cross the center are paired in the same row. Their sum is always 110. Thus, 49 + 61 = 110. Or, 35 + 75 = 110. The 110 can be pulled out of the square in 16 ways. Thus, 16 X 110 = 1,760. The center then becomes 55. It is surrounded by 440
Characteristic Number Square List of Antiquity
The 3 x 3 is 10.
The 4 x 4 equals 17.
The 5 x 5 totals 26
The 6 x 6 is 37.
The 7 x 7 is 50.
The 8 x 8 is 65
The 9 x 9 is 82.
So where is the hidden number code? Take the prime characteristic number of the 3 x 3 number square. Its sum is 10 as described. Next, total the numbers from 1 to 10. They equal 55. You have just seen how the center of the 3 x 3 number square becomes 55 when viewed two numbers at the time. Today many scoff at this. The ancients of a lost Golden Age accepted it. My Indian spirit guide also offered a book of poetry, filled with her wisdom.
Performer Composer Concept is Long Overdue. The idea for this blog came from: The Great Pianists- from Mozart to the Present. It is written by Harold C. Schonberg. He was the former senior music critic for the New York Times. I was quite taken with his text on John Baptist Cramer. What he wrote about can be applied to our current musical situation. From the following, I concluded that Cramer was instrumental in creating our current performer composer dichotomy.
Today, few pianists play their own compositions exclusively in concert. As a matter of fact, few pianists today even compose. It is all about other people’s music. The equivalent in the theatrical community is the entire genre of “tributes.” Thus, we have countless tributes to Rogers and Hammerstein, Steven Sondheim, Leonard Bernstein, etc. Pianists often feature one or two composers in their concerts. Beethoven seems to be preferred. Then comes some of the Romantics like Chopin or Schubert. Regardless, playing ones own music has fallen out of favor. As a result we have tribute after tribute. Sorry, but after a while this becomes “old hat.”
So How Did the Performer Composer Concept Come to be Abandoned?
First, who was John Baptist Cramer? Johann Baptist Cramer (24 February 1771 – 16 April 1858) was an English pianist and composer of German origin. He was the son of Wilhelm Cramer. His father was a famous London violinist and conductor. The family is identified with the progress of music during the 18th and 19th centuries. My knowledge of him is through his masterful book of piano etudes entitled: gradus ad Parnassum. It translates from Latin to”steps to Parnassus”. It is sometimes shortened to gradus. The name Parnassus was used to denote the loftiest part of a mountain range in central Greece. It is a few miles north of Delphi. In Greek mythology, one of the peaks was sacred to Apollo and the nine Muses. It had two peaks. One dedicated to inspiring deities of the arts. The other to Dionysus.
As per Schonberg, Cramer was one of the 1st pianists to feature music other than his own in concerts. He especially performed Mozart and Bach. I personally am a great believer in cycles. With few exceptions, pianist composers have left the scene. Witness the return. I hope to be a leader in this way. Enjoy my compositions at the Gasparilla Inn.
Plato is my friend — Aristotle is my friend — but my greatest friend is truth.
So What Are Ten Eighty Musings?
First, to define 1080. Numbers, in the lost past, had associations. 1080 was lunar and terrestrial. The establish four elements were earth, air fir and water. 1080 was water. It expressed the Moon’s influence on the cycles of nature.With the psyche, it represents intuition. Ten eighty guides the unconscious mind.
So where does 1080 figure into today’s theme? First, let’s look at the ancient attitude to “zero”. It wasn’t a real number. It was synthetic. Ten was a combination of two opposite numbers on the 3 x 3 number square. Therefore, past civilizations could read 1080 as 18. They had the option of reading it as 108.
So how were Ten Eighty Musings Used By Advanced, Lost Civilizations, Including Atlantis?
Day of Week
Note the Moon. Its diameter was taken on 1080 miles. Its metal was silver. Note silver’s standard atomic weight average of 107.8682(2).
Earth Moon System and 27 x 27 Number Square. The barycenter is the center of mass of two or more bodies that are orbiting each other. Earth and Moon have a shared barycenter. As such they are a dual planetary system. Barycenters are an important concept astronomy and astrophysics. This is the case for the Earth–Moon system. The barycenter is located on average 2,902 mi from the Earth’s center. This is well within the planet’s radius of 3,963 miles.
What do things have in common? That was the definition of wisdom in antiquity. Look at the internal link just above. Above, this Moon link applies to our four types of musical triads.
Earth Moon system and the 27 x 27 number square
Four Hundred Fortieth Post Defines Genesis You might want to review the previous post. My current post (441) is simply a continuation. The common Earth based system for both is implied on the 27 x 27 number square. Here’s how:
Look at the core number of this number square. It is numbered three hundred and sixty-five. That defines the days of our solar year. Its core is the essence of any number square.
Look at the white diagonal from #352 to #378. Each each lunation is approximately 291⁄2 days (29 days, 12 hours, 44 minutes, 3 seconds, or 29.530588 days). It is common for the months of a lunar calendar to alternate between 29 and 30 days. There are twelve such lunations. The Lunar year is is therefore 354 days, 8 hours, 48 minutes, 34 seconds (354.367056 days). Both 354 and 355 are included in this same diagonal.
Both the timing of the the Earth and Moon are found the the aforementioned diagonal line. The Earth is the main and central planet. The Moon has its center of gravity on the same diagonal. Likewise, Moon is part of the 365 day Earth based system.
At one time civilization was structured by number squares. It was a time of peace and prosperity. Does that describe the legend of Atlantis? Plato describes in Critias what his grandfather was told by King Solon. Solon heard the story from the Egyptians. Atlantis was a mighty power based on an island in the Atlantic Ocean. Perhaps, over time, they also lost their interaction with number squares? Many blogs on DSOworks.com cover number square mathematics.
New Musical Theory Model Based on the Dodecahedron. We know about the circle of fifths. A quick review: In music theory, the circle of fifths (or circle of fourths) is the relationship among the 12 tones of the chromatic scale. It shows their corresponding key signatures. Also found arethe associated major and minor keys. Musical tones use 7 letters of the alphabet. They are A-B-C-D-E-F-G. These letters repeat over and over to encompass the full key signature span.
At the top of the circle, the key of C Major has no sharps or flats. Starting from the apex and proceed clockwise by ascending fifths. The key of G has one sharp. The key of D has 2 sharps….. Proceed counterclockwise from the apex by descending fifths: The key of F has one flat. The key of B♭ has 2 flats…… At the bottom of the circle, the sharp and flat keys overlap, showing pairs of enharmonically equivalent key signatures.
Click on the above internal link. It offers background on the 5 Platonic solids. The Platonic Solid we are concerned with here is the dodecahedron. In antiquity it symbolized the overall shape of the Universe. By this rational,we live in a musical Universe. As for the featured picture, note: The major keys are written in the center of each pentagon. Start in consecutive order (from C major) from its lower left point. The tone on the lower right completes the 5 tones. In the case of “C” major, it is the tone “G”. This lower right begins the next pentagon. It is completed at “D” …
Ascend 5 consecutive tones with each pentagon.
The fifth tone on the lower right of each pentagon defines the key signature name of the next pentagon. This goes for the complete cycle: “G major, D major, A major…”
The 12 pentagons make the complete cycle at F major. “F” major’s lower right hand tone is “C”. The outline of the dodecahedron is complete at this point.
Ticking Antiquity Though the Prime Number Square. The inner workings behind this number square are responsible for ticking antiquity. Actually, it makes the entire cosmos tick. Though it seems simple, it is infinitely complex. I mean that literally. I now have over 430 blogs on DSOworks.com. Part of these are about music. Many are about ancient number squares. Number squares once bundled a Golden Age of Peace and Plenty. I’ve included a couple of internal links. Looking at these links first might give you a background.
Next, I will post an excerpt from my book, The Staff of God Volume II. It is from page 29. I believe most of the knowledge I gleamed was by Oquaga Lake. My duties there included playing piano for the Scott family shows and other revues. . I was their pianist for some 15 years. It is perched high in the Catskills. A matriarchal American Indian tribe once lived there. A female spirit from the Lennie Lenape was my instructor. As my book of poetry called The Oquaga Spirit Speaks describes her as such: “So much she needed an ear, she ignored my tranquility.”
Ticking Antiquity on Oquaga Lake
Number squares pair opposite numbers in the same system. Two opposite numbers achieve a state of balance through their addition. In the featured picture opposite numbers always total 10. However, doubling or tripling the numbers and totally them was ancient practice. Again, read the internal links. 1 + 9 = 10. Then 11 + 99 = 110. Then 111 + 999 = 1110. These totals straight number reads on the number square. An example being: 492 + 618 = 1110. Or 951 + 159 = 1110. With double numbers, 95 + 15 =110. However, if you read the numbers in curves, they go to infinity.
Worldly Word Reveals Knowledge of Ancient Egypt. This blog is based on one word. It is the Hebraic word for “world.” עולם. How is this possible? In Hebrew letters doubled as numbers. This is also true of numerous Middle Eastern languages. There were no separate symbols for letters and numbers. They shared the same glyph. This commonality is called by a Greek term – gematria:
Gematria/ɡəˈmeɪtriə/ (Hebrew: גמטריא גימטריא, plural גמטראות or גמטריאות, gematriot) originated as an Assyro-Babylonian-Greek system of alphanumeric code or cipher. It was later adopted into Jewish culture that assigns numerical value to a word, name, or phrase. The belief was that words or phrases with identical numerical values bear some relation to each other or bear some relation to the number itself. It can apply to Nature, a person’s age, the calendar year, or the like…
So What’s with the Hebraic Worldly Word that Holds the Egyptian Remen?
The gematria of עולם which means world, is 146: Ayin is 70, vav is 6, lamed is 30 and mem is 40. Thus, 70 + 6 + 30 + 40 = 146. One remen = 14.6 inches. In antiquity numbers were freely multiplied by powers of 10. Their concept of nfinity is blogged about on DSOworks. Also the inch existed in ancient civilizations. John Michell discusses, in his View Over Atlantis, how the standard of weight in the ancient world was the cubic inch of gold. To verify this, simply go to the British Museum. A number of specimens from various regions are to be found there. How did the Egyptian remen also become the 146 gematria for Hebrew word for world as the standard of worldly word measure? As the Egyptian link, the answer is Moses. He would be well versed in Egyptian mysteries.
Musical Quaternity is analogous to the Four Elements. Here are the players:
The musical quaternity for this blog includes melody, harmony, rhythm and counterpoint.
The four elements are alchemical. They comprise earth, air fire and water. On the wheel of the zodiac they each occur in rotation three times. This covers the 12 zodiac signs.
Analogy (from Greek ἀναλογία, analogia, “proportion”) is a cognitive process of transferring information or meaning from a particular subject – the analog or source, to another. It has been argued that analogy is “the core of cognition”.
Air is counterpoint. It represents the quality of reason. Counterpoint requires structure, rules and thought. Alchemists thought that air contains the vital spirits of life. The words for spirit and psyche come from the same Greek word: ” From from Greek psykhe “the soul, mind, spirit; breath; life, one’s life. It is the invisible animating principle or entity. The psyche occupies and directs the physical body; understanding It is akin to psykhein “to blow, cool,” from PIE root *bhes- “to blow, to breathe”.
Alchemist Heating a Pot, by David Teniers the Younger (1610 – 1690), oil on canvas.
Harmony is more like the combined, unified yet undifferentiated background. Harmony is the vertical aspect or sound of musical. It represents the combination of sounds at any given moment. Those qualities parallel water. Counterpoint is the horizontal direction of various lines the harmony holds. The two are thus interconneted. horizontal axis.
Melody is tied to rhythm. You cannot have melody without rhythm. In alchemy, fire represents maximum molecular activity. Earth is minimum activity. It is grounded. With the vertical axis, fire rise. Rhythm gives melody shape and purpose. It provides the substance of melody. They are interconnected as the vertical axis.
Discovering Number Squares in the Shema Yisroel. First, what is the Shema Yisroel? It is an alliteration into English of the name of a key Hebraic prayer. This blog will concern itself with the opening first line.The quote below explains its extreme significance.I believe it harbors the gateway to a Golden Age Age of peace and plenty. The hidden values offer a path to a forgotten, lost universal order that was based on number squares. Wikipedia explains this first line as follows:
Shema Yisrael (or Sh’ma Yisrael; Hebrew: שְׁמַע יִשְׂרָאֵל; “Hear, [O] Israel”) are the first two words of a section of the Torah, and is the title (better known as The Shema) of a prayer that serves as a centerpiece of the morning and evening Jewish prayer services. The first verse encapsulates the monotheistic essence of Judaism: “Hear, O Israel: the LORD our God, the LORD is one” (Hebrew: שְׁמַע יִשְׂרָאֵל יְהוָה אֱלֹהֵינוּ יְהוָה אֶחָֽד׃), found in Deuteronomy 6:4, sometimes alternatively translated as “The LORD is our God, the LORD is one.” Observant Jews consider the Shema to be the most important part of the prayer service in Judaism, and its twice-daily recitation as a mitzvah (religious commandment). It is traditional for Jews to say the Shema as their last words, and for parents to teach their children to say it before they go to sleep at night. Now to the task at hand- discovering number squares.
Discovering Number Squares in this Key Creed of Judaism
As a prelude, in Hebrew letters doubled as numbers. There were no separate numbers. The same symbol represented both. Look up the Greek word, Gematria. To double check the arithmetic in this blog , ask someone fluent in Hebrew. Also refer to the featured picture as I list the Shema’s words and the words with their numerical equivalents.
Shema has a gematria of 410. The 9 x 9 number square has a core number of 41. In antiquity, zero was not only the absence of number, it was considered to be a synthetic number. Look at the smallest number square. The 3 x 3 pictured above. Any 2 opposite numbers on this square total 10. Hence, 10 and its various powers are not their own independent single numbers. They result on this basic number square by adding any two opposite numbers on the perimeter. The 410 was taken as 41. The 9 x 9 number square was called the lunar number square.Here is the spelling of the word Shema: שְׁמַע.
Yisroel has a gematria of 541. By the rules of gematria, plus one was allowed per words in a phrase. I believe the number was 540 plus 1 for the Deity. Geometrically speaking, a pentagon totals 540° among its 5 vertices. Five is the core number on the 3 x 3 number square. It is the seed of all number squares. It ancient Greek it is the equivalent of The Grail.Here is the spelling in Hebrew: יִשְׂרָאֵל
The next word is so important, it appears in two of the basic ancient number squares, Yahweh. This is the unutterable name of God. On the 5 x 5 number square, any 2 opposite numbers on the perimeter total 26. This square is dedicated to the planet, Mars. The Hebrew spelling is יְהוָה
Next word is Elohaynu. Its numerical equivalent is 102. Look at the 4 x 4 number square. It is the number square of Jupiter. The 12 numbers around its perimeter total 102.אֱלֹהֵינוּ
The 2nd use of the sacred 4 letter name of God refers to the 8 x 8 number square. The 8 x 8 and 5 x 5 number squares share common numbers. The 8 x 8 square of numbers was dedicated to Mercury the messenger. Any row of 8 numbers totals 260. On the 5 x 5 number square, any 2 opposite numbers total 26. Without the zero, it is the second reference to Yahweh יְהוָה
The final word, “echad” declares the oneness of God. Its numerical equivalent is 13. The number is at the core of the 5 x 5 number square אֶחָֽד
Discovering Number Squares of Higher Order in these 6 words (and the next 6)
More on Discovering Number Squares: Aryeh Kaplan was a physicist/philosopher. The book referenced here He offers the formula on page 163 for determining the row total. It is also termed the (S)ide total, for any number square:
S = (n³ + n) ÷ 2.
When the double yud spelling is substituted for the four letter name, as it is the custom in prayer books, the sum of the 6 words becomes 1106. The prayer book spelling of the six words is pictured below.
Next, take the 13 x 13 number square. Fit it to the formula: (13 x 13 x 13) + 13 ÷ 2 = 1105. By the ancient rules of gematria one may be added to the value to arrive at the prayer book gematria of 1106. Again, becomes the unity of God. Kaplan discusses how the 13 x 13 number square represents- Chesed or love on the Tree of Life. The next 6 words (see diagram below) are whispered) will be covered in future blogs. It directly points out the 17 x 17 number square. That square is dedicated to Netzach or victory on the Tree of Life. Used together, 13 x 13 magic square and the 17 x 17 display an ancient temple plan. Indeed, Victory is found in Love as all our religious teachers and prophets taught.