Octahedron Unifies Space Time in Ancient Cultures. It does so from an Earthly viewpoint. First of all, what is an octahedron? It is one of the 5 regular polyhedrons. The other 4 are the tetrahedon, icosahedron, cube and dodecahedron. However you view any one of them, it is totally symmetrical. . Together they are also called the Five Platonic Solids. How is the octahedron identified? By its number corners, edges and faces. It has the following:
These total 26 topological features. See the featured picture above
The octahedron has a non- identical twin brother (or sister). It is called a cube. They don’t look alike. But consider this. The cube has:
The twelve edges are the same in both. Whereas, the number of faces and corners trade places. They are as closely connected as twins. The octahedron pictured below contains a cube. The 6 corners of the octahedron have their points touching the center on the 6 faces of the cube. For that reason, they are called dual polyhedrons.
So How is it That the Octahedron Unifies Space Time?
Unfortunately, the Egyptian Library at Alexandria was burned down. Its wisdom describing prehistory was destroyed. Both the cube and octahedron were considered to be harmonious figures. This thought actually goes back to at least 11,000 B.C. Why harmonious? Because of the numerical relationship of its topology.
12 is one-third greater than 8
6 is one-third less than 8.
Eight is the number that defines the musical octave. That is the most harmonious and fundamental overtone of the entire overtone series. Guy Murchie thoroughly explains this in his two volumes of The Music of the Spheres.
How Does This Knowledge Date Back to Prehistoric Times?
The holiest sites of antiquity were designed as cubes or square base pyramids. The square base upright pyramid is found in the top half of the octahedron. Although the bottom half is not there, it is implied. As a cube, the Biblical Holy of Holies was set in back third of Solomon’s Temple. The total rectangular perimeter of the temple was 60 x 20 cubits. The 20 x 20 cubit back third becomes cubic. Also, the Ka-aba in Arabic literally means, cube.
Much of the world order of antiquity was destroyed. The cause was invaders from Afghanistan. The invaders were called Kurgans. Riane Eisler discusses this her The Chalice and the Blade.
What was the purpose of these Holy Sites? – To spread harmony and peace throughout the world. This was effected by their geometric harmony. Since many were destroyed, war has ensued. In unity we find peace. In division we find war. The octahedron unifies space time. It defines space as a geometric form. How does it define time? Each vertex of the regular triangles holds 60°. The 4 upper triangles of the octahedron have a total of 12 vertices. 12 x 60° = 720°. The lower 4 triangles total 12 vertices. They also total 720°. The upper 4 triangles represent the 720 minutes in 12 hours of daytime at the equinox. The lower 4 triangles represent 720 minutes contained in 12 hours of nighttime also marked by the equinox.
Conclusion: Look for harmonious models. Base civilization on these models. Peace follows. The ancients did in through geometry. The same can also help us today.
Civilization Has a Key Number – Six Hundred and Sixty (660). It is mostly known as the number of feet in a furlong. In the featured picture distances for horses are usually marked by furlongs. A furlong is a measure of distance in imperial units and U.S. customary units equal to one-eighth of a mile, equivalent to 660 feet, 220 yards, 40 rods, or 10 chains. Six hundred and sixty also specifies a musical tone: Diatonic E in vibrations per second. Ancient instruments have been unearthed. We know how their tones vibrate.
In Civilization the Furlong and Farming Once Went Together With Racing Horses
Originally a furlong represented the distance that a team of oxen could plow a furrow (a long shallow trench in a field), on average, before they had to rest. This was also the length of an acre, which in Anglo-Saxon times was considered to be 40 × 4 rods (660 × 66 feet). A furlong appears to have been used as a horse racing measurement because in early days racing took place in fields next to ground that had been plowed. Therefore, the distance could be assessed quickly by comparing the racetrack with the number of furrows made in the neighboring plowed field.
Where Does Number 660 Stem From?
660 appears in two prominent ways. I was shown this by an American Indian spirit around Oquaga Lake. The poetry she spoke to me is below. When she made her introduction, our family was residing at Bluestone Farm. It said: “If you wish to know the secrets of antiquity, erase the lines on this number square. Read them by three or two numbers at the time. Do it as I will show you. At that time I was a full time pianist for the Scott family on Oquaga Lake
The same 660 can be reached with the double digit vertical totals when added in a similar manner.
660 is a Prominent Feature of the 5 Platonic Solids
The hidden 660 also runs parallel to the 5 Platonic solids. The core number is “5”. Of the solids, the tetrahedron has 4 faces. The cube has 6. An octahedron has 8 faces. The Dodecahedron has 12. The icosahedron has 20. Add them together by their squares: 4² + 6² + 8² + 12² + 20² = 660. If you studied the blogs, here is what becomes apparent: Neolithic priests knew the 3 x 3 number square as the stamping mill of the Universe.
Characteristic numbers where converted into set musical tones. Our A-440 comes also from this square. Add the perimeter two numbers at the time. Overlap them: 49 + 92 + 27 + 76 + 61 +18 + 83 + 34 = 440. Treating the numbers diagonally in the same way gives you the same total again. The ratio of the musical 5th for civilization is set out by this number square:
660/440 = 3/2 which is a diatonic fifth.
660 and 440 were made congruent with diatonic A and E by our ancestors.
Conclusion: Making our civilization harmonious was key to the founders of culture. The musical fifth is a “perfect” interval. Let us reinfuse our culture with “harmonious peace” as referred to by the Oquaga Spirit:
Fifth is Basic to Music Throughout History. A pentagon has five vertices. A fifth encompasses five consequtive tones in the scale. Parallels through by number were sought between two seemingly dissimilar things. Similarities were considered a higher form of knowing. Today, looking for differences is now the main thrust. Differences were also considered in prehistoric times. They were not as important as the similarities. This is graphically pictured on the Tree of Life. It is the central figure of Kabbalah. Here is how they are pictured: Understanding(3) is Biyna. Wisdom (2) is Chokmah. Therefore in looking for similarities, you were closer to the source than in looking for differences.
HOW DOES THE MUSICAL INTERVAL OF THE FIFTH TIE INTO THE TREE OF LIFE?
Again, by number. The Tree has 3 vertical pillars. They are headed, from left to right, by numbers 3,1, and 2. These numbers define the “perfect” intervals. The two notes of the octave vibrate in a 1 to 2; or 2 to 1 ratio. On the Tree, this is Kether to Chokmah. For, example, the lower octave of A-440 is A -220. The octave is considered the first perfect interval. The second perfect interval is the fifth. It vibrates in a 3 to 2; or 2 to 3 ratio (for the lower fifth). This is defined by Chokmah to Binya. The frequency ratio 4:5 is called a major third, and 5:6 is a minor third. A minor sixth is the interval which together with a major third, makes an octave. Its ratio is 5:8. A major sixth together with a minor third also make an octave. The major sixth’s ratio is 3:5. These relationships are also pictured on the Tree of Life by emanation number. A system of meditation based on the numerical musical intervals on the Tree of Life is thereby illuminated.
Reviving Antiquity. We are proud and pleased to announce we are refocusing our energies into two websites. Our web posts on DSOworks are currently at over 260 blogs. DSOworks will now be directed toward music, the performing arts and theater. All subjects relating specifically to antiquity will have its own website: revivingantiquity.com. Poetry by the Oquaga Spirit will appear on both.
REVIVING ANTIQUITY THROUGH MUSICAL TONES IN A NEW VISION OF PEACE
In the forgotten past was strong bond between music and architecture. From musical instruments dating from the 2nd and 3rd millenium B.C., we know vibrations per second of their pitches. These vibrations were translated by building designers into numbers of measurements prominent in their particular sites. A prime example is Stonehenge on the Wiltshire plains.
There were three main building phases, each between about 3100 BC and 1950 BC. The first circle, ~3000 BC, was made of timber. The post holes for the timber have been found. Around 2600 BC, the builders gave up timber in favour of stone. Most of the construction took place between 2640 and 2480 BC.
On page 127 Michell discusses how: The 17 surviving stone pillars are still suported by six curved stone lintels. He further states: As it once was, the circle of sarsen lintels was “one of the most exact and symmetrical works …ever created. The width is taken as 3,52 feet by many metrologists. Also, the distance from its center to the outside heel stone is 264 feet. Here are some its parallels to music:
The old diatonic “C” vibrates 264 times/second.
The old diatonic “F” vibrates 352 times/ second.
In closing: Our new website, revivingantiquity.com, will refocus on the unity art and science once share through number squares. Keep checking on its progress. The goal of the site is to work at redirecting mankind to a harmonious existence as once was envisioned in our forgotten and lost past. This, of course, is no small task. But as Hillel said: “If not now, when?”.
Sing to the Lord all the Earth ref. Johannes Kepler. First of all, most of us have an idea about the Lord. Who was Kepler? Johannes Kepler, (born December 27, 1571, Weil der Stadt, Württemberg [Germany]—died November 15, 1630, Regensburg) German astronomer who discovered three major laws of planetary motion, The ones were will consider in are: Laws 2: The time necessary to traverse any arc of a planetary orbit is proportional to the area of the sector between the central body and that arc. It is known as the “area law.” Law 3: there is an exact relationship between the squares of the planets’ periodic times and the cubes of the radii of their orbits (the “harmonic law”). Harmonic? Does the Earth have song? Do we need a new song? The Psalms continually refer to a “new song.” If we do, what exactly is wrong with the old one?
Psalm 33:1-22Shout for joy in the Lord, O you righteous! Praise befits the upright. Give thanks to the Lord with the lyre; make melody to him with the harp of ten strings! Sing to him a new song;
Psalm 96:1 Oh sing to the Lord a new song; sing to the Lord, all the earth!
For the Earth’s musical motif as per Kepler, we have “Mi, Fa, Mi”. He stated this stood for “Misery, Famine and more Misery.” In this regard, the psalms are what we need. They can eliminate this condition. It would be a worthwhile undertaking to sing this new song. Enough negativity. Read the psalms and join the happy chorus in the featured picture! Best of the holidays from DSOworks.com Isaiah 42:10 – Sing unto the LORD a new song, [and] his praise from the end of the earth, ye that go down to the sea, and all that is therein; the isles, and the inhabitants thereof.
Fifths of Tones Sets the Future and was the Neolithic Standard. Why the featured picture? The answers are all on the piano keyboard. Piano playing develops a talent for working with numbers. The solfeggio of the fifth set the way for the building of Neolithic temples. In Close Encounters of the Third Kind, the tones Do and So are the 5th. Do to So are a prototype for all fifths. The ancient temples used specific diatonic tones. The fifth relationship (3 to 2 ratio) was there. The only difference was the set specific tones. They were the fifth of A to E in Neolithic times; not the C to G as pictured on this staff.
Ancient diatonic tones had a primary fifth. The lower was set at A-440 vibrations per second. The higher was E-660 vibrations per second. Various historical cultures set the numbers of these tones into their own units of measure. Instruments dating back to the Sumerian times have been found. We know of their vibrations per second.
Neolithic cultures thrived on number squares. That’s what I have blogging about on DSOworks. Please read them all. This is lost knowledge that I have found. They also had knowledge of the hidden number codes on the 3 x 3 number square.
Consider the 3 x 3 number square by double numbers: First we view horizontally: (49 + 35 + 81 + 94 + 53 + 18) + (92 + 57 + 16 + 61 + 75 + 29) = 660. Now view vertically: (43 + 95 + 27 + 34 + 59 + 72) + (83 + 15 + 67 + 38 + 51 + 76) = 660. That numbers our diatonic “E”.
Consider the perimeter of 3 x 3 number square by overlapping double numbers as: 49 + 92 + 27 + 76 + 61 + 18 + 83 + 34 = 440. Reverse the numbers and get the same total. That numbers our diatonic “A”.
We have just found the following: (1) The lower diatonic “A” 440 of the fifth. (2) The higher interval of the fifth. That is, E- 660. Many readers are experiencing this information for first time. Please recognize that Neolithic, priestly ancestors knew this over 6,000 years ago. How did I come by this knowledge? On Oquaga Lake an Indian Spirit from the Lennie Lenape tribe was anxious to share her wisdom with me. Below is a free sampling of her poetry. Enjoy!
Eight and Its Harmonic Usage by Even Ancient Civilizations. There’s nothing ancient about our newest CD. It’s a hit with ballroom dancers from across the country. I wrote the music and Sharon is the skillful arranger. Our daughter, Kathryn Parks, is dancing with Charlie Logan. We worked many years in the Catskill Mountains. Like the movie, Dirty Dancing, ballroom dancing is big in the Catskills. I, David Ohrenstein, composed, the music. Wife, Sharon Lesley Ohrenstein is the orchestrator and arranger. Ballroom dancing and ballet use the 8 bar phrase. An eight bar phrase expresses a complete thought in music. Skip to My Lou is an example. However, its use in music goes back to earliest times.
First of all Egyptians and Greeks called 8 an harmonious number. The basic octave of 8 notes is the strongest musical overtone. Here’s an experiment.
All tones have overtones: They are notes that vibrate sympathetically. Usually they can’t be easily heard. The primary note is so much stronger. Yet, the octave is the strongest overtone of any note. Here’s how to hear one. Go to the piano. Press the “C” above middle “C” down. Press it silently. Then, play the middle “C” and release it. Keep holding the higher “C” down. You’ll hear the silently struck higher “C” quite strongly. This octave is the fundamental overtone. Other overtones are also there, but weaker.
The top note of the octave vibrates in a 2 to 1 ratio with the lower. In the diatonic scale of the ancients the lower middle “C” vibrated 264 times per second. The higher was double, or 528 times per second.
So Where’s the Harmonic Number Eight?
Here’s another bit of old technical knowledge. Eight was actually called an harmonic number. Why, you might ask? Music was venerated by the ancients. So was the cube. Temples were built or concieved by this form. Examples are the Heavenly Jerusalem, the Holy of Holies in Solomon’s Temple, and the Ka-aba. Now, note the following
The cube has 12 edges. It has 6 faces. That’s the musical octave’s two to one ratio (12 t0 6). So where is the harmonic 8? Count the corners. They total 8.
Ancients said 8 was harmonic because it is 1/3 larger than six (6 + 2 = 8). It is 1/3 smaller than twelve (12 -4 = 8). It brought the octave together by the same fraction (1/3). Finally, back to the keyboard. Look at one “C” to the next. The octave contains 12 half tones (count the black and white keys). It also has 6 whole tone intervals. The notes are bridged by the 8 tone “C” major scale. These are the white keys from one “C” to the next.
Keep checking our products page on DSOworks.com. I offer piano lessons in Sarasota until I start playing piano in Boca Grande at the Gaparilla Inn. We will also be posting a number of upcoming events. In the meanwhile, I’ll keep on blogging.
Sexagesimal Mathematics Fuses Yin and Yang by Number. Civilization supposedly began in the 3rd millennium B.C. with the Sumerians. What is not known is this: Their math is an extension of numbers 5 and 6. Five is yin. Six is yang. John Michell, in City of Revelation, page 73- talks about the history of the rose and lily. The 5 petalled rose symbolizes yin. The 6 petalled lily symbolizes yang. This belief held firm through the Middle Ages.
Eightball: Understanding the Significance of #8 This topic, by necessity, will requite many blogs. In the game of pool sinking the 8 ball in a pocket, can make you win or loose the game. Being a composer/pianist, I will mainly cover the use of #8 in music with my first blog. The first fundamental overtone of music is the octave. This tone sounds at the same time as the octave “overtone” of its lower note. Although it’s softer, it still can be heard. The ratio of the speed of its vibration of the higher to the lower is 2 to 1. Count the white keys under the outstreched hand in the picture below. There are eight white keys.
Go to piano.
Depress the higher “C” with your thumb(as in the picture) without making a sound.
Keep it down.
Then depress and play the lower “C”. It is being played by the “pinky.”The two notes are pictured above
You will then hear the formerly quiet higher “C” resonate quite strongly and clearly.
The white keys, from the fifth finger to the thumb, define the “C” major scale. Major and minor scales are defined by eight tones. So are the more ancient chruch modes. These include the dorian, phrygian, lydian, aoelian…Scales are at the basis of playing any instrument. I offer piano lessons in Sarasota. Now, back to number 8.
A complete musical thought or phrase has 8 bars of music. That gives it stablity. Think of the nursery rhyme “Mary Had a Little Lamb”: “Mary had a little lamb, little lamb, little lamb. Mary had a little lamb. Its fleece was white as snow.” These words cover eight bars of music. This is an example of musical sentence.
In the realm of chemistry eight also has special properties. Eight electrons in an atoms or shared by compounds in the outer shell does the following:
It stablizies any compound.
It defines a “period” on the periodic chart. Or, it makes for totally stable or inert element. Similarly, a period stablizes or completes a sentence.
Eightball and its Mystique of “8” are also in the World’s Religions
Buddha taught of the eightfold noble path. It led to enligtenment. In Islam a fascinating parallel exits between music and heaven. This is in the belief that there are 7 hells and 8 heavens. The title Hasht bihisht ( 8 paradises) is used several times in Persian literature. This I found in the book, The Mystery of Numbers by Annemarie Schimmel. I worked with maestro Rubinoff and His Violin as his arranger. Any musical idea that only had 7 bars sounded “wrong.” Eight bars sounded correct. That always turned out to be the case. Rubinoff was extremely successful as an arranger and violinist. While at Wayne State University, I was a music major. I also was Rubinoff’s accompanist and arranger. Conclusion: Get on the “eightball”. Learn to enjoy life, and feel fulfilled. Most important: partake of music- David.
Harmonic Ideal in Marriage, Partnerships and Friendships. Pythagoras stated the harmonic mean (average) “was one of the most divine endowments.” He relates how it is found in music, nature, the heavens, flowers, hills, moving animals and even the waves of the sea. Pythagoras was reputed have have worked extensively with this “new” mathematical ratio”. The harmonic mean was considered the most subtle. The average mean is the even split of two numbers into halves.
The arithmetic mean is the average of any two numbers. The two numbers chosen for this blog are twelve and six. Add them together: (12 + 6= 18 ). When split into two equal parts they equal 9.
The valued harmonic mean of 12 and 6 is 8. Here’s how and why it was extremely important to the ancient Greek and other civilizations.
An Explanation of the Harmonic Mean and its Importance to Civilizations of the Past
With the harmonious average I am blogging about, each number bends towards the other in proportion to its size. Thus 12 reaches to number 6 in the same proportion that 6 reaches to twelve. It works like this:
Take 1/3 off of number twelve. Then it equals 8. ( 12 – 4 = 8)
Increase the size of number 6 by 1/3. Then it also equals 8. (6 + 2 =8)
The harmonic mean of 6 and 12 are both 8!
So how does this concept help in Marriage, Partnerships and Friendships? With this type of balance, one number bends to the other in proportion to its size. Smaller people usually do not have the physique and stamina work as hard as a larger person. It takes much more effort on their part. The arithmetic mean does not consider the smallness of #6. It does not balance at 8 in harmonious existence. Rather with the arithmetic mean, it needs to work harder to balance number 12 at the assigned number of 9.
So Why the Featured Picture of the Cube?
This blog has been about how numbers 6, 8 and 12 express the harmonic average or “mean”. The cube is the embodiment in a solid figure of this harmonious relationship. It has 6 faces, 8 corners and 12 edges (see featured image). This is the reason that the most sacred temples and visions of mankind were conceived as cubes. These temples are a reminder to place the element of harmony into daily living. Certainly, the Ka’aba of Islam, the vision of the Christian Heavenly Jerusalem in the Book of Revelations, even the Holy of Holies in Solomon’s Temple were cubic. Harmony in relationships is based, in this regard, on one thing: Kindness, mercy and consideration for the smaller on the part of the larger. Of course, sometimes and under some special circumstances (age, illness) the smaller may have to work more than the larger. That is why Pythagoras stated the harmonic mean (average) “was one of the most divine endowments.” It gives the people the blessings of mercy in all relationships.