Randomness of the 12 Tone Technique Also Applies to our math. The initial proponent of this technique was Arnold Schoenberg (1874–1951), Austrian-American composer. The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded as often as one another in a piece of music while preventing the emphasis of any one note through the use of tone rows, orderings of the 12 pitch classes. All 12 notes are thus given more or less equal importance, and the music avoids being in a key.
Randomness of Music and Numbers
Our modern use of numbers parallels the 12 tone technique. The 12 tone technique is best described as willful randomness. Antiquity thought of numbers one to nine as belonging to a system. It was called the 3 x 3 number square. In our music that is set in the circle of fifths, this is called a key signature. The numerical key signature of the ancients was the vehicle of the number square. They favored 7 primary number squares. This could equate with 7 key signatures. The simplest and first was 3 x 3. Their favored squares ranged from 3 x 3 to 9 x 9. They did use higher numeric squares. However, the basic 7 were most common. Sacred prayers in Judaism coded higher number squares. Two favored ones were 13 x 13 and 17 x 17. I have blogs on this subject on DSOworks.com. Some 10,000 years ago, and maybe further back in time, all numbers belonged to unified systems. They were also connected to words. For example, “order” could be 264. Each symbol of the ancients represented a letter and a number. There were no separate letters and numbers. Their unity called by a Greek name, gematria. Look it up online. At one time there was no randomness. You can sample ancient unity on the 3 x 3 number square picture below.
Any two opposite numbers around the perimeter total 10. Examples are 4 + 6= 10 ; 9 + 1 = 10; etc.
The average of any two opposite numbers around the perimeter is 5. Five is the core number.
Each number contributes to a perimeter whose total around #5 equals 40.
The total of all the numbers on the square is 45. . (That equals the sum of the numbers from 1 to 9).
Each number is set so that any row of three totals 15. This is true vertically, horizontally or diagonally.
The high level of organization of numbers in antiquity is staggering. Today, with our modern sciences, we totally lack such an organizing system for our numbers. I believe that result is social conflict. The genius of Arnold Schoenberg made a powerful musical statement as to where our culture was heading. Let us return to the way of the ancients. Reviving number squares is what many of my blogs are about. Enjoy the illuminating sample of the 12 tone technique below!
My blog traces the history of “to the nines” to prehistoric times. Number squares were of prime importance. What set the concept and pattern of the number squares in motion was the smallest. It is referred to as the grain of mustard seed in the Bible. It uses the numbers one to nine. Nine becomes the maximum. Higher numbers are synthetic. For example: Ten is the total of any two opposite numbers around the perimeter of the featured picture. Examples are 9 + 1 or, 3 + 7. They combine two or more numbers in set patterns. Ten, in the distant past, did not exist as an independent number. In musical terms repeated patterns on different tones is called a sequence. They musically demonstrate a property we will study in number squares.
J.S. Bach Concerto for Two Violins in D minor, first movement, bars 22-24
Ancient Burial Sites Used the Perfect Fifth Ratio 3/2. Many Neolithic cultures placed the numbers of harmonious ratios of musical intervals into their buildings and environment. How can musical intervals possibly apply to burial sites? What was the purpose of seeking harmonious intervals for interment? Where and when did this happen?
The tradition belongs to yin-yang concept of the ancient Chinese
The ideal was the 3/2 ratio. Three parts yang to 2 parts yin. 3/2 defines the musical interval of a perfect fifth. The higher note vibrates 3 times; for 2 of the lower.
The tradition characterizes ancient burial sites in China. I found what I thought was such a location in Wiki commons. It is pictured as the ALMATY, KAZAKHSTAN. See featured pictured above.
The fifth has always been considered a perfect interval. In Western music, intervals are most commonly differences between notes of a diatonic scale. The smallest of these intervals is a semitone. In music, an interval ratio is a ratio of the frequencies of the pitches in a musical interval. For example, a justperfect fifth (for example C to G) is 3:2. There are only 3 perfect intervals in our scale system. They are the octave, fourth and fifth. They are called perfect for the following reason: They vibrate in whole number ratios from 1 to 4. They sound the most harmonious. Major and minor intervals vibrate with higher number integers. Note the following list:
The interval between C and D is a major 2nd (major second).
The interval between C and E is a major 3rd (major third).
The interval between C and F is a perfect 4th (perfect fourth).
The interval between C and G is a perfect 5th (perfect fifth).
The interval between C and A is a major 6th (major sixth).
The interval between C and B is a major 7th (major seventh).
The interval between C and C is a perfect 8th (perfect octave).
Ancient Burial Sites share the 3 to 2 Perfect 5th ratio with other disciplines
(1) Microbiotic cooking uses the 3/2 ratio for healing. It advocates 3 foods that grow above the ground in addition to 2 that grow under.
(2) Chinese geomancers detect yang and yin currents. Yang is the blue dragon, Yin is the white tiger. Yang current takes the path over steep mountains. Yin mainly flows over chains of low hills. Most favored is where 2 streams meet surrounded by three parts yang and 2 parts yin. That was the spot where Chinese ancient burial sites were built.
Chinese believed that proper burial of ancestors controlled the course of the surviving family’s fortune. Great dynasties are said to have arisen from proper placement of tombs. Also, the 1st action of a government facing rebellion was to destroy the family burial grounds of the revolutionary leaders.
If Ancient Burial Sites are Beyond You, Here’s a Simple Musical Exercise to Help Your Health and Fortune
Twinkle, Twinkle Little Star incessantly uses the interval of the perfect fifth. So does Baa, Baa Black Sheep. Sing the first 4 notes of each. With both nursery rhymes, the interval between the 2nd and 3rd notes is a perfect fifth. You have your choice: (1) Sing the first four notes over and over, Or (2) simply and just sing the 2nd and 3rd notes over and over. Another choice is take piano lessons. Play Mozart.
Musical Inversions Run Parallel to Platonic Solids. Two concepts must be understood. (1) Inversions of triads. (2) The regular polyhedron property called duality. I will demonstrate musical inversions with the “C” major triad. For our purposes, every other note starting with “Middle “C” on the piano. That makes for C-E-G. These notes can be turned around, A.K.A. inverted. Then we have E-G-C and G-C-E. Musical inversions once more returns us to C-E-G. They look and even sound different. But they are still the same basic 3 tones.
Now for the parallel property with the regular polyhedrons. First, we must look at a chart that defines their topological features. Note the octahedron-cube pair. The octahedron has 8 faces. The cube has 8 vertices. The octahedron has 6 vertices. The cube has 6 faces. Like musical inversion, the order changes from one to the next. We could also say the 2 geometrical figures are related like a musical inversion of the “C” triad.
Look at the next pair: The icosahedron has 20 faces. The dodecahedron has 12 faces. Next: The icosahedron has 12 vertices. The dodecahedron has 20 vertices. Again we have a parallel to musical inversion. They may seem or look different. However, they simply re-arrange their topology but the same numbers.
The octahedron can be drawn inside the cube with vertices centered on each face of the cube (picture below). The same applies to the pair of the pair of the icosahedron and dodecahedron (picture below). Again, they are as closely related as inversions of the basic musical triad.
The grandest parallel between our music and the Platonic solids is found between the dodecahedron and our circle of fifths. Our circle of fifths has 12 basic key signatures (not counting enharmonic keys). Each one is located the distance of a musical fifth from the last one. The dodecahedron has 12 faces of pentagons (5 faces). You can superimpose the basic outline of the circle of fifths on a dodecahedron. Conclusion: over 2,500 years ago ancient civilizations thought of architecture as frozen music. Indeed, music and these 5 geometrical solids have strong parallels. To acquire the ability to gain such insights, I suggest musical instruction for our children. Plato said music should be mandatory study until the age of 30.
Neolithic Number Eight Permeates the Great Pyramid of Egypt. Also the modern piano keyboard. Here’s how.
First use of eight (8). The featured picture illustrates an octahedron. It is a symmetrical, eight-faced, triangulated figure. All angles at their corners are 60°. Bisect the featured picture across the square at the center. The bisected octahedron then becomes two square based pyramids. The above I call the positive. The below I call the negative. All square base pyramids imply an attached equal and opposite pyramid. The mere existence of any square base pyramid, implies a counterpart. Granted, the Great Pyramid of Egypt has differing angles. It uses isosceles triangles. But, the extra four reverse-faced pyramid is still implied. When they are joined, the square bases become internal. They literally disappear. There no longer is a separated square base. We have our first usage eight. As, 4 faces (postive) + 4 (negative) faces = 8.
2nd Usage of Neolithic Number Eight
Each side of the square base measures 440 shorter Egyptian cubits. Shorter cubits are 1.718…feet. A more encompassing measure is the Great Cubit. It measures 55 shorter Egyptian cubits. Thus each side of the Great Pyramid of Egypt is 8 Great Cubits. 440⁄ 8 = 55. Reference John Michell, The View Over Atlantis. Therefore the Great Pyramid is 8 x 8 Great Cubits.
Neolithic Number Eight and Musical Octaves on the Piano Keyboard
Last, but not least. We will tie the Great Pyramid into concert note A-440 and its octaves. Its essential measures come from octaves of the concert note A 440. A higher octave doubles the vibrations per second. The lower octave cuts them in half. The lowest note on the 88-keyed piano is “A”. It vibrates 27.5 times per second. On the Steinway below, it is the furthest note to the left.
The musical keyboard of a Steinway concert grand piano
Here’s the connection. The height of the Great Pyramid is 275 cubits. Neolithic builders freely multiplied and divided by 10’s. This is because 10 ten was considered a synthetic number in antiquity. Reason: It totaled any two opposite numbers on the 3 x 3 number square. Diagram is below. 4 + 6 = 10. Or, 9 + 1 = 10. Etc. We now have the following:
The note A, underneath Steinway’s name, vibrates 440/per second.
The lowest note on the piano, also an “A” vibrates 27.5 /second.
The length of any side of the square base on the pyramid is 440 cubits.
The height of the truncated Great Pyramid of Egypt is 275 cubits
Suite Sonata or are Sonatas No Longer Sweet? In my blog this means is the sonata form no longer sweet or in vogue? Let’s define our two featured terms. Firstly, I must state that by sonata, I mean the sonata form. Here are the two terms with definition:
Suite: In music, a suite (pronounce “sweet”) is a collection of short musical pieces which can be played one after another. The pieces are usually dancemovements. The French word “suite” means “a sequence” of things, i.e. one thing following another. In the 17th century many composers such as Bach and Handel wrote suites. In the Baroque period, a sonata was for one or more instruments almost always with continuo. A continuo is mostly not used in the sonata form of the classical area. A continuo means a continuous base line.
Sonata form, also known as sonata-allegro form, is an organizational structure based on contrasting musical ideas. It consists of three main sections – exposition, development, and recapitulation – and sometimes includes an optional coda at the end. In the exposition, the main melodic ideas, or themes, are introduced. After the Baroque period most works designated as sonatas specifically are performed by a solo instrument, most often a keyboard instrument, or by a solo instrument accompanied by a keyboard instrument. Quite frequently, the older baroque “sonata” was performed by a group of instruments. The term evolved through the history of music, designating a variety of forms until the Classical era, when it took on its own specific importance.
The Sonata form was, in a way, a rebellion against the musical vehicle of the suite. Styles in fashion, furniture, music, manners etc, change in cycles. The earlier Beethoven sonatas used the sonata form. His later extended sonatas are more of the freer Romantic era. Most agree that Beethoven was the transition composer that launhced that Romantic era of music.
Suite Sonata or Are Sonatas no Longer Sweet?
I predict that styles, taste and music, the Suite will rise above other forms. Suites are perfect form carrying beautiful melodies. Each number in a suite can carry its own melody. This was the practice of the romantic era. The Holberg Suite by Grieg is such an example. As a composer, I love the form of sites. Here are 2 examples of my compositions:
The Dance of the Zodiac- with numbers for each of the 12 zodiac signs.
The Ringling Suite- inspired by paintings at the John Ringling Museum in Sarasota, Fl.
The Elemental Suite depicting the ancient belief in Earth, air, fire and water as elements.
Conclusion on Suite Sonata -The future will give sweets to the Suite.
Glamorous Returns for Dress and the Arts. Even with the Great Depression, the 1930’s was the era of escapism and glamour in the arts. Hollywood starlets adorning billboards. It was also the golden age of of radio entertainment. I worked with David Rubinoff and His violin. He was featured on the Eddie Cantor radio program in the 1930’s. His music and style were glamour personified.
Glamorous returns with the beauty with ladies clothing styles. Simple classic, flowing lines. Nothing elaborate. You could almost say simplicity makes the style: Just as the lyrics of Irving Berlin declare in “Play a Simple Melody”.
Won’t you play some simple melody
Like my mother sang to me
One with a good old-fashioned harmony
Play some simple melody
Yes, beautiful is back. Romanticism is back. J.S. Bach and counterpoint are back.- Both were popular in the Romantic era of Music.- Melody is back. Three cheers! How about the Berlin lyrics of A Pretty Girl is Like a Melody?
A pretty girl is like a melody
That haunts you night and day
Just like the strain of a haunting refrain
She’ll start upon a marathon
And run around your brain
Glamorous Returns At Last!
Why do we need glamour now? First, it is not an overly expensive style. Unless, of course, you buy designer. The patterns use simple lines. For a competent sewer, that means less time spent on complicated lines and seams. When times are tough, as they are now, the last thing we need is the grundge look. Go to any major metropolis. With so many homeless, it is common to spot so many that have the look of hardship. It was even more commonplace in the early 1930’s. The depression originated in the United States, after a major fall in stock prices that began around September 4, 1929, and became worldwide news with the stock market crash of October 29, 1929 (known as Black Tuesday). Between 1929 and 1932, worldwide GDP fell by an estimated 15%. We need happy. We need melody. We need pretty girls. We need glamour once more. No more doldrums.
Requiem for Rock and Roll with the Passing of Chuck Berry. Charles Edward Anderson “Chuck” Berry (October 18, 1926 – March 18, 2017) was an American guitarist, singer and songwriter and one of the pioneers of rock and roll music. With songs such as “Maybellene” (1955), “Roll Over Beethoven” (1956), “Rock and Roll Music” (1957) and “Johnny B. Goode” (1958), Berry refined and developed rhythm and blues into the major elements that made rock and roll distinctive. The quote below is from NYT dated March 18, 2017:
Berry in 1957
Requiem for Rock and Roll
The following is an excerpt from the New Yorks Times. This quote below is from NYT dated March 18, 2017. Jon Pareles, a music critic for The New York Times, reflects on the pioneering music and attitude of the rock legend Chuck Berry. ” While Elvis Presley was rock’s first pop star and teenage heartthrob, Mr. Berry was its master theorist and conceptual genius, the songwriter who understood what the kids wanted before they knew themselves.”
As a teenager, I, David, was ousted from Rock and Roll central. I had an interview at Motown with Marvin Gaye. At the time I was giving Motown’s attorney’s children piano lessons. My compositions have always been melodic to the “nth” degree. Rhythm was in. Melody was okay, but quite secondary. Bottom line: Times are now difficult. The public needs beautiful once more. Kind of like the early 1930’s. Think of “Stardust.” It was the leader song that gave the 20’s rhythm songs their requiem. Here’s what most people do not realize: Rock and roll has outlasted the entire era of classical music. The heyday of classical style was 1750 to 1800. That is 50 years. This included Mozart, Haydn and early Beethoven. Above is a picture of Chuck Berry. It is dated 1957. That is 60 years ago. The only thing for sure is change. I unhumbly state: “Watch for my music. I intend to be at the forefront of the new style with new and beautiful music. This is not only as a piano player, but as a composer”. My wife, Sharon Lesley Ohrenstein is the book writer and lyricist. Shortly, our new musical “Golden Roads” will be making an appearance. In this free youtube presentation Sharon is singing and being interviewed. I am at the piano. In the meanwhile you can hear me play on vintage Steinways at the Gasparilla Inn on the exotic isle of Boca Grande. This is my 8th season. I’m under contract until April 16. Watch this short interview and excerpt from Golden Roads. Enjoy the new sound we are presenting and get on the bandwagon. There’s room for everybody.
Triad Trinity and Temples Play Tick-Tack-Toe. Musical Temples Become a Reality in Tick Tack Toe Design. Here’s how: Right below is a blurry picture of the tick tack toe board blueprint that includes the basis of both the Holy Temples in Jerusalem. The First Temple based on the middle row of 3 vertical boxes. That corresponds to the pictured middle, vertical row of the C – E – G triad. On the 3 x 3 number square, that relates to 9-5-1. The Second Temple was built to include the entire nine-boxed tick tack toe board. The 2nd temple extends the dimensions of the 1st to the left and right of 9-5-1. The First Temple was 60 x 20 cubits. According to the Tanach (Hebrew for Bible), he 2nd temple becomes 60 x 60 cubits.
Judaism and much of the beliefs of sacred antiquity springs from this 3 x 3 board. It becomes apparent when the boxes are filled with numbers one to nine arranged so that any row of three totals 15. These 9 boxes, in a parallel way can also hold the 9 tones of the primary triads that define a key.The triad trinity is named (Vertically left to right) tonic, dominant and sub dominant. In the key of “C”, the tonic is C-E-G. It rests on the central vertical row of the number square pictured below. Thus:
The triple-boxed shape of the 1st Temple is likened to the middle 9-5-1 row of the 3 x 3 square.
The dominant of G-B-D occupies the same position as the 2-7-6 to the right.
The sub-dominant of F-A-C. occupies the same position as 4-3-8 to the left.
When used in combination, a triad trinity can be seen as outlining the boundaries of the 2nd Temple. They also define the primary triads of C major. The grid can hold the three primary triads of any key signature. These three key defining triads comprise 9 tones altogether.
Triad Trinity is, Top to Bottom and Vertically Left to Right- Sub Dominant, Tonic, Dominant
So Where else in the Grid Do We Find the Concept of Musical Temples?
The same grid that was the foundation of the two Jerusalem Temples sets the basic diatonic musical interval of the fifth by vibrations per second. They are A-440 and E- 660. Take the numbers two at the time. Go around the perimeter either way. Here is how to find the A-440: 49 + 92 + 27 + 76 + 61 + 18 + 83 + 34 = 440. Here is how to find the E- 660. You get the same sum either vertically or horizontally. (49 + 35 + 81) + reversed as 94 + 53 + 18) + from the other side: (29 + 75 + 61) + and again reversed (92 + 57 +16) = 660.
The basic musical interval from which ancient and modern musical systems is the musical 5th. Our more modern music uses key signatures of the Circle of Fifths. Ancient music used individual tones derived by the actual fifth. The key or core number of the 3 x 3 number square is 5. Any other number placed in the center destroys its symmetry. This is the basis of its sacred order.
So How Did I Discover This Approach to the Trinity of Triads?
There is an American Indian spiritual presence on Oquaga Lake in the Catskill Mountains. For years I had been the piano player at Scott’s Oquaga Lake House. This spirit would accompany me on walks in wilderness. I call on it by the name of the Oquaga Spirit. On my product page of DSOworks I have some 80 of her poems. It is called, The Oquaga Spirit Speaks. I also have a free thumbnail of me reading the spirit’s poetry. It is on the front page.Here is a sample couplet: If it’s life you wish to live and enjoy to the marrow, then get thee a walking stick and hear the morning sparrow.
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.