Musicalmile is a Masonic Unit of Measure. Ancient tones of the diatonic musical scale are well known and defined. Their numbers by vibrations per second were also used for measure. Issac Asimov, for one, lists these tones in On Physics. Guy Murchie, in Music of the Spheres, lists the same numbers. Every single tone was used in for measure in the Neolithic goddess culture construction. The general practice was to translate vibrations per second to units of measure that characterized a particular culture. Ancient Greek writers allude to this tradition. They call call architecture frozen music. Goethe elaborates on this quote:
REVEALING THE MUSICALMILE AND OTHER MEASURES FROM ANTIQUITY
“Music is liquid architecture; Architecture is frozen music.”
Here are some tones of the diatonic scale. Vibrations per second of the ascending diatonic scale in the key of “C” . I’ve blogged about a master temple plan that was made from musical numbers. The Indian Oquaga Spirit gave me a vision of the design. The list below from the sources given above:
Middle “C” vibrates to 264 times per second.
D” vibrates to 297 times per second.
E – vibrates to 330 times per second.
F – vibrates to 352 times per second.
G – vibrates to 396 times per second.
A – vibrates to 440 times per second.
B – vibrates to 495 times per second.
C – vibrates to 528 times per second.
These numbers were freely multiplied by 10 when larger measurements were desired. Thus, we have the musicalmile. Many of my blogs are about number squares. The characteristic number of the 3 x 3 square is 10. Any two opposite numbers around the perimeter total 10. Antiquity favored such associations. The 3 x 3 number square was “the grain of mustard seed.” Also, it was considered the numerical square of the ancient god of engineering, Saturn, par excellence. Read my blogs on DSOworks.com
Why bother with all this? At one time civilization had harmony and peace. Lack of warfare was not uncommon in goddess cultures. They existed before 4350 B.C. Riane Eisler covers the subject in The Chalice and the Blade. We are about to return to a Golden Age of peace and plenty. Music will lead the way. That’s why King David was a musician first. Over time, I will blog about sites built by music. Part of this return to a Golden Age is to rebuild or refurbish “musical” sites. We must create a greater awareness of what music and harmony can do for mankind.
Mirrors: The Music is the Mirror. Dancers practice with mirrors. Mirrors are also part of musical intervals. First, any interval when added to its “inversion” totals nine. Tonal qualities of intervals are also inverted when the tones are reversed. . Every major interval, when inverted becomes, a minor interval. Every augmented interval, when inverted, becomes a diminished interval. Interval assume their opposite by sound. Inversion means to reverse the order of the notes. For example, with C to G; when inverted, we have G to C. The fifth is defined by C to G (G-A-B-C-D or five tones, a 5th). Its inversion to a fourth is defined by G-C (G-A-B-C or 4 tones, a 4th). The total of the sample of these two inverted intervals is: 4 + 5 = 9. Only perfected intervals do not change quality when inverted. They remain perfect.
Mirrors are part of the Quality and Quantity of Musical Intervals
Octave (8) inverts to a unison (1), or vice versa (8 +1 = 9)
2nd inverts to a 7th as 2 + 7 = 9
3rd inverts to a 6th as 3 + 6 = 9
4th inverts to a 5th as 4 + 5 = 9
When intervals are inverted, their tone qualities also invert. Thus we have:
Any major interval becomes a minor when inverted. Conversely any minor interval becomes a major.
Any diminished interval becomes augmented when inverted. Conversely, any augmented interval becomes diminished.
Only one type of interval remains the same when inverted: The Perfect Interval. In this manner the perfect unison inverts to a perfect octave ( 1 + 8 = 9) The perfect fifth inverts to a perfect fourth (5 + 4 = 9).
The Five Regular Polyhedrons Behave ExactlyAs Musical Intervals
The octahedron “inverts” to a cube. Look at these two figures. The octahedron fits into the cube. Its six corners can bisect the six mid- faces of the cube.
In a similar way, the icosahedron fits into the dodecahedron. The 12 corners of the icosahedron can bisect the 12 faces is the dodecahedron.
The tetrahedron is the only “perfect interval” of the 5 regular polyhedrons. It is the only figure which can inscribe itself in itself: A smaller and up-side-downed tetrahedron is inscribed by the tetrahedron’s 4 corners into the four faces of its self-dual tetrahedron. When these points are connected. The tetrahedron inside is then up-side-down.
Finally, musical intervals and the Platonic solids share the “rule by nine”. Again, look at the overall picture. The unison is the basic musical interval. The tetrahedron is the basic regular polyhedron. This is for the following reason:
A tetrahedron has 4 triangles. At 180 degrees/triangle, the total degrees is 4 x 180 = 720.
The polyhedron with the greatest number of degrees is the dodecahedron with 6,480. This is exactly 9 x 720 = 6,480.
Conclusion: Musical intervals and the five regular polyhedrons of geometry share the rule of nine. The also share the principle of inversion. Music mirrors geometry.
Therefore, our music mirrors the 5 regular polyhedrons to perfection. When you play music, you are working with the same material that our cosmos is made of. Check out DSOworks.com for many more blogs.
(Above picture: Sharon and I wrote a full two act opera in English on the love that could have existed between Cleopatra and Octavian, who had just conquered Egypt. It presents how Octavian became the first emperor of Rome and a great ruler as a result of their encounter. We own the opera and have the video of the full production.Contact us through the website if you are interested,)
Love Describes God and Creation. The 4 x 4 number square is not only about Genesis, but about our music. Any student of music knows that music is written by phrases and periods as listed below. The 4 x4 number square neatly lays out its composition elements.
The initial phrase is four bars of music.
A half phrase equals its 1st two bars.
A double phrase, also called a period, is eight measures.
The double period is sixteen bars in length.
Each of the 7 known planets of antiquity were connected to their own number square. Author, John Michell, has written extensively about this subject. The 4×4 square was of Jupiter. It is filled with number combinations that are found the Fibonacci series of natural growth. My blogs on DSOworks.com discuss this series. Here is a list of its starting numbers. The higher it goes, the closer the ratio of one number to the next approaches a “Golden Section”: 1,1,2,3,5,8,13,21,34,55… Each new number is the sum of the preceding two numbers. Now, look at the above square as I define the numbers below:
16 + 5 =21
3 + 10 =13
2 + 11 =13
13 + 8 = 21 etc.
Of course, any horizontal row, vertical or diagonal row of 4 numbers total 34, the next Fibonacci number.
HOW GOD IS LOVE
How do these numbers tie into our theme: Love Describes Music, God and Creation? The Fibonacci numbers grow, as the numbers increase, by a ratio called “phi” which is 1.618… to 1. The Hebrew verb for “Love” is אָהַב (Ahav). Next, phi = (√5 + 1) / 2. Here’s the connection between “Ahav” and “phi”. The three letter verbal root for love is Alef (אָ), which is also the symbol for number 1; Hei (הַ) which is also the symbol for number 5; and Veis (ב), which is also the symbol for number 2. As phi ratio is behind the natural growth that nurtures, develops and grows; love does the same. We this in mind, the expression “God is love” becomes most appropriate. Thus, being at one with God is accomplished by- practicing love.
Where did the measure of 2.72 foot megalithic yard, re-discovered by Professor Alexander Thom of Oxford University in the 1960’s, really come from? Thousands of years ago, Plato called 272 the number of harmony. John Michell writes about the subject in his City of Revelation. Thom found this unit at at 600 sites located in England, Scotland, Wales and Brittany. In the 1900’s, Jay Hambridge discovered that the megalithic yard was an extension of the Egyptian remen: The 1.2165 foot remen x square root of 5 = 2.72 feet. Hambridge uncovered the source of numerous ancient measurements by multiplying the Egyptian remen by the square roots of 2,3, 4,5 etc.
MUSIC AND MEASURE
I discovered that many older measurements, including those that Hambridge uncovered are found in the 3 X 3 square pictured above. It was the cornerstone of ancient builders. In my blog on Genesis tunes to A-440, I talk about the hidden number codes. Please follow the numbers on the tick-tack-toe board above: By single digits the perimeter totals 40 as: 4 + 9 + 2 +7 + 6+1 + 8+ 3 = 40. But overlapping double digits, the total becomes 440 as: 49 + 92 + 27 + 76 + 61 + 18 + 83 + 34 = 440 (we still tune to A-440). Overlapping the digits, three at the time, corner to corner, we have 2220 as: 492 + 276 + 618 + 834 = 2220. The formula for deriving the megalithic yard from this number square is: P1 (40) + P2(440) + P3 (2220)/(divided by) P3(2220) times the square root of the central number,5.
THE 3 MATHEMATICAL GEMS ARE HERE
The 3 X 3 magic square can have some different number arrangements, as books on number squares illustrate. John Michell, states that the above diagram is the traditional way it is viewed, Now why is the traditional solution important? Because, other key megalithic measures and mathematical amazements are found when looking at the bottom row horizontally: As the numbers across the bottom are 816 or in reverse 618 we find: (1) One megalithic rod = 81.6 inches (2) One megalithic inch = 0.816 inches. When these three figures are reversed as 618, magically, the Golden Section appears. Ancient sites around the globe used the 1 to 1.618 ratio for construction. After they were constructed by the Golden Section, they were measured by megalithic units. This will be the subject of future blogs. Jericho was such a site. .618 is diminutive expression of the Golden section: 1/1.618…= o.618… Finally the megalithic yard as 2.72 references another mathematical gem: the exponential factor of growth: 2.72 is a close approximation that expresses the limits by which systems can grow. I will save the appearance of pi for another blog. Thank you for your patience.
Music and Temples: David gave Solomon a musical blueprint to build a holy temple How did David come by it? It goes back to Moses. He acquired it from former Egyptian rulers. Then Moses passed it on to the leaders of Israel. It illustrates how musical tones were connected to the arts and sciences by common number. At the crux of the design are six circles that surrounded a central circle; all of equal diameter. The diameter of each of the 7 circles is 352. This number also defines the old (pre-well tempered) musical tone- “F” in vibrations per second of the diatonic scale. Issac Asimov lists the vibrations per second of these tones in his book, On Physics. Guy Murchie lists the same tones as having the same vibrations per second in his treatise: The Music of the Spheres. The types of units by which temples were measured could vary from culture to culture. They could utilize Egyptian remens, Palestinian cubits, Roman paces, or even the English yard- but the numbers had to be the same as the musical tones. The picture of the plan with the digits came into my mind as I was hiking around Oquaga Lake. Here is what its looks like:
SO WHERE ARE MORE MUSICAL TONES FOUND?
On the plan,(1) EG = FC = 440 which defines the musical tone “A”. (2) LK = FE = RQ = 352 which defines the musical tone “F”. (3) DG = DC which defines “C”. (4) DG = FC = 792 which defines the octave higher tone “G”. This plan, steeped in music tones, was used by builders and masons, at one time, in order to keep order and harmony in the world. In my decades of study, I’ve researched measurements of holy sites. Major sites everywhere are built by musical tones. I believe this discovery could provide all with a uniting vision and purpose. This makes the study of music, and in my case, composing music and playing the piano, quite relevant. Also relevant is my piano instruction for those who are genuinely interested in leaning to play the piano. We collectively need to put the muse back in music. Otherwise, we might just end up with the “ic” part.
Being a musician, I developed an aptitude for numbers. Parents should know that study after study concludes that whether playing an instrument or singing ; music greatly increases a child’s aptitude for mathematics. When music is practiced before school, it raises the IQ as much as 10% for the entire school day. In its effect, practicing music is like a multiple vitamin for the brain. An example is Albert Einstein, arguably the smartest man ever, who prided himself on playing the violin.
THE CIRCLE OF FIFTHS AND THE DODECAHEDRON
Our music of equal temperament helped to create what’s called a Circle of Fifths. Every time you ascend five tones in the first scale you can arrive at the new scale that hold the next key signature. After twelve scales by fifths, you complete an entire cycle and go back to the beginning key. You could easily frame the 12 keys of the Circle of Fifths on the 12 regular pentagons that make up the dodecahedron (see picture below), Not only the modern well-tempered scale; but the ancient diatonic scale was based on a series of ascending fifths with a final lower fifth from the starting tone. 5 solids that are regular: a numerical parallel.
HOW THE SCRIPTURE — USES NUMBERS
Music and Math: One helps the other, and how this helped me: I believe that because of my work with music, I was able to uncover a unique number code. Its use was first discovered by emperor Yu, a ruler of China about 2,000 BC. The 5 Platonic solids, pictured below, are totally patterned by code that I discovered. The code is hidden in a 3 x 3 number square, which in China is called Lo shu. The way to crack thelo shu code is found in Isaiah 45:2-3: “I will go before thee, and make the crooked places straight. I will break in pieces the gates of brass, and cut asunder the bars of iron. And I will give you the treasure of darkness and hidden riches of secret places, that thou mayest know that, I the Lord, which call thee by thy name, am the God of Israel.”
SURROUND YOURSELF WITH MUSIC
I believe that my years with music through formal education, private lessons and working with great concert artists, helped me to develop the mathematical side of my thinking. I talk about the Lo Shu, pictured below, on my blog about the The Mysteries of Music Unearthed by Tick-Tack-Toe. Incidentally, the Bible is pointed in the use of scripture number to reveal its preference for this ancient magic square: Not only is 45 the chapter number in which Isaiah’s reference occurs, but 45 totals the numbers in this number square (1 + 2+ 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45). While 2 + 3 ( the two verses in chapter 45) whose numbers when added together = 5. I think that sharply defines of the number square.
“E-660” in Feet Measured the Glastonbury Abbey- Turning the numbers of vibrations per second of the old diatonic musical scale into the numbers of linear measures is one my themes. It demonstrates how builders in antiquity sought to construct by the beauty of musical tones, poetic though it be. Most cannot grasp this concept. We are trained by birth to look for differences. The computer, to my knowledge, also does not grasp metaphors very well. As the popularity of poetry has faded, so has metaphor.
The length of the vesica is defined by BA and the width by PO. The Abbey was placed in the turquoise area of the vesica.
BUILDING BY NUMBERS OF MUSICAL TONES
In a remote undocumented time, builders used the numbers of musical tones for construction. Consider: John Michell, in his View Over Atlantis, explains how 660 was taken by builders to represent the diameter of the Earth. It measures the number of feet in one furlong. Furthermore, one 660 foot furlong equals 7.920 inches. On a inch to mile basis it closely replicates the average diameter of the Earth. This gives the measure of the Earth a tonal or music point dimension. And so it was- in a former age of peace and plenty. The Abbey (image above) first had its dimensions sketched in the vessel of the fish (vesica piscis). The vesica of Glastonbury’s blueprint is the turquoise oval part in the center to center overlapping circles. Each circle has a 660 foot diameter. Any vesicas ratio of length to width length to width is always the square root of three to one. Across many cultures it is considered sacred. It outlines the shape of a fish, so it is also a significant Christian symbol. Historically it has been used by most religions by the builders of sacred sights throughout recorded history.
THE INTERVAL OF THE MUSICAL FIFTH
John Michell, in his works, describes how the Abbey was conceived as the English Jerusalem. Its design was section off into 74 foot squares laid out in a 9 X 4 pattern. The church was placed on a section of this pattern Musically, the complete patter reduces reduces to 3 x 2 which is the sound ratio of the two tones of musical fifth. Michell describes how if a circle with radius 660 feet is struck from the center of the 74 foot system of squares, its circumference passes through the sacred abbey fish pond. Further down its marks Glastonbury’s Catholic church. In a future blog, I will relate how 660 refers directly to the five Platonic solids in a remarkable way.
Mysteries of Music Unearthed By Tick-Tack-Toe. To understand the profound, look to the simple. Pairing by opposites is the way of nature. Understanding complexity is as simple as Tick-Tack-Toe. Grappling with the profound by studying the complex is dead-ended. I believe that’s why Einstein never found the unified field theory of relativity. Children love to play tick-tack-toe. When numbers are set in this board, secret codes come and open the doors to mysteries of music- as well as many other formerly unsolvable problems.
Set the numbers 1 to 9 in this board as pictured so that any row of three numbers equals 15. There are other possible arrangements, but the totals of 15 must always be the same. When added vertically, horizontally or diagonally in a straight line; the total must always be 15. On Oquaga Lake, some 25 years ago, I had an epiphany. There was a bad drought that summer and we had to leave our residence at Bluestone Farm situated on Bluestone Mountain. Our well dried up. As we were packing up to leave Bluestone Mountain, a spiritual presence told me to erase the tic-tack-toe frame. Then keep the numbers in the same position. With this simple act, I could then unlock the mysteries of science and art.
Having pondered over the books of John Michell for years, I memorized his lists measures of the sacred places that he wrote about. Suddenly it came together in a flash of lightning. I touched on this topic on my blog on Music and Measure: Both the A of the modern well-tempered scale and of the old diatonic scale, vibrate at 440 times per second. The old diatonic “E” vibrated at 660 times per second. Both of these numbers are prominent on the tick-tack-toe board. Please watch the above board as I define these numbers.
The numbers of the vertical and horizontal cross by tens each total 440: ( 95 + 15 =110) + ( 59 + 51 = 110) +(53 + 57= 110)+ (35 +75 = 110). Thus, 4 X 110 =440. The X diagonals total 440 in the same manner (45 + 65 = 110) + (54 + 56 =110) +( 52 + 58 = 110) +( 85 + 35 = 110). Now, working around the perimeter two numbers at the time either way, we again find 440 in two ways: Counterclockwise we have: 43 + 38 +81 +16 + 67 + 72 + 29 + 94 = 440. Clockwise we have 49 + 92 + 27 + 76 + 61 + 18 + 83 + 34 = 440.
660, the vibrations per second for diatonic “E”, are found around the number square forwards and backwards as follows: Counterclockwise- 43 + 38 + 81 + 16 + 67 + 72 + 29 + 94 = 660. Clockwise- 49 + 92 + 27 + 76 + 61 + 18 + 83 + 34 = 660. The basic musical fifth, A to E, is found by vibrations per second in of all places, a Tick-Tack-Toe board. After more than 25 years of searching for the source of all our arts and sciences, I am convinced this grain of mustard seed is it. The Great Pyramid, also blogged about here, exists in great measure to define the myriads of ways that the numbers of this grain of mustard seed work. It takes the 440 that is found in four ways in this grid and measures each side of its square base as 440 cubits of 1.718 feet. I am certain that Tick-Tack-Toe will be found as the backbone of civilizations on other planets with advanced life. Stay tuned for more blogs on the subject in the future. Hope you have enjoyed the mysteries of music unearthed by Tick-Tack-Toe.
Music and math share the rule of 9’s. I find this very appropriate because music and numbers also share in usage of the same side of the brain. Words, on the other hand, use other side of the brain. I will first demonstrate the rule of 9’s by music. Then I will demonstrate it with numbers. Inversion means to reverse the order, be it of numbers or the two tones of a musical interval sounding at the same time. A unison inverts to an octave as 1 + 8 = 9. The second inverts to the seventh as 2 + 7 = 9. The third inverts to a sixth as 3 + 6 = 9. The fourth inverts to a fifth as 4 + 5 = 9. Change in the quality ( major to minor intervals or diminished to augmented)) will be the subject of a future blog
HOW ADDITION — USES THE RULE OF 9’S
Now let’s look at inverted numbers. If someone is adding an entire column of numbers in a ledger, once in a while the digits in any one number might be mistakenly reversed. For example, instead of writing 189, you write 198; or instead of writing 235, you write 532. This act is comparable to inverting or reversing musical tones. If what you expected the total to be, as opposed to what it is, differs by a multiple of nine, then you inverted or reversed the digits of the numbers in the manner that I have just demonstrated. Here is the proof: 198-189 = 9. With the second example, 532 – 235 = 297 When you divide 297 by 9, the quotient is 33. Let’s take a larger number: When you record 23,572 as 32,572 the difference is 9,000. That is also a multiple of nine.
In conclusion, since math and music are virtually twins, to study one without the other is like separating these twins, How sad! The study of mathematics must be complemented by the study of music.
Every child in school should be given the opportunity to learn music through piano lessons or musical programs at school.
The point I made above is amply demonstrated by Albert Einstein; a great mathematician who played the violin. The fictional detective genius sleuth, Sherlock Holmes, also played the violin. Arthur Conan Doyle realized the importance of music and how it is a part of superior intellect. One more word on the rule by 9’s. In the highest court of our land, the Supreme Court, we also have a rule by nine. The founding fathers of America were also brilliant.
Albert Einstein is the prototype of the musical mathematician. He played the violin. In his writings he discusses how one the the best moments of his life was one he received a good review by a music critic for playing .
The 4 x 4 number square and music? The meaning of of number squares has degenerated to nothing more than a puzzle or a simple curiosity. In antiquity the magic number square had a multitude of associations. They were of extreme importance. Ancient builders recognized 7 primary number squares. Each one was thought to invoke the power of one of the seven recognized planets. For example: 3 x 3 invoked Saturn. 5 x 5 called on Mars. The 4×4 magic square, pictured below, was said to invoke Jupiter. John Michell, in The View Over Atlantis, points out how the statue of Jupiter at Olympus was built by the numbers of this square.
The wood carving above was done by Albrecht Durer in 1514. It is called Melancholia. The picture on the right is a blowup of a section of the same woodcarving of the angels wing against numbers one and fourteen. The angel is apparently depressed because she is overwhelmed by all her labors. The 4 x 4 square holds the cure for the angel’s melancholy mood. Gustav Holst, in his The Planets, refers to Jupiter as the bringer of Joviality. Don’t worry. Help is on the way for this angel!
Now, how can you invoke this number square through music and get rid of sadness and melancholy? King David was able to cure Saul’s melancholy with music: If each square represents one measure, four measures (the top row) represents the smallest complete unit of musical form. Two phrases are often placed together in a “question-answer format”. Hum the opening of Twinkle,Twinkle, Twinkle Little Star, how I wonder what you are? The first part is the question the second is the answer. Phrases are sometimes placed together to make a 16 bar musical double period. Dancing is often done to units 16 bar measures of music. Joining phrases in such a manner gives the listener or dancer a sense of symmetry and balance. That in turn brings happiness. Viva la music!