Musical sequences

Musical Sequences are Both Universal and Basic

Musical Sequences are Both Universal and Basic. In music, a sequence is the restatement of a motif or longer melodic (or harmonic) passage at a higher or lower pitch in the same voice.[1] It is one of the most common and simple methods of elaborating a melody in eighteenth and nineteenth century classical music[1](Classical period and Romantic music).  Examples of characteristics of sequences:[1]  

Look at the music of the featured picture: The sequence is well known in America, Canada and England. In the U.S. the music is an excerpt from “My Country Tis’ of Thee.” In England it is “God Save the Queen (King)”. Bars 3 and 4 form a sequence with bars 1 and 2. They use the same pattern, only one tone lower. Just as a refresher, here is the British and American music on youtube. The British words are “Send him victories, Happy and glorious.” In America the corresponding words are “Land where my fathers died, Land of the pilgram’s pride.”

Examples of how Musical Sequences are Universal and Basic

God save the King – The national anthem of the British … – YouTube

My Country, ‘Tis of Thee (with lyrics) – YouTube

Musical Sequences Applies to the Sciences

Let’s look at basic scientific sequences. They work on the same principle as music. In Platonic style, here’s two basic groupings of numbers: 3-4-5 and 6-7-8. We have a true pattern for musical sequence operating in math and the sciences.

  • 3-4-5 has geometrical import.  One is the single line that begins the process. The classic example is the 3-4-5 Pythagorean  right triangle. The formula is 3² + 4² = 5². Of course, with the 5 Platonic solids,  three use triangles (3 sides).These include the tetrahedron, octahedron and icosahedron.  The cube uses squares (4 sides). The dodecahedron uses pentagons (5 sides). Pictures are below.
Image result for picture of the 5 platonic solids on DSOworks
Platonic solids have regular polygons of either 3 4 or 5 sides.
  • 6-7-8 has implications for organic chemistry. Hydrogen begins the count. It is like the single line that begins form in geometry.  Hydrogen’s atomic number is one. Six is carbon’s. Seven is nitrogen’s. Eight is oxygen’s.
Ethanol-structure.svg
An example of an organic compound. Carbon + 6. Hydrogen = 1. Oxygen = 8.

Ethanol-CRC-MW-trans-3D-balls.png  Ethanol-2D-skeletal.svg

 

 

Conclusions: This blog puts forth mathematical Platonism.   Here mathematical entities are abstract They have no spatial, temporal or causal properties.  They are eternal and unchanging.  Numbers represent eternal truths. They are behind everything. Musical sequences, by sound,  express their beaty through sound.

 

 

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Tones plus overtones both come from a number square

Tones Plus Overtones Prove Former Advanced Civilization

Tones Plus Overtones Prove Former Advanced Civilization. This civilization knew the ways  peace. It was a time when “yin” ruled. This is according to Chinese tradition. Also according to Chinese tradition is Feng shui.  Both peace and Feng  shui are based on the 3 x 3 number square. So are two key points of this blog, (1) the primary overtones ratios.  (2) Their vibrations per second  in antiquity.

An overtone is any frequency greater than the fundamental frequency of a sound. Here is the illustration: Play a low “C” on the piano. It is tone “1” in the illustration.  Call this low “C” the fundamental. When played, this tone sets off a series of tones. The strongest are the first five above the fundamental. They also make for the most pleasing ratios in sound. For example 1:2 is the octave.  2 :3 is the fifth. 3:4 is the fourth.

Above is the harmonic series in musical notation.  We see the names of the intervals above the fundamental. . The relative amplitudes (strengths) of the various harmonics primarily determine the timbre of different instruments and sounds.  For example, the clarinet and saxophone have similar mouthpieces and reeds.  Both produce sound through resonance of air inside a chamber.  Each mouthpiece end is considered closed. The clarinet’s resonator is cylindrical. This means even-numbered harmonics are less present. The saxophone’s resonator is conical.  That allows the even-numbered harmonics to sound more strongly.

TONES PLUS OVERTONES PROVE AN ADVANCED, ANCIENT CIVILIZATION

Tones plus overtones of the ancient scale are found here
The simplest of number squares will spearhead a New Golden Age as it did in the past.

Here’s how tones plus overtones work together. Our Neolithic ancestors of this: All “magic square” have characteristic numbers. But this one also has secret number codes. Here are its characteristic numbers:

  • Any two opposite numbers = 10. Examples 4 + 6 or 3 + 7.
  • The single central number is 5.
  • Any straight row of 3 numbers totals 15.
  • The perimeter of 8 numbers totals 40.
  • The perimeter + the center = 45.

Next, here’s how the characteristic numbers relate to fundamental overtones. These are constructed with numbers one thru four. This are expressed by ratios of two consecutive numbers.

  • 1 to 2 is a perfect octave. On the above number square, the ratio of the central 5 to opposite combination on the perimeter of 10 is is 1:2.
  • 3 to 2 is a perfect fifth. On the above square, the ratio of any row of 3 (15) to any 2 opposite numbers (10) is  3:2.
  • 4 to 3 is a perfect fourth. The ratio of the 4 even corner numbers (20) to any row of three (15) is the 4:3 ratio.

Harmonic overtones of fundamental perfect harmonics are defined by these characteristic numbers. They are the octave, fifth and fourth. There are no other Perfect Intervals.

Tones and overtones and number squares.
Knowledge, for me came, from a spiritual presence Oquaga Lake. See products on DSOworks.com.

So Where are the Actual Tones in Terms of V/S on the Number Square?

Go around the perimeter in either direction. Add two numbers at the time as follows.

  • 49 + 92 + 27 + 76 + 61 + 18 + 83 + 34 = 440. Diatonic “A” vibrates 440 times per second.
  • 49 +94 + 35 +53 + 18 + 81 + 92 + 29 + 57 + 75 + 16 + 61 = 660 Diatonic “E” vibrates 660 times per second.
  • 660 to 440 define the 3/2 ratio. These define a section of tones plus overtones.

Other tones of the ancient scale are to found in this number square.  So, the number square holds musical tones.  It has overtones. The number block has interval ratios and their tones. The square of three allows us passage to a lost Golden Age.

 

 

 

Regal Leo the Lionheated

Regal Leo and Audio Musical Preferences

Regal Leo and Audio Musical Preferences. Music Under the Zodiac is the name of my upcoming book. As a musician, I have an interest in the zodiac. There are many parallels, for example:

  • We use the well-tempered scale. It has twelve 12 tones within the octave. There are 12 zodiac signs.
  • We have four types of triads. They are major, minor diminished and augmented.  The zodiac has four elements, They are earth, air, fire and water. Earth is dense. The diminished triad is the most compact. Fire is the most effusive of the signs. An augmented triad is the most expansive of the triads. Water and air parallel minor and major respectively. They fit in their size of 7 half tones from the first note between the earth and fire triads. Earth uses 6 half steps, fire uses eight.

    Types of triadsAbout this sound I About this sound i About this sound io About this sound I+ 

    In music, a triad is a set of three notes (or “pitches“) that can be stacked vertically in thirds.[1] The term “harmonic triad” was coined by Johannes Lippius in his Synopsis musicae novae (1612).

  • Speaking of triads, there are three categories of zodiac signs. They are set by cardinal, fixed and mutable. Cardinal is the month that begins a season. Like the 1st month of Spring under Aries is cardinal. Fixed is the second month of the season. It is Taurus in Spring. The third, a mutable zodiac sign, ends the season.  It is called mutable because it prepares for the next trio of the summer zodiac months. This last month of Spring is Gemini.

What About Regal Leo?

 

 

four aspects of time are cyclic

Four Aspects of the Moon and Four Types of Musical Triads

Four Aspects of the Moon and Four Types of Musical Triads. Time is cyclic. A cycle may be divided into four distinct parts. I call these the four aspects of time. The four aspects of time are continuous. One part of the cycle follows the other in the same order over and over. If we know what point the cycle is at, we can predict the next point.  Just for the sake of starting somewhere in the cycle of time, I listed the up swing of the cycle first.

  1. The winding up of a cycle is the increase of cyclic activity.
  2. The maximum point at which cyclic activity is the greatest is most intense.
  3. After  maximum intensity, the cycle unwinds.
  4. Finally, the point of least activity is reach. Tension disappears. Immediately after this point, the cycle starts another upswing.
Image result for picture of the Moon and its four primary phases
Four aspects of the Moon can be compared to the 4 types of musical triads.

Next we have four types of triads. From smallest to largest they are: Diminished, major and minor, and augmented.

  • Diminished is the most contracted. Counting from the first note, in root position, it has six half steps up to the last note.
  • Major and minor triads are middle of the road. The have 7 half tones from the first note up to the last.
  • Finally, augmented is the largest. It has 8 half tones from the first to the last.
  • Types of triadsAbout this sound I About this sound i About this sound io About this sound I+ 

    In music, a triad is a set of three notes (or “pitches“) that can be stacked vertically in thirds.[1] The term “harmonic triad” was coined by Johannes Lippius in his Synopsis musicae novae (1612).

Here’s how to animate the four phases of the Moon by musical triads:

  1. The new Moon has the least light. The diminished triad is the smallest triad. It has the 6 half tones as described above.
  2. The full Moon has the most light. The augmented triad is the largest triad. It has the 8 half tones.
  3. The waxing and waning Moon are neither the smallest or largest aspect of the Moon. They are in between. They correspond to the major and minor triads respectively. The major would represent the waxing cycle. The minor represents the waning cycle.  Major and minor triads both use 7 half tones from the 1st note.

Four aspects, be they  four elements, the cyclic view of time, or musical triads- all correspond.  The goal is to seek a grand unity of science and art in the same manner as did Neolithic and pre-Neolithic cultures. In unity we find harmony and co-operation.

 

 

Interesting repetition of the bass line.

Interesting Repetition With the Musical Canon by Pachelbel

Interesting Repetition With the Musical Canon by Pachelbel. . Since the 1980s, Pachelbel’s Canon has also been used frequently in weddings and funeral ceremonies  throughout the western world. It uses a continually repeating bass line. Off season in Florida (that means summertime), I extend my services for weddings.

Repetition has different levels of sophistication. In this present day and age, words are frequently repeated over and over. The word choice word  seems to be “baby”. Also, in today’s musical palette, four bars of music are often repeated over and over- like a chant. Simplistic chants are used in advertisements. They can hypnotize you into buying a product.

Interesting Repetition in Pachelbel’s Canon in D

Sarasota Wedding Pianist plays Pachelbel’s Canon – YouTube

https://www.youtube.com/watch?v=5m-IpXovpHk
1 day ago – Uploaded by Dso Works

Pianist David Ohrenstein plays Pachelbel’s Canon. Now available to play for Sarasota weddings. For more …

Pachelbel’s Canon combines the techniques of canon and ground bass. Canon is a polyphonic device in which several voices play the same music, entering in sequence. In Pachelbel’s piece, there are three voices engaged in canon (see Example 1), but there is also a fourth voice, the basso continuo, which plays an independent part.

Interesting repetition as the bass plays the same notes over and over underneath florid violins.
Interesting repetition becomes an art form in Pachelbel’s Canon in “D”

Example 1. The first 9 bars of the Canon in D. The violins play a three-voice canon over the ground bass to provide the harmonic structure. Colors highlight the individual canonic entries. The bass voice keeps repeating the same two-bar line throughout the piece. The common musical term for this is ostinato, or ground bass (see the example below).

Related image
 Why is the Canon in “D” and the canon form so popular with weddings? The canon provided a grounded bass over which the music above changes and flows. A man and wife can change over the years. However, the sacredness of the wedding vows remain constant. They make the part of the grounded bass. The grounded by can be compared to the presence of the Divine.  Now is that beautiful, or what? I play  the Canon as part of my repertoire at the Crab and Fin Restaurant at St Armand’s Circle season outdoors on  Mondays, Tuesdays and Wednesdays. If it rains, no show! Check events on DSOworks.com for times.
Randomness in Music With the 12 Tone Technique

Randomness of the 12 Tone Technique Applies to our Math

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[3] 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.

With the ancients, randomness is lacking.
Every number relates to the others in a meaningful way in the Neolithic times.
  • 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!

 

 

Mexican Sun Pyramid has a blueprint

Mexican Sun Pyramid Draws on Platonic Codes

Mexican Sun Pyramid Draws on Platonic Codes. Yes, there is an ancient temple plan. It dates back to Neolithic times. Plato used it. It was employed all around the world in antiquity. I discovered it in a vision while hiking around the loop by Oquaga Lake.  The same Ancient Temple Plan also graces the Mexican Sun Pyramid.  I discovered it by means a vision while hiking around Oquaga Lake. The special character of the lake nature is described in my book of poetry on DSOworks.com: The Oquaga Spirit Speaks. It can be downloaded.

I was walking down the main road by Scott’s golf course when I had the insight that forms the basis of this blog.

Teotihuacán
 Pyramid of the  Sun (click to see picture source)

Coordinates: 19°41′33″N 98°50′37.68″W

Add the length of  the perimeters of the four  triangles ABC, ADC, ABD and CDB.  Each one totals 2520′ ( 738 + 738 + 1044 = 2520) .  Four triangles = 10,080. Next, use pi as 22/7. A circle around diameter of length 10,080 = 31,680.

Mexican Sun Pyramid Parallels Plato’s Writings

Plato’s Ideal City uses the same numbers in his desciption of the Ideal City.  He states in Laws V: “(1) Mark off 5040 allotments. They must be cut in two so that “each contains a near piece and a distant piece- joining the piece next to the city with the piece furthest off.”. That totals 10,080 markings of land (5040 on each side of the radius). That equals the total of the sum of perimeters around the 4 triangles of the Sun Pyramid as described above.  A circle drawn around diameter 10,080 has a circumference of 31,680 . As 10,080 x 22/7 = 31,680. The co-incidence goes even further. John Michell explains defines the area of each of its 2520 pairs of rings. The combined area of each of the pairs is 31,680. Both the Mexican Sun Pyramid and the Ideal City use the same number tradition of prehistory.  I refer my reader to The City of Revelation by John Michell pgs. 84-86

Conclusion: At one time there existed a peaceful formula for civilization. Due to some kind of cataclysm, everything was destroyed.  This possibility is discussed by Immanuel Velikovsky (/ˌvɛliˈkɒfski/; Russian: Иммануи́л Велико́вский; IPA: [ɪmənʊˈil vʲɪlʲɪˈkofskʲɪj]; 10 June [O.S. 29 May] 1895 – 17 November 1979) He was a Russian-Jewish independent scholar best known as the author of a number of controversial books reinterpreting the events of ancient history, in particular the US bestseller Worlds in Collision published in 1950.[1] Earlier, he played a role in the founding of the Hebrew University of Jerusalem in Israel, and was a psychiatrist and psychoanalyst.

Conclusion: I think that ancient ruins hold lost knowledge. Uncovering and understanding what’s in these ruins provides possible pathway way to peace. I think we are approaching another Golden Age. How good is that?

Image result for picture of Book cover of John Michell's City of Revelation
John Michell quotes Plato’s Laws V which one of my sources for this blog.

This is a candidate for one of the ancient burial sites by its yin yang characteristics.

Ancient Burial Sites Used the Perfect Fifth Ratio 3/2

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?

  1. The tradition belongs to  yin-yang concept of the ancient Chinese
  2. 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.
  3. 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.
    railroad tracks interrupted the yin yang flow of ancient Chinese burial sites
    The natural flow of yin yang was thought to be interrupted by railroad tracks.

    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 just perfect 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 parallel the 5 Platonic solids

Musical Inversions of Triads Run Parallel to Platonic Solids

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.

Image result for Wikicommons illustration of the C major triad with inversions on the piano keyboard
The same C major triad in different inversions
Musical Inversions Parallel a Property called Duality Possessed by the Platonic Solids
The Circle of Fifths Fits the properties of the 5 Platonic Solids Like a hand fits a glove.

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.

Cartesian coordinates
FigureTetrahedronOctahedronCubeIcosahedronDodecahedron
Faces4862012
Vertices46 (2 × 3)812 (4 × 3)20 (8 + 4 × 3)
Orientation
set
121212
Coordinates(1, 1, 1)
(1, −1, −1)
(−1, 1, −1)
(−1, −1, 1)
(−1, −1, −1)
(−1, 1, 1)
(1, −1, 1)
(1, 1, −1)
(±1, 0, 0)
(0, ±1, 0)
(0, 0, ±1)
(±1, ±1, ±1)(0, ±1, ±φ)
(±1, ±φ, 0)
φ, 0, ±1)
(0, ±φ, ±1)
φ, ±1, 0)
(±1, 0, ±φ)
(±1, ±1, ±1)
(0, ±1/φ, ±φ)
1/φ, ±φ, 0)
φ, 0, ±1/φ)
(±1, ±1, ±1)
(0, ±φ, ±1/φ)
φ, ±1/φ, 0)
1/φ, 0, ±φ)
ImageCubeAndStel.svgDual Cube-Octahedron.svgIcosahedron-golden-rectangles.svgCube in dodecahedron.png

 

Neolithic number eight is on the piano keyboard.

Neolithic Number Eight Permeates the Great Pyramid of Egypt

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

  • Image result for picture of the book cover by John Michell the View Over Atlantis
  •  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:
  1.  The note A,  underneath Steinway’s name, vibrates 440/per second.
  2. The lowest note on the piano, also an “A” vibrates 27.5 /second.
  3. The length of any side of the square base on the pyramid is 440 cubits.
  4. The height of the truncated Great Pyramid of Egypt is 275 cubits

Image result for picture of the 3 x 3 number square on dsoworks.com