Measurement message

Measurement Message from Altamira 11,000 B.C.

Measurement Message from Altamira 11,000 B.C.- Under the name Cave of Altamira 18 caves are grouped together northern Spain. They represent the apogee of Upper Paleolithic cave art in Europe. This was between 35,000 and 11,000 years ago (AurignacianGravettianSolutreanMagdalenianAzilian). Collectively, the caves were designated as a World Heritage Site by the UNESCO in 2008.

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Measurement message of the primary cave of Altamira in its overall rectangular outline.

The Painted Hall of the Altamira Cave houses houses a prehistoric gallery. It was discovered in 1868. Since then, the floor has been lowered. This was to study the painted animals on the low ceiling at the time of the discovery. The floor measures 60 feet in length to 30 feet in width. My source for the dimensions is The Atlas of Legendary Places by James Harpur and Jennifer Westwood.  The  12″ foot  is the intended unit of measure. In fact, this now called “English” foot dates back to an indeterminable distant past. At the British Museum you can find several examples of a cubic inch of gold. It was the standard of weight ancient Greece, Babylon, and Egypt. Here’s how a segmented foot appears on the cube:

  • A cube has 12 edges.
  • Twelve edges of one inch per side =  12″= 1 foot.

 Measurement Message from the 60 x 30 foot foundation of the Painted Hall

Image result for Wiki commons painting from the Altamira Cave
Great hall of polychromes of Altamira, published by M. Sanz de Sautuola in 1880.
  • Musicians will most likely notice the 2 to 1 ratio of the floor’s proportions. These same proportions  were recommended by Pythagoras. 10.500 years later this Greek philosopher stated the same ratio, after the unison, was most harmonious : The perfect interval of not the same tone (unison) and 1st overtone is the octave. It vibrates in a 2:1 ratio. The designers of the cave exhibition most likely knew this.

1:1 (unison),

2:1 (octave),

3:2 (perfect fifth),

4:3 (perfect fourth),

5:4 (major third),

6:5 (minor third).


  • Its measure is the product of basic consecutive numbers.  5 x 6 = 30 (the width in feet). 3 x 4 x 5 = 60 (the length in feet). Very important: The formula for the megalithic yard uses all fives and sixes: (5 x 6)  ÷ ( 5 + 6) = 2.727272… One megalithic yard is 2.72 feet.  The builders of the Great Hall of Altamira knew this.
  • 2nd factor uses 3,4,5 as 3 x 4 x 5 = 60. Numbers 3, 4 and 5 are the basis of the Pythagorean Theorem: 3² x 4² = 5². Also, look at the musical intervals above. These 3,4, and 5 factors figure into these basic harmonious intervals: 4:3 = perfect fourth. 5:4 = the major third.

Megalithic Measure Survives in Unexpected Ways

Marduk and His Temple are a Billboard for Measure


  • The diagonal of the 30 x 60 rectangle would be 67 feet. The perimeter around this  first  half triangle is :30 + 60 + 67 = 157 feet. This figure (157) is one half of the pi figure of 314 made by the triangles made from a diagonal in a rectangle.

Conclusion: The wisdom of a lost civilization is preserved in measure at the Cave of Altamira. Perhaps the builders and artists were the survivors of Atlantis?  Measurement message and music message are there. Of course, that the advanced artwork is there is a given!


common musical geometrical ratios

Common Musical Geometrical Ratios

Common Musical Geometrical Ratios. First, what is a ratio?

common musical geometrical ratios
Ratio example of intervals that make a perfect musical fourth.

Musically, in the diagram above: Every time a higher tone vibrates four times, the lower vibrates three. This creates the sound of a perfect fourth. All the perfect intervals and most harmonious tones of nature can be found at a bowling alley. Also, in the link below I explore the ratios of 6 to 5 found at Atlantis.  The size of an interval between two notes may be measured by the ratio of their frequencies. When a musical instrument is tuned using a just intonation tuning system, the size of the main intervals can be expressed by small-integer ratios, such as:

1:1 (unison),

2:1 (octave),

3:2 (perfect fifth),

4:3 (perfect fourth),

5:4 (major third),

6:5 (minor third).

Below are the only the Perfect Intervals found by bowling pins in an alley

  • The unison becomes the single, front standing pin.
  • The perfect octave is the 1st pin divided by the 2 pins in the 2nd row: 2:1 is the higher octave.
  • A perfect fifth is the ratio of the 3 pins in the third row divided by the two in the second: 3/2.
  • As mentioned, the 4 divided by the 3 makes the ratio of the perfect fourth.
 Ratios are often used to describe other items as: The ratio of width to height of standard-definition television.

In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second.[1]

Common Musical Geometrical Ratios of 5 and 6 were used by Atlanteans!

Clues about Atlantis are also found in the Temples on Malta
The ratio of the minor 3rd is 6 to 5.  It was the basis of a multitude of ancient measures. Read the internal link about Atlantis.  One of my books, The Ancient Engineers’ Philosophy: The Pinnacle of Thought in the Unified Culture of Ancient Builders, is placed in a triangle at a temple in Malta built circa 3500 B.C.


Clues in the Search for Atlantis Come With # 5 and #6.

When it comes to music, Atlantis lives!

Plato wrote of Atlantis in Timaeus that numbers 5 and 6  were prominently featured: People were gathered every 5th and 6th years alternately: Thus giving equal honor to odd and even numbers. The gathering of the population was for judgement and atonement.

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Clues about Atlantis are also found in the Temples on Malta

Clues in the Search for Atlantis Come With # 5 and #6.

Clues in the Search for Atlantis Come With Numbers 5 and 6. The story of Atlantis comes to us from Timaeus, a Socratic dialogue, written in about 360 B.C. by Plato.  In Timaeus 5 and 6 are featured as follows: People were gathered every 5th and 6th years alternately: Thus giving equal honor to odd and even numbers. The gathering of the population was for judgement and atonement.

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Music had a place of honor in the distant past.  Harmonious music vibrates in whole number ratios.  Plato, in his Republic, required it to be mandatory study until the age of 30.

The Clues are Here about how 5 and 6 Were brought together in the Distant Past to Create Peace

Five and Six were unified by a Neolithic measure called megalithic yard. It is 2.72 feet. Professor A. Thom of Oxford University discovered it in the late 1960’s. It’s use was worldwide. Below is the formula for the measure.  The product below was then taken as feet. The 12 inch foot is of great antiquity. It is not an anachronism, The cubic inch of gold was a standard unit of weight in Sumeria, Babylon and Greece. Examples can currently be found at the British Museum. A cube has 12 edges. Thus, 12 edges x 1 inch = 1 foot. Very important: note how 5 and 6 alternate in the formulas below. This gives equal honor to odd and even numbers.

  • 5 x 6/ 5 + 6 = 2.727272……the numbers of the megalithic yard

The 2.72 foot measure was also projected by the Egyptian Canon of measures. I think the MY’s relationship of 5 to 6 was rediscovered by myself?  The Egyptian formula was expressed differently. The megalithic yard was: the square root of 5  x  1.2165 foot Egyptian remen = 2.72 feet. 

Israel Partakes of the 5 and 6 Tradition for Peace.

Six is obvious. It is the 6-pointed Star of David on the flag is Israel.  Finding the 5 involves gematria. This is a word that expresses the total unity the numbers and letters once had. There were no separate letter and number systems. Israel in Hebrew translates to 541  (יִשְׂרָאֵל). One (1) was often added to words for the presence of God. The tradition was called colel. How does that relate to number five? A pentagon (five-sided, plane geometrical figure) has 540 degreees. The the 540 defines the pentagon’s five sides. Again, odd and even numbers are given honor equally. This is through the pentagon that expressed Israel and hexagon that is formed its Star of David. 


Units of measure in the past had longer and shorter values. The example of ratio of 175 to 176 ratio of measure was almost universal. John Michell gives examples in his New View Over Atlantis. Here’s the connection of the hunab with 5 and 6:   (6 x 6 x 6) +  (5 x 5 x 5)  =  341. That figure, as 3.41 feet for the hunab, is within 98.7% of the value of the shorter hunab. It is based on the 175 ratio of 3.456 feet. Some units of measure even had three expressions: Such was the Egyptian cubit. The longer was 1.728 feet, A middle sized one was 1.72 feet. The shorter Egyptian cubit was 1.81818…feet.

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The Clues: How the Egyptians Interacted 5 and 6

The longer Egyptian cubit was 1.728 feet.It was expressed through the two feature numbers: 6 x 6 x 6 feet/ 5 x 5 x 5 feet  = 1.728 feet.

Conclusion:  Consecutive whole numbers are a great part of harmony. And, 5 and 6 were brought together in harmonious measurement. Harmonious numbers, interacting  in such low whole number ratios, produce beautiful sounds. 2:1 is the octave, 2:3 , is the fifth, 3:4 was the fourth. 4:5 was the third. It’s time to place harmonious ratios back into civilization: Be it through music, art, and architecture. Hopefully, it will rub off on us.

Music and Math Share the Rule of 9’s


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


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.

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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 .