## Periodic Chart Harmony Favors the Octave Interval

Periodic Chart Harmony Favors the Octave Interval. In music, an octave (Latinoctavus: eighth) or perfect octave is the interval between one musical pitch and another with half or double its frequency. It is defined by ANSI[2] as the unit of frequency level when the base of the logarithm is two. The octave relationship is a natural phenomenon that has been referred to as the “basic miracle of music”, the use of which is “common in most musical systems”.[3]

### So where is the periodic chart harmony of the octave?

Here is a quote from blog #400. It is also about the periodic chart.

• The system begins with hydrogen-1. The next vertical element is Lithium-3. So, 3-1 = 2. This is the first coding number on the chart.
• Lithium is atomic number 3. Sodium is 11.  By subtraction 11 – 3 = 8. Sodium has 8 more protons than lithium.
• Potassium has 19 protons. Sodium has 11. We see another 8 protons by subtraction. As, 19 – 11 = 8.
• Next, Rubidium has 37 protons. Potassium has 19. We have our 1st 18 proton difference:  37 – 19 = 18.
• Cesium is atomic number 55. Rubidium is atomic number 37. Thus, 55 -37 = 18.
• That is followed by a 32 proton number difference. Francium is atomic number 87. Cesium is 55. Thus, 87 – 55 is a 32 number difference.
• GaffuriusTheorica musicae (1492)

The chart finds periodic or repeating properties with atomic numbers 2, 4, 18, and 32. The first vertical row sets the pattern. Periodic chart harmony is found with these numbers. Simply write the 2 to 1 interval of the octave as follows. 2/1,   4 /2,   6/3,   8/4. The number of each fraction expresses an octave when multiplied as:

• 2 x 1 = 2
• 4 x 2 = 8
• 6 x 3 = 18
• 8 x 4 = 32.

Blogs on DSOworks.com are attempting to place our planet in harmony with the cosmos. Pythagoras saw the basic unity of music with our world. He defined it by string lengths. If one string was 2 x as long as the other, the shorter sounded an octave higher to the longer.  An octave is (1) The most harmonious interval. It is also the most “perfect” of the perfect intervals. (2) It is also the first overtone in the series of overtones.  Why not take the musical view of our cosmos? For those who are interested, I’m offering piano lessons in Sarasota.

## Vast Ancient Temple Plan is Based on Music

Vast Ancient Temple Plan is Based on Music. The outer hexagon is greater than the inner by the ratio of 3/2. That is the ratio of the higher note of a perfect fifth to the lower in terms of vibrations per second. First, what is the Ancient Temple Plan?

• It is a master blueprint used since prehistoric times for measuring temples by musical ratios. It is based on musical tones and geometry.  Numbers used in the plan are those enumerating vibrations per second of the various tones of the ancient diatonic scale. The geometry used is based on the  central circle of the seven as in the featured picture. It is crossed by three equidistant diameters through central point “D”.   In the ancient temple plan, any one of  these three diameters ( FE, RG or LK)  equals 352.
• Why 352 by number only with no attached measures? The answer in a word is gematria.  So what is gematria? /ɡəˈm.tri.ə/ originated as an Assyro-Babylonian-Greek system of alphanumeric code/cipher later adopted into Jewish culture that assigns numerical value to a word/name/phrase in the belief that words or phrases with identical numerical values bear some relation to each other or bear some relation to the number itself as it may apply to Nature, a person’s age, the calendar year, or the like.
• In Judaism word appear together in the Torah. They are milk and honey. They have a combined gematria of 352. These key words appear in a prime place: Deuteronomy 6:3. With the very next line, being, Deuteronomy 6:4, we find the opening 6 words of the  most sacred prayer in Judaism- the “Shema Yisroel”.
 milk חָלָ֖ב cha·lav 2461 milk and honey. וּדְבָֽשׁ׃ u·de·vash. 1706 honey

So where is the music? The tone “F” above what we would call middle “C”  vibrates in the diatonic scale  at the rate of 352 times per second. This equals the 352 Hebrew gematria by letters of “milk and honey. The old diatonic “Middle “C” vibrated 264 times per second. “C”. The next higher octave, 528 “C”, is one octave higher than middle “C”. This higher “C” is also in the ancient temple plan. Each side of the larger hexagon measures 528 by number.  Ancient unearthed instruments prove the vibrations per second of the notes or tones of this diatonic scale.

### Vast Ancient Temple Plan Holds the 3/2 Musical Fifth Ratio

Let’s look at the following for a model. Refer to the featured picture to read the lines by letters.

• Triangle MPD forms an equilateral triangle. Each side is 352.
• Extend DP to point “O”
• Or extend DM to point “N”

In a view of the vast ancient temple plan, an inclusive new triangle is defined by DNO. It includes DMP.  Thus DNO than DPM by the ratio of 3/2.  We see that 352 x 3/2 = 528. We now have a second tone in terms of vibrations per second. The “C” 528 vibrations per second is one octave higher than the diatonic middle “C” of 264 vibrations per second. This is significant because in ancient and modern systems, all tuning is based on fifths. Music by numbers applied to vibrations per second of music tones fill the ancient temple plan. Its inclusion of the ratios of perfect harmony calls for the following: Rebuilding the sites all over the world that were once conceived by this plan. Future blogs as well as some already on the website will cover or have already covered this topic.

The goal of building by the math of sound pleasing ratios of  musical tones was to have the same ratios please the visual sense in architecture. These qualities need to find their way into our collective culture.

## Fifth is Basic to Music Throughout History

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.

## Eightball: Understanding the Significance of #8

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.

1. Go to piano.
2. Depress the higher “C” with your thumb(as in the picture) without making a sound.
3. Keep it down.
4. Then depress and play the lower “C”.  It is being played by the “pinky.”The two notes are pictured above
5. 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.

## Congruous:Perfect Musical Intervals and Fibonacci Series

Congruous:Perfect Musical Intervals and Fibonacci Series. Perfect intervals have the most pleasing sound. They have been judged so since antiquity. These intervals vibrate in whole number ratios. A unison vibrates in the ratio of 1:1. The octaves vibrates 2:1. The fifth vibrates 3:2. The fourth is an inverted fifth. Instead of C-G (C-D-E-F-G); we have G-C (G-A-B-C). The fourth is merely an “inverted fifth” in the 7 letter musical scale of A,B,C,D,E,F,G, A,B,C,D,E,F,G,…. We count 5 letters from C-G. We count four letters from G-C.

Inverted musical intervals have a rule by nine. When a fifth is inverted (C-G); it becomes a fourth (G-C). 5 + 4 = 9. When a unison is inverted (c-c), it becomes an octave(c-c’): 1 + 8 = 9. When a 3rd is inverted c-e) , it becomes a sixth (e-c’): 3 + 6 = 9. When a second is inverted (c-d), it becomes a seventh (d-c’): 2 + 7 = 9.

Let’s look at the first numbers of the Fibonacci series. They grow by successive addition. At first, the “one” repeats. Then we continue adding the adjacent numbers.  We thus have: 1,1,2,3,5,8,13 etc.

### Congruous: Three  Basic Perfect Intervals With the First Four Fibonacci Numbers

• Look the the musical unison, the one; but in terms of its complementary octave. The one is really two, i.e. the unison and the octave. The one therefore repeats. We have “1,1,…” Likewise the “vesica piscis” shows one circle in the process of becoming two. They second is its complement. Numberous geometrical forms and shapes are generation by geometrical construction from this vesica. In a similar way, the shapes and forms of the Universe are generated by the Fibonacci series.
• The vesica piscis demonstrates the “one” becoming the “two”. One circle is morphing itself into two circles. The length of the vesica is defined by BA and the width by PO.  Read my blog on DSO works about the 1st Christian church, the Glastonbury Abbey in the town of Glastonbury, England on DSOworks.com.  It was most probably built by the disciples of Christ including St Joseph of  Arimathea. He settled in Gastonbury with a grant of 12 hides of land right after the crucifixion.  Its proportions were set by the turquoise area of the interlocking “vessel”.
• I’ve blogged about the Glastonbury Abbey  in the town of Glastonbury England. John Michell, in The View Over Atlantis, explains the basis of its foundation: Two circles interlocking center to center of 660 feet each.
• After the musical  unison (1 to 1); we have the first perfect interval, the octave. It vibrates in the ratio of  2:1.
• After the octave, the next perfect interval is the fifth. It vibrates in the ratio 3/2.
• Thus we see the repeated one with the next two Fibonacci numbers form  the basis of perfect musical intervals. The first four numbers being  1,1,2,3…
• Of course, the piano keyboard merely continues the series: Two black keys. Then 3 black keys. The total is 5. Then we have 8 tones from one octave to the next. Then we have 13 half tones altogether: The 5 blacks are added to the 8 whites. Behold the series: 1,1,2,3,5,8,13…Music works with the same numbers as life.

In the distant past, this knowledge spanned the Earth.  Life was harmonious and perfect at one time in Eden. I propose reviving this wisdom with its vision of peace and plenty. In this manner, our lives will seem congruous with each other. Paradise is projected by the mind.

## Was Bowling Invented by the Ancient Greeks?

 Pythagoras

Was Bowling Invented by the Ancient Greeks? When dots are substituted for these for these 10 bowling pins, their arrangement in ancient Greece was called the “tetraktys”. Note the dots in the triangle over his head of Pythagoras in the picture. He lived from 569 BC up to somewhere between 500 and 475 BC and described the 10 dots of the tetraktys as follows: “It is both a mathematical and physical symbol that embraces within itself the principles of the natural world, the harmony of the cosmos, the ancient ascent to the divine, and the mysteries of the divine realm” (Quote from The Illustrated Signs and Symbols Sourcebook by Adelle Nozedar).

### HOW THE ANCIENT GREEKS USED THE BOWLING PIN ARRANGEMENT

Here’s how it ties into music: The two to one relationship of the 1st three pins represents the vibration ratio of the musical octave. Pins 2 and 3 to 4, 5, and 6 expresses the ratio of the musical fifth. Finally, rows three to four, being to 4,5,6 to the 7,8,9, and 10 pins, are the vibration ratio of the perfect fourth. Here is the crux: The musical intervals of the octave, fifth and fourth are the most perfect and fundamental overtones of nature. If you work at building your civilization on the bowling pin idea, you have an harmonious and well functioning society. The thought behind this being that same ratios that please our ears through sound, also please our eyes by sight. The perfect harmony in your surroundings helps to make the person who lives in such a society happier, and more content. We need to follow the path of peace.

## The Musical Octave and the Periodic Chart

The Musical Octave and the Periodic Chart. Be it chemistry or music, numbers are the key to unlocking an almost incredible parallel Universe. Most obviously, as the octave is considered not only the first fundamental overtone, but it is also the first perfect musical interval.  The perfect fifth and perfect fourth come next. Because of this we could say the octave is the most stable and “happy” interval.

Now look at the color coded periodic chart. Each of the  eight colored  groups of elements are the vertical rows that have the same colors. The basic, stable and most “happy” of the groups is the purple- the kingly (or queenly) number, if you will,  each “purple” has 8 electrons in the outside shell (except for purple helium at the top-to be explained). Harry Potter fans, elements and music come from the same wave of the magical wand.

By the way, the elements in the white boxes are called transition elements. Again, appropriate to musical content. A transition in music takes you from one section to the next just as the white boxes are the go-between the colors. Here’s how transitions work in music:

• In a sonata we have a transition from  the exposition to the development section
• Then from  development section to the repeat of the exposition
• In an (ABA) song form, a transition takes us from the A section to the B section
• Then transition sometimes occurs from the B section back to the A

If we really wanted to get fancy, the bottom two white  horizontal rows can become the coda!

Now let’s place one more filter on the periodic chart concerning the principle of the center and the two types of centers that are found in all number squares:

• All odd number squares have one boxed number at the center, like the single, lonely red hydrogen on the left side. Its  atomic number is one.
• All even number squares have four boxed numbers at the center as the helium atom has an atomic weight of four. This parallels the top purple box of helium on the right side.  Number squares develop the principle of the center in the same way that hydrogen and helium develop into the elements on periodic chart; as the are being fused into heavier elements on a star.

As everything is ultimately related, mankind is one family. Guy Murchie tells this story in his treatise, the Seven Mysteries of Life: He called up every leading geneticist around the world and they all agreed on one point: If you multiply out the possibilities, everyone is related to everyone no further than a fiftieth cousin.  Studying music, composing, music theory, taking piano lessons helps to open the doors of understanding; for, to know music is to know the sciences; and inversely: no music means no science. My favorite story is about Andrew Llyod Webber to illustrate this point. In this Sunday’s New York Times (11/22), in Theater, Webber talks about how he would have become an  architect had it not been for music. He loves architecture so much that he almost bought  the Tower House in London. His then wife put the nix on  the purchase.  Jimmy Page, legendary guitarist of the Led Zepplin band, bought it instead.

## 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

### 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 .

## Our Music, Bodies, etc. Use the Same Numbers

THE SPIRALS ON THIS CLEF GROW BY THE SAME RATIOS AS THE HUMAN BODY. READ AND FIND OUT HOW

Our music, bodies, etc. use the same numbers. As Fibonacci  numbers develop by successive addition of numbers that are adjacent; man, music and even love, yes-love,  use the exact, same numbers.   When the larger number of the two in this series is divided by the adjacent smaller number; the ratio keeps getting closer to what is called the Golden Section or phi. This ratio never comes out evenly: It is 1.6180339… The Fibonacci numbers are named after an Italian mathematician.   Numbers that develop into this ratio, in order of size are: 1,1,2,3,5,8,13,21… The higher the numbers by successive addition,  the closer it comes to phi.

The Use of Phi in Music

The formula for the phi ratio is: square root of 5 + 1; whose total is then divided by two. The piano keyboard is set up by the Fibonacci series. We have two spacing of black keys. They are by 2’s and by 3’s for a total of 5. Taking C major as the prototype, from one “C” to the next is 8 tones on the white keys. Thus, from C to C’  in addition to the 1 octave we have, 2 black keys, then 3 black keys and 8 white keys. The total black and white keys are 13.

— USE OF PHI IN OVERTONES

All tones have what’s called overtones that vibrate sympathetically with  the fundamental tone. The 1st overtone  is the octave of 8 notes. The second overtone is the 5th, Both overtones are Fibonacci numbers. Not co-incidentally, the Great Pyramid of Egypt uses the same numbers in its 5 to 8 ratio of its height to one length of the square base.

THE HUMAN FORM FACTORS THE FORMULA OF THE GOLDEN SECTION

The factors of the Golden Section ( another name for phi) are 1,2 and 5 (as already described above). People have one torso, one head, two arms, two legs, five fingers on each hand and five toes on each foot. We are the mathematical manifestation of the factors of phi.   Most significantly, love ties the whole system together: The Hebraic verb for love (pronounced, Ahav) uses three Hebrew letters.  Spelled out in English they are: aleph, hei and beis. Aleph is also the Hebrew symbol for 1; hei is also the symbol for 5; and beis is also the symbol for 2. What is the lesson? Life and music are all about love.

## Uniting Music and Measure

Uniting music and measure raises a basic question. How? I have briefly blogged about this in Stonehenge Was Built by Musical Tones.  I will be developing  a theme sporadically throughout my blogs which is:  How the numbers by which architecture was measured duplicated the numbers of musical tones of the ancient diatonic scale.  As one philosopher put it: Architecture is frozen music. The units of measure by which ancient buildings could be  measured  varied by the culture.  Numbers, however, were the same.   Units of measure could include the shorter (1.718′) or longer Egyptian cubits (1.728′). They could have used the Palestinian cubit (2.107′).  The megalithic yard (2.72′) was extremely popular. The Roman pace (2.433′) or even the 12 inch English foot were utilized.   In the realm of the old diatonic scale,  a number of authors document their numbers in terms of vibrations per second. Thus I was able to see how the numbers of measure and music happily correspond. Authors that document the old diatonic scale in terms of vibrations per second include Issac Asimov in On Physics and Guy Murchie in The Music of the Spheres.

A 175 to 176 ratio of measures were used by cultures across the face of antiquity. This is well documented in John Michell’s  scholarly treatise entitled Ancient Metrology. The ratio takes in consideration the diameter across the equatorial bulge (176)  and the polar diameter (175). Michell discusses how the northern latitude measure of the Egyptian foot was 1.152 feet (the 176 ratio) at fifty degrees latitude. While the southern measure was was 1.145 feet (175 ratio) at ten degrees latitude.

ANCIENT BUILDINGS AND MUSICAL NUMBERS ARE CONGRUENT

As I have already discussed in my blog about Stonehenge, diatonic “F” above middle “C”  on the piano vibrates at 352 times per second. The standard of measure in antiquity, as I’ve already stated,  is based on a 176 ratio to 175.  One hundred and seventy-six is one-half of 352. Musically, in terms of vibrations per second, it is exactly an octave lower than the 352-F. Now, if we take the shorter 175 ratio of measure of 1.152 feet; then the perimeter around the great Pyramid is 2.640 feet. Diatonic “C” vibrates 264 times per second.  This perimeter, in terms of this shorter Egyptian foot, is exactly ten times the number by which the old diatonic “C” vibrates.

THE TIME HONORED TRADITION OF A-440

Another diatonic musical tone is duplicated in measure at the Great Pyramid. When shorter Egyptian cubit of 1.718 feet is used to measure the perimeter around the Great Pyramid, then each side is 440 cubits. The note “A” vibrates to 440 times per second. This is the standard not only of the old diatonic scale, but also the well-tempered scale still in use. A-440 is the only tone that is being used from the ancient diatonic scale by musicians- at least in England and America. In this regard, an essential dimension of the Great Pyramid is alive and well; and is still being tuned to by at least some of our orchestras. Music and empire: No wonder King David was considered a musician first and was a king only later.