Mysteries of Music Unearthed By Tick-Tack-Toe.

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


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 .

The 4 x 4 Magic Square and Music?

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.


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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!


Our Music, Bodies, etc. Use the Same Numbers

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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.


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 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.


How About Great Caesar’s Ghost for Halloween?



How about Great Caesar’s ghost for Halloween? When was the last time you heard the expression, Great Caesar’s ghost?  For me, it was on the old Superman TV show that played in the 1950’s. The newspaper editor of the Daily Planet, Perry White, would exclaim to Lois, Lane or Jimmy Olson or Clark Kent every time he was frustrated: Great Caesar’s ghost! In our opera, Octavian and  Cleopatra, we did one better than that. We actually have great Caesar’s ghost appearing on the stage. He sings to Cleopatra a beautiful aria that I and Sharon wrote called: My Lily of the Nile.


Of course, a second ghost shows up: The ghost of her other Roman  husband, Mark Antony. The ghosts of Caesar and Antony immediately argue about what would be the proper course of action to take over Cleopatra’s conqueror, Octavian. Caesar says Cleopatra should trust Octavian. Mark Antony takes a totally opposing point of view. Of course, Cleopatra makes a scene where she screams over the arguing ghosts. Her two ladies in waiting witness her demise and try to calm her down with a potion. They think that Cleopatra’s totally lost her mind over the grief she has for her husband, Mark Antony, who has just killed himself.

Our thrilling opera was performed in Sarasota and St Petersburg, Florida with a cast of seven.  We have a complete piano-vocal score and the performance was recorded on DVD. Sharon Lesley Ohrenstein wrote the book and lyrics and I wrote the music. We are in the process of arranging this for a chamber orchestra. My favorite musical moment in the show is a trio which features the Ghosts of Caesar and Antony singing with a living Octavian. They ghosts urge Octavian to  go back to Cleopatra and show her that he loves her.  Octavian rejects their plea, saying that his motto and words he lives by are; “make haste slowly”.  Reserve this show for your theater season so your patrons can be thrilled by the glory that was Rome and Egypt!

Brookdale colonial park performance

Maximum Stretch for the Piano

Maximum stretch for the piano is essential. There seems to be very few ideally sized hands. Short fingers make wide stretches on the piano difficult. Playing closely with stubby fingers is difficult. Wide palms slow down tucking the thumb under for scales or arpeggios.  My instructions through piano lessons has helped many of my students understand how to get the most out of their reach.


There are ways to overcome inherent difficulties without going to extremes. An example of going to extremes involves Robert Schumann, the composer. He thought that surgery would correct an inherent difficulty: Fingers four and five work best together. It’s difficult to move 4th without the fifth finger. These two weaker fingers share a common tendon. Unfortunately, his surgery did not work.


Another method to acquire maximum stretch for the piano is the piano itself. Josef Hoffman took his piano with him on concert tours. His piano was specially designed for small hands: The distance from key to key is shorter.

I, having a small to medium sized hand, invented a five finger stretch. In all my years of playing etudes, I’ve never encountered this idea.  I feel this is an essential exercise for anyone who shares my hand limitation: Some composers, for example, Sergei Rachmaninoff; had hand huge hands. With small hands, that creates difficulties. I call my exercise, simply: The Five Finger Stretch. It stretches the webbing of the fingers by fifths and octaves.


Here is the finger sequence for the right hand by fifths and then by octaves. It ascends and then descends based on the solfeggio notes of the one octave C major scale. By fifths we have: 1-2-3-2; 1-2-3-2; etc. then 3-4-5-3, 3-4-5-3 etc; then 2-3-4-3; 2-3-4-3. The fingering up and down the scale are reversed for the left hand.  Then I use the octave stretch with the following fingerings: 1-2-5-2, 1-2-5-2; and secondly, 1-3-5-3; 1-3-5-3. By note we have: c-c’-c”-c’; d-d’-d”-d’. This stretch encompasses two octaves.

The exercise is no guarantee that the small handed person will be able to play Rachmaninoff. However, it will stretch your hand to its maximum. Important: Should you experience fatigue or pain in your fingers, stop. Shake your hands and fingers out. Only play this exercise if you feel stretching without pain. How about the size of Rachmaninoff’s hand?

Sergei Rachmaninoff
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Rachmaninoff in 1921

Edmond De Mattia, distinguished conductor

Edmond De Mattia, distinguished conductor

Edmond De Mattia, distinguished conductor of the Wind Song 5 offered a popular concert for the benefit the Salvation Army.  It was given at the chapel on Sunday this last May 24, 2015 at 1701 S. Tuttle Av. in Sarasota, Fl. The woodwind instrumentalists of the Wind Song 5 include Edmond De Mattia on oboe, David Lieberman on clarinet, John Stinespring on bassoon.  Sharon Lesley Ohrenstein   is the soprano/arranger of the group.  Her husband, David Ohrenstein is the composer/pianist.   The works they performed spanned from Mozart to  Scott Joplin; from opera to the Broadway stage. Several of David and Sharon’s acclaimed original theatrical works were also offered.


Maestro de Mattia recently gave a concert in the Cleveland with his musically acclaimed family. We were so honored to have them feature three of our original compositions. One in particular, we were told, brought the house down: The Iguana Farm. I actually composed it on the island of Roatan off the coast of Honduras. An iguana farm is there where Iguanas are raised. Sharon skillfully arranged it for oboe and piano.  Their concert at the Lakewood Presbyterian Church this last September 20th featured Ed De Mattia on oboe. He is both the founder and president of the American Concert Band Association. His nephew, Alan De Mattia, also plays the French horn with the Cleveland Symphony. Richard De Mattia is the choir director and organist-pianist of the church. Sullen De Mattia was the flutist.


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Look to the Past to Face the Future

Look to the past to face the future with absolute confidence.  The very thought has a built in paradox: How can looking backwards get you ahead? Yet, this is exactly what happened in the musical arts of France in the latter part of the 19th century and the early 20th centuries.  In my opinion the action of looking backwards to go forward took the extremely brilliant mind of Claude Debussy as well as his contemporary composer friend, Maurice Ravel and others.  I have been reading and studying L’art de Toucher Le Clavcin by Francois Couperin. It was first published in 1716. I feel that in some ways, it lays the groundwork for the impressionistic movement. Of course, the harmonies of impressionism differ dramatically from the Couperin’s earlier prototype.

Claude Debussy in 1908.
                                                                                                                                              Debussy is not the man who would be king:
                                                                                                                                               He is the king!  



One extremely important instruction that Couperin offers today’s performers of Debussy involves dynamics. That is, whether or not to play loudly or softly in a particular musical passage. Couperin writes in his musical treatise that it is up to the composer to make the music louder or softer by the notes on the page. For a louder section, he places more notes in his chord or musical passage.  For softer passages, notes are be removed.  Melodies were often supported by thinly realized harmonies. This helps in making subtle playing even when many notes sound at once. Old keyboards did not play louder and softer by degrees: They could only contrast loud and soft by use of a special pedal.  According to Couperin, the quantity of notes that  sounded at once made the volumeThis kept both vulgar and excessively loud playing to a minimum.  My teacher learned these techniques from Alfred Cortot in the 1920’s, and I offer piano lessons which offer these techniques.

Today’s pianists, by and large, overplay the compositions of the impressionistic composers. For the most part,the sound of the music takes care of itself by means of the extra notes that that Debussy or Ravel wrote into the musical score. I have been preparing one hour of the of Debussy’s music to be available on this website.  In doing so, I have discovered a hidden technique that Debussy used. Its purpose was to tell the pianist what note or chord to emphasize. Also, the absence of the use of this device  meant to play the notes or chords in a gentler manner.  Since beginning this project, I have nothing but awe for the genius of Debussy. In my humble opinion, I think he was not only had a totally brilliant mind, but he was a great, great innovator with good taste.  I cannot describe the wonderful feeling I have anytime I get even a tiny insight into what Debussy had in mind in his music.  Stay tuned for more Debussy and Ravel blogs.

Harmony’s Number


 Harmony’s Number is 272. My unpublished manuscript, entitled, The Sacred Engineers Philosophy, the Pinnacle of Thought in the Unified Culture of Ancient Builders, was placed on the etched stone triangle at the Mnajdra Temple on the Island of Malta. The treatise discusses the number codes that the ancient engineers used for building temples. These same codes defined the vibrations per second of the musical tones of the ancient diatonic scale. I merely rediscovered the codes that they used.

Harmony’s number is 272. What can this possibly mean?  In antiquity, measure and music shared a common bond. The scale in use by the ancient Greeks was called diatonic. They knew the vibrations per second of each tone (Refer to Issac Asimov’s On Physics for the list).  Middle “C” vibrated 264 times per second. “C”, and octave higher, vibrated twice as fast: 528 times per second.  “A” still vibrates in symphony orchestras today at 440/sec. “E” above middle “C” was 264 times per second, etc. Numbers are readily available.

In antiquity, harmony referred to a balance of forces that were able to co-exist in peace. Harmony, according to Webster,  is an agreement or an accord. In music Webster states that it is a simultaneous sounding of tones that are pleasing to the ear. When a pair is in accord, be it people or music, they are able to co-exist harmoniously. John Michell in The View Over Atlantis elaborates on how 272 was connected by gematria  (defined as the former unity  that letters and numbers shared). The example that Michell uses goes back to ancient Greece with Harmonia who was the wife of Cadmus. The gematria of her name in Greek equaled 272. Numbers, in antiquity, could represent words, things and forces. Many ancient languages did not have separate symbols for numbers. Letter doubled as numbers. You could therefore  total the numerical values of the letters in a single  word, phrase or even a lengthy sentence. Each had a sum. The writings of John Michell covers the subject amply.


Harmony’s number  is 272.  Question: In what possible way can 272 bind opposing forces as one? Answer: Numbers 5 and 6 were considered polar opposite numbers. Five was yin. Six was yang. The five pointed star was a symbol of man. The hexagon, with 6 sides, was connected to the cosmos and the inanimate. In the Medieval gardens and decorations the five strong petaled rose was thought of yin; while the six- petaled lily was yang (refer to John Michell in City of Revelation). Many crystalline forms, the snowflake, even the cells of a honeycomb are six sided…So how does 272 unite man and the cosmos through numbers 5 and 6? Answer:  272 results from basic arithmetic of numbers 5 (yin) and 6 (yang). As, 6 x 5/ 6 + 5 = 2.72727272… Or stated in another way, 30/11= 2.727272….


As harmony’s number in ancient Greece was 2.72; even older megalithic cultures all over the world used 2.72…. as it defined the 2.72 feet of the megalithic yard.  Its hidden existence was  discovered by professor Alexander Thom of Oxford  in the 1960’s  He found that it measured most of the ancient sites in England.  Among the sites that were built by the megalithic yard are (1 Karnak Temple in Egypt whose length of either side of the rectangular base was 440MY. (2) the placement of the Sphinx in relationship to the Great Pyramid which was 440 MY distant,  (3) the  perimeter around the foundation of Persepolis in Iran was a square that measured 4 x 440 MY. (4) Rhe rectangular lengths of Troy in Turkey (2 x 220MY) combine to equal 440 MY. (5) The Akapana of Tiahuanaco in Mexico had one length and one width of its rectangular foundation together span 440 MY.  “A” , at 440, exists in two systems: (1) the old diatonic note “A” above middle “C” and (2) the modern well tempered “A” of our current tuning system.   As far back as 3500 BC the megalithic yard is found on Malta at the Mnajdra Temple at the higher section of the North entrance.  A triangle is etched in this section. Gerald J. Formosa found its dimensions and most of the temples in Malta that were defined  by the MY. He wrote about it in, The  Megalithic Monuments of Malta. Yes, music married architecture. The minister was Mr. Megalithic Yard, and their child was called harmony!


A very significant use of 272 bonds Islam and Judaism. The three letter root of “Arab” in Hebrew is ayin (70), reisch (200), and  veis (2). Its gematria is 272. The word, Hebrew, uses the same letters, re-arranged as: ayin (70), beis (2),and reisch (200)= 272. In this manner, both cultures have an harmonic accord. Also, the two primary Hebrew names for God in the Torah equal 272 but in a hidden way.. Scholars have pyramided the letters of a word to come up with the hidden pyramided value.  Thus the Tetragrammaton becomes: yud (10)  +  yud, hei(15)  +  yud, hei,vav (21)  + the full name- yud, hei, vav, hei (26).  The total is 72.  Using the same technique for the other primary name, Elohim, the total is 200. Therefore, the sum of these two pyramided names also equals  272.  I can only conclude that if we allow it, the natural state of the Middle East and the world  is all about peace and harmony. One last 272 point. When you multiply the Hebraic factors of the pyramided names of the Lord (described above) as 72 X 200, you get 14, 400…….. 2.72  defines the number of feet in a megalithic yard, 14,400 defines the number of feet in the “megalithic mile” which is even found in China as a measure called the Pu.

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.

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The Great Pyramid of Gizeh is the large pyramid on the left side.


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.


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.


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.