Was Bowling Invented by the Ancient Greeks?

These, pins, arranged in pyramided fashion, demonstrate the ultimate model of a  paradox: In complexity there is simplicity. In simplicity there is complexity.

Picture of 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).


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.

Nietzsche Loved Carmen by Bizet Over Wagner

Nietzsche Loved Carmen by Bizet Over Wagner. Alfred Einstein, in his Music in the Romantic Era, gives  the following quote by Nietzsche about Bizet’s Carmen: “It is rich. It is precise. It builds, organizes, gets finished: therein it establishes a contrast to the excrescence in music, the “infinite melody.” Nietzsche stated that Bizet was in fact refreshing and  southern music, that allows a person to take leave of the damp North (referring to Wagner’ s music). He further declared that Bizet, who he loved, was the antithesis of Wagner. Whereas Bizet in Carmen used a closed form, Wagner went on and on with his motifs, seemingly forever. I personally find this amusing because so many have bound Nietzsche’s philosophy with Wagner’s music which often presents musical motifs on a seemingly endless scale. .

Publicity shots for the Carmen revival at the Metropolitan Opera, New York, in January 1915, with Enrico Caruso and Geraldine Farrar. Caruso is centre in the upper row, Farrar top left and bottom right.


I had the honor of arranging and accompanying”David Rubinoff and His Violin”.  He told me the following story involving the great tenor, Caruso (picture above) and Mme. Schumann-Heink, “the greatest contra-alto singer”, possibly of all time: Victor Herbert brought Rubinoff and his family to America in 1911. Herbert heard Rubinoff playing a recital at the Warsaw Conservatory, then  under the leadership of Paderewski. He said to Rubinoff, who was 13 years of age at the time, “son, you belong to America.” Rubinoff told me the story of how Victor Herbert, then conductor of the Pittsburgh Symphony, had Sunday soirees at his residence in Pittsburgh.  Caruso and Mme. Schumann-Heink were among the famous regular guests. They would sing opera duets while Herbert played the cello and Rubinoff played the violin. They would often sing and play selections from Carmen. Herbert, by the way, loved to both compose and orchestrate his own music while standing up byusing a tall dresser that he used for writing.


In conclusion, I believe that George Bizet knew that he had a super hit on his hands with Carmen. Even the great Johannes Brahms told his publisher, Simrock in June of 1882, to please send him the score to Carmen. He declared he loved it more than any other of the works in Simrock’s catalogue, including, wrote Brahms, his own. Unfortunately, as happens with so many composers, Bizet never lived to see its  ultimate triumph. He died of illness three months after its opening at age 36.  May I suggest getting a recording of the great piano virtuoso, V. Horowitz playing it. He made an amazing arrangement of hit songs from the score.


Jacques Offenbach wrote for France

As Gershwin wrote for America, Jacques Offenbach wrote for France. As Gershwin felt the tempo and spirit of America, Offenbach sensed and wrote for the culture that was about to blossom in Paris. Offenbach (1819-1880) quite incredibly, wrote over 130 works for the musical stage. Both Gershwin and Offenbach loved the musical theater. Both he and Gershwin were considered kings of popular music.Light romantic opera was only beginning to come into vogue in 1855 and Offenbach helped to set the tempo of the times. Offenbach’s composition style was as gay and witty as his stories were irreverent.

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Jacques Offenbach
 Jacques Offenbach : Wrote a superhit, The Barcarolle from his opera: Tales of Hoffman, which honors the Venice Gondolier:


Although he worked as a cellist  and conductor from 1835 to 1855, he wanted to satisfy his passion for musical theater. In 1858 he fulfilled this goal when he wrote his first full length opera, Orpheus in the Underworld. He had a great penchant for melody which he spearheaded in operettas. Emporer Napoleon III loved his music so much that Offenbach not only did he give him French citizenship, but also given coveted the Legion d’Honneur award. When he fell out of public favor because of his German birth and imperial favor, he went to London and Vienna where he was received with great acclaim. Afterwards, of course, he was again accepted with open arms in Paris.


On as personal note, I will be playing the vintage Steinway grand pianos at the Gasparilla Inn in Boca Grande, Fl this season, 6 nights weekly from Dec 18 through Easter for my 7th straight year. Check out our events listing on this website, DSOworks.com. Whenever I play the Barcarolle from Offenbach’s Tales of Hoffman, many guests go up to the piano to ask the name of this wonderful melody. I believe that Jacques Offenbach not only set the tempo of the times for Paris, but also held the tempo of our times when he wrote his works for stage. Yes, melody is returning!

What was in the music of King David?

What was in the music of King David?  Key concepts of Judaism.

  • It used an ancient standard of musical tuning that was also known to the Greeks. It is called by diatonic scale; defined and documented by Issac Asimov and Guy Murchie.
  • The dimensions of a universal temple plan were used the by tones of David’s diatonic scale.  In terms of numbers of vibrations per second these tones were translated into numbers of measurement used by the masons. David tuned his lyre to these tones.  Basic units have varied from culture to culture; but the numbers had to stay true to the numbers of the vibrations/second.
  •  The opening 12 words of Judaism’s most sacred prayer, referred to as the Shema Yisrael,  forms the basis of the  blueprint that was used by King David in planning the Holy Temple, actualized by Solomon.   Hebrew, as other Middle Eastern languages, uses gematria.  This is a Greek term describing how the same symbol that represents a letter, also represents a number. Most languages, like English, use separate letter and number systems. In Hebrew every word, phrase, sentence etc. has a numerical equivalent. Those knowledgeable in Hebrew can and I’m sure will, double check my figures.
  • The key to the entire system is the two last words of Deuteronomy 6:3 that translates to “milk and honey.”:  חָלָב, וּדְבָשׁ. Their gematria is 352 which defines the vibrations per second the diatonic tone “F”. The message is this: If you follow the Law by seeking the unity of Creation with our Creator, all the lands will flow not only with music, but with “milk and honey.”
Shema Yisrael, spelled in Hebrew letters at the Knesset Menorah in Jerusalem


  •  The circumference around each of the 7 smaller circles that have a diameter of 352  is 1106.  The Shema’s 0pening 6 words (the 1st 6 words of Deuteronomy 6:4) as it is spelled in  Hebrew prayer book uses the double yud for the name of the Creator, making the total 1106. It is less by 12 than the Hebrew spelling in the Torah as you will see below.
  • בָּרוּךְ שֵׁם כְּבוֹד מַלְכוּתוֹ לְעוֹלָם וָעֶד – “Blessed be the name of His glorious kingdom for ever and ever” (these words are not found in the Torah, but is the standard six word congregational reply upon hearing the 1st 6 words). These six words total 1358. First, 358, besides being the Hebrew gematria of Messiah, defines the harmony of the third, fifth and octave to the initial tone; thus, 1358 defines the full four note musical chord.
  • 1358 + 1106 (again, the prayer book spelling of the Shema in the Siddur) = 2464, using in the 12 inch foot, totals the perimeter around the Holy Temple.  This is confirmed by the recent find of an imitation temple, built by the Samaritans, whose foundations were measured and found in the town of Nablus.  The perimeter around the inner rectangle by number in the picture below (MSPJ) is (610 + 352) x 2 = 1924. That matches the perimeter around the imitation foundations of the temple.
  • As spelled in the Torah, with the sacred 4 letter name of our Creator, the declaration of the One God totals 1118.
    ד  שְׁמַע, יִשְׂרָאֵל:  יְהוָה אֱלֹהֵינוּ, יְהוָה אֶחָד.4 Hear, O Israel: the LORD our God, the LORD is one.

    At the turn of the 1900’s a Canon of Measures was discovered by Jay Hambridge. It is based on the diagonal drawn from the upper corner of a square that bisects the base in half. This diagonal is 1.118 times longer than any of the square’s sides. Hambridge demonstrated how this 1.118 “half” diagonal forms the basis of measure of major ancient civilizations such as the Egyptian remen, Palestinian cubit, Roman pace, megalithic yard and the British yard. The Ruler, being the One God, literally rules, or in this case meaning- He measures, by the staff of the opening 6 words of the Shema.




Ancient Musical Temple Plan

 For examples of musical diatonic tones represented by numbers in the above illustration we have: D to G which represents diatonic “C” 264.  (NO) + (MP) = 880 which is an octave higher than 440.   Then DG  (264) + NO (528) = 792 which is the diatonic tone  “F”.  One begins to see how music, architecture, harmony and religion are part of the the same pattern. Moral of the story: Where there is unity, there is peace. Perhaps this concept can help?


Gabriel Fauré and his misunderstood Pavane

Fauré in 1887

The Pavane in F-sharp minor, Op. 50, is a pavane by the French composer Gabriel Fauré written in 1887. It was originally a piano piece, but was known. at one time in Fauré’s version, as a version for orchestra, optional chorus and dancers.


Gabriel Fauré and his misunderstood Pavane. The pavane, as a musical form, has taken a bad rap in recent times. As an opus, the pavane has acquired an overly sad, even funeral-like character. However, the impressionistic composers often  looked to the 16th and 17th century for inspiration. The pavane was a slow and dignified court dance from Spain. It possibly comes from the Spanish word, “pavo”, which means “peacock”. Certainly, from the given description, the dancers strut around like peacocks. In the 1500’s the dance used bowing, curtsying and walking. Musically it is  a slow and expressive section of the dance suite.


Before writing this blog, I thought that the Pavane was a commemorative musical work for someone who is deceased. Perhaps my erroneous conception came from the title of Maurice Ravel’s work Pavane for a Dead Princess. The pavane itself has nothing to do with funerals. Ravel simply chose this dignified dance form and mood to express his sentiment. Another misconception I had was that it was originally written as an orchestral work. However, in 1887 Fauré  played it as a piano work and it was only orchestrated later. Furthermore, I assumed it should be played slowly. When the great conductor, Sir Adrian Boult heard  Fauré play it, he remarked that it went no slower than quater note =100. Soon after its world premier by  Fauré, his patroness comtesse Greffulhe, financed the work to add  an orchestra, dancers and a chorus. She even provided a venue with  choreographic space  at one of her garden parties. Stravinsky’s choreographer, Diahilev, loved the Pavane by Fauré it so much that he made it a standard part of the Ballet Russes repetoire after he introduced it to the company in 1917. I ordered his music from Paris in the original piano score version. I hope to play it myself at an all French piano concert- time and place to be announced. I will also include piano works by Ravel and Debussy. I will preview a number of selections starting Dec 18th at the Gasparilla Inn in Boca grande, Fl where I will be playing on the Steinway vintage pianos 6 nights a weekly (see events on this website).

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Charles Gounod’s Ave-Marie: A Beautiful Christmas Story



Charles Gounod in 1859
Johnann Sebastian Bach
Fanny and Felix Mendelssohn relied on each other to shape their very different musical careers.
Felix Mendelssohn and his sister Fannie who sparked Gounod’s interest in J.S. Bach which caused a most beautiful Ave Maria to be written on Bach’s 1st Prelude from the 1st book of the Well-Tempered Clavichord.

Charles Gounod’s Ave-Marie: A Beautiful Christmas Story.  During the year of 1852, Charles Gounod spent many evenings in the home of his fiancee, Anna Zimmerman. Anna’s father, Pierre was a pianist and  composer with the Paris Opera House. One night Mr Zimmerman overheard Gounod improvising a beautiful melody over Bach’s 1st Prelude in “”C”. Mr Zimmerman was so excited by this beautiful melody, that he organized a house party a few days later where the new opus was then arranged for violin, piano and a small choir. This, in fact was the 1st official Christening of the famous of Ave Marie that graces the holiday season. Schubert’s, of course was a second, but that’s another story.


What I find most inspiring about this history, is that the Bach-Gounod Ave Marie was totality born out of love. Felix Mendelssohn and his sister, Fannie, loved J.S. Bach so much that they introduced Gounod to the music. Of course, they loved and admired one another as brother and sister. Charles Gounod loved the 1st Prelude so much that he set it to a beautiful melody. Gounod’s father loved and accepted his daughter’s finace, Charles Gounod. Finally, the father loved Gounod’s melody so much that he arranged for the group to give a concert at his house that in effect introduced it to the world. There are many wonderful holiday stories, but I think that this relatively unknown one is with the best. Please share it with your friends for some extra great Christmas and holiday cheer! My own best wishes for the holiday season, David.










Beethoven was Born Under Sagittarius


Beethoven was Born Under Sagittarius. The sign has the distinction of being the only one that is half animal and half human. It is a centaur with an upper human body and the lower part is a horse. The bow and arrow points to the heavens as aspiration is lofty. Certainly, Beethoven had high goals as his crowning work, the 9th symphony, was about the brotherhood of man. As Sagittarius is not affected by hardship. as most people are, he wrote his 9th under the strain of deafness. As Sagittarius people love the outdoors, Beethoven came up with many of his themes while walking through the woods in Vienna. Sagittarius loves their freedom and independence. A famous Beethoven story goes something like this: Beethoven was strolling in Vienna with his friend, Heinrich Heine as the King of Austria was passing by. Heinrich immediately bowed before the king but Beethoven didn’t. The incensed king said “Beethoven, why did you not bow before me?” To which he answered, “After you are dead and gone, there will be many kings like you, but there will only be one Beethoven.” The king thought for a m0ment and then said “You are right.” He then went on his way. Now, is that nervy or what?

Beethoven’s Sagittarius-like Accomplishments

As Sagittarius has a great mind for business, Beethoven  broke the pattern of dependency on royalty that other musicians had. He thereby elevated the stature of the composer-performer.  As pianists would challenge each other with judges on hand to duels on the piano, Beethoven won every “piano duel”. He elongated the symphony, added new instruments and every  featured a grand chorus in his 9th singing Ode to Joy, titled after Schiller’s poem.  Having the will power to write your greatest major work while deaf takes determination.  The older I become, the more I stand in awe of the great composers of our civilization. After years of giving piano lessons in Sarasota, I have found that almost every girl wants to play Beethoven’s Fur Elise; and every boy wants to learn his Moonlight Sonata. I accomplished this feat, and from memory, after one year of piano lessons.  Also, keep looking for my book, Music Under the Zodiac. 

Music is a higher revelation than all wisdom and philosophy–  Beethoven.

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Beethoven: in his studio and wrestling with the forces of nature as he searches out the highest revelations  through the muse of music.





A Ballet Blog on the Nutcracker

A Ballet Blog on the Nutcracker:  That so many versions of Tschaikovsky’s Nutcracker Suite are thriving proves that all over people love beauty and melody. I would go so far as to say that a performance of the Nutcracker in your city or town by the residences of your area is even wonderful, not only for spiritual values, but for real estate values. Who doesn’t want to move into a town with a thriving ballet like we have in Sarasota?

Carnegie Hall in New York City



Andrew Carnegie said:”No man becomes rich unless he enriches others.” I have that motto with his picture posted in my studio. Tchaikovsky’s Nutcracker Suite has enriched all of us. I feel compelled to share a list with you presented by the New York Times in a front page feature article entitled- “All flavors of sugar plums”. Of course, this is an allusion to the Dance of the Sugar Plum Fairies from the Nutcracker Suite. The list of companies  is both surprisingly and even shockingly long. These are merely the more well known ones.

  • Nutcracker Rouge under Austin McCormick
  • New York City Ballet under George Balanchine
  • Nutcracker Winter Suite by  Valentina Kozlova’s Dance Conservatory Company
  • The Yorkville Nutcracker Dances- Patrelle
  • Great Russian Nutcracker by Moscow Ballet
  • The Nutcracker by Gelsey Kirland Ballet
  • The Knickerbocker Suite by the Manhattan Movement and Arts Center
  • Keith Michael’s The Nutcracker, NY Ballet Theater
  • The Hard Nut by the Mark Morris Dance Group
  • The Colonial Nutcracker by Dance Theater in Winchester
  • Nutcracker by the Staten Island Ballet. This concert is free to special needs children and the elderly!

I certainly believe that Andrew Carnegie was right in his enriching quote above.  On a personal note, my wife and I are achieving recognition as composer/arrangers. Listen to some of our work on the thumb nails on the front page of DSOworks. com.  Notice: The performance by Joyce Valentine of our Elemental Suite and some of our other music at the Neel Auditorium on January 14, has just been cancelled as of December 2. – Sorry.




Another Fibonacci Discovery

Another Fibonacci Discovery: I believe that the four writers of the 4 Gospels had the 3 x 3 number square in mind when they wrote about “the grain of mustard seed.” They describe the a mustard seed as the tiniest of seeds that grows into a huge plant. Indeed, the 3 x 3 number square is the smallest number squares: It grows into the largest of the seven squares of antiquity. A 2 x 2 block  only holds  the central numbers of even numbered squares as in 4 x 4 or 6 x 6 (see illustration); whereas only one number is at the center of the odd numbered squares.

As you can see, the even 4 x 4 number square has 4 numbers in the center ( and the 3 x 3 has one number (5).  For this reason, complete number squares begin with the 3 x 3 number square pictured below. For a quick review: I have demonstrated in these blogs the triple system of balance in the 3 x 3 square. How 5 is the center by single numbers, 55 by double numbers and 555 by triple numbers. Anyone who doubts this should go to Washington DC and look at Washington’s Monument. It is 555 feet tall (not a simple co-incidence).

Another Fibonacci Discovery. Let’s begin by listing the numbers of the series in order of size and see if 555 comes up:……oops! somehow it seems like we missed it. We have number 5 as the 5th number, number 55 as the 10th number; and it would seem like the 15th number should have been 555, but it is 610. That threw me until I realized that 610 is merely a summation of 55 +555=610. How is this another Fibonacci discovery? The entire framework of the Fibonacci series grows out of the core number of the first number square that ancient civilizations associated with the planet, Saturn, the giver of law.  I would say that the placement of Washington’s pinnacle at the center of our nation makes it a wonderful architectural monument  not only for America, but for the entire world and for all time.           Image result for Picture of George Washington's Monument out of copyright

Musical tones come from this basic number square and is a Universal constant

Beethoven: His Fibonacci Fifth

Beethoven: His Fibonacci Fifth: Most of the world, I hope, knows of Beethoven and his 5th Symphony with its famous opening four note motif- a quick rhythmic repetition of four notes with a repetition on a different tone.  In contrast, few know who Fibonacci was and the numerical system that was named after him.{\clef treble \key c \minor \time 2/4 {r8 g'8[ g'8 g'8] | ees'2\fermata | r8 f'8[ f'8 f'8] | d'2~ | d'2\fermata | } }

We are about to tie Beethoven and Fibonacci together. Now who was Fibonacci? Leonardo Bonacci (c. 1170 – c. 1250)—known as Fibonacci (Italian: [fiboˈnattʃi]), and also Leonardo of Pisa, Leonardo Pisano Bigollo, Leonardo Fibonacci—was an Italian mathematician, considered to be “the most talented Western mathematician of the Middle Ages”. Before I tie the two together, here is another question: Most musical motifs and phrases come in either in two or four bars of music. Beethoven deliberately set his musical motif in five. He could have simply placed another bird’s eye (which hold the note longer and is called  a fermata) on the “D” in the fourth bar, but  he adds a fifth bar and places the “bird’s eye” over that note. It’s Leonardo Bonacci to the rescue.

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Leonardo Bonacci who was born 600 years before Beethoven. The Fibonacci series, named after him. is colored in red.


Leonardo Bonacci recorded an ancient series of numbers which not only explains biological growth, galaxies and even shows us when to invest in the stock market. Stock brokers study this principle which I will blog about in the future. Since “0” is not a number, starting with one, we see that 5 is the fifth number. Now. at this point  you have every right to say, that’s just a silly co-incidence with Beethoven’s 5th.  My source is Trudi Hammel Garland in, Fascinating Fibonaccis: Mystey and Magic in Numbers: With the opening 5 bar motif given above, the “A” section of the 1st movement is 233 bars long. The “B” section, also known as the development, is 377 bars long.


Behind Leonardo Bonacci’s back, the highest red number is 55. Each new number is the sum of the preceding two. Number 34 precedes 55. So, let’s continue the series: 34 + 55 = 89. Next, 55 + 89 = 144. Next 89 + 144 = 233 (the length of Beethoven’s opening section). Next 144 + 233 = 377 (which  the length of Beethoven’s development section). Beethoven, being the brilliant genius that he was, knew exactly what he was doing. When we listen to the symphony it sounds so natural; but can you imagine how he must have struggled to make the bar length come out right and still sound like that’s how it should be? Leonard Bernstein says of Beethoven and the 1st movement in The Joy of Music: “he will give away his life just to make sure that one note follows another inevitably.” In conclusion, I think that in addition to an even greater appreciation of Beethoven, we have graphic proof the relationship between music and numbers; and why piano lessons, music theory and composition increase aptitude for mathematics.