Numerical nature of ancient mathematics

Numerical Nature of Ancient Philosophy is Number Squares

Numerical Nature of Ancient Philosophy is Number Squares. There are three varied approaches to ancient mathematics. Today we will only examine “real numbers.” Categories 2 and 3 will be future blogs.

  1. Use of “Real numbers” being numbers 1 – 9.
  2. Synthetic numbers being 10, 110, 1110, 11110.
  3. Repeated “real numbers” as 11, 22, 33…Or; 111, 222, 333…Also; 111,222,333…. to the nines.*

Numerical Nature of Ancient Philosophy is Found in the Phrase “To the nines.”

Lyrics from “Don’t Cry for Me Argentina”. You won’t believe me, all you will see is a girl you once knew
Although she’s dressed up to the nines.

  • Evita (New Broadway Cast Recording)


My blog traces the history of “to the nines” to prehistoric times. Number squares were of prime importance. What set the concept and pattern of the number squares in motion was the smallest. It is referred to as the grain of mustard seed in the Bible. It uses the numbers one to nine. Nine becomes the maximum. Higher numbers are synthetic.  For example: Ten is the total of any two opposite numbers around the perimeter of the featured picture.  Examples are 9 + 1 or, 3 + 7. They combine two or more numbers in set patterns. Ten, in the distant past, did not exist as an independent number.  In musical terms repeated patterns on different tones is called a sequence. They musically demonstrate a property we will study in number squares.

J.S. Bach Concerto for Two Violins in D minor, first movement, bars 22-24


The meaning of this ancient number square is revealed in the phrase Dressed to the nines.  But the history of nines is much older than this defining quote. Perhaps some 10,000 years older. *”To the nines” is an English idiom meaning “to perfection” or “to the highest degree” or to dress “buoyantly and high class”. In modern English usage, the phrase most commonly appears as “dressed to the nines” or “dressed up to the nines”.[1][2]The phrase “dressed to the nines” is just a specific application of the Scottish phrase “to the nine ” The earliest written evidence of this phrase appeared in the late 18th century in the poetry of Robert Burns. Its meaning is “to perfection; just right.

Much more to come on the featured picture of the Grain of Mustard Seed  and categories 2 and 3. Keep checking the blogs.

Musical underurrents of J.S. Bach revived in the Romantic Era

Musical Undercurrents Are About to Surface

Musical Undercurrents Are About to Surface. The following sequence attaches itself to musical styles:

  • A style begins with the 1st generation.
  • The 2nd generation literally buries the style of the 1st. It has a new concept for music.
  • The 3rd generation of style buries the 2nd. It then resurrects the ideas from the 1st.

Here’s how it has worked in our western music history. Let’s begin with the Baroque Era:

  • J.S, Bach culminated the Baroque Era of counterpoint. It transitioned to a simpler style around 1750.
  • The Rococo era and early classical were the next musical trends. They used a melody and accompaniment approach. Simplicity was preferred.
  • The Romantic Era came with Beethoven’s middle and later works. This was after 1800. Bach, counterpoint and complexity came back into vogue.

Baroque Musical Undercurrents Resurfaced  Romantic Era

Musical undercurrents of J.S, Bach resurfaced in the Romantic Era
The Autograph of J.S. Bach in musical notes

In music, the BACH motif is the motif, a succession of notes important or characteristic to a piece, B flat, A, C, B natural. In German musical nomenclature, in which the note B natural is written as H and the B flat as B, it forms Johann Sebastian Bach‘s family name. One of the most frequently occurring examples of a musical cryptogram, the motif has been used by countless composers, especially after the Bach Revival in the first half of the 19th century.

How Do the Musical Undercurrents Apply to Today?

Either rap, puck and rock and roll have have been in the forefront of popular music from Elvis in the 50’s to the present time.  This is about 65 years. It has outlasted the earlier Rococo and early classical styles of  European western music. Inevitably, music  with strong melody, like in the 1930’s, will resurface as a main thrust. Rhythm, of course, always must be there, regardless of style. Our new musical, Golden Roads, is avant guard in this respect. Yes, it also has the element of counterpoint. I say, welcome to another return of the Romantic Era.

Triads are at the basis of our harmony in music.. My Boogie Man of the Opera starts with the Bach and goes wild from there,

Triads – Their Bond With Alchemy and Chemistry

Triads – Their Bond With Alchemy and Chemistry. The first hidden code of alchemy is that is the 4 elements. They are earth, air fire and water. Here is what they hide:

  • Fire is the code for hydrogen. The primary stellar source of fire is hydrogen.
  • Earth represents carbon. The hardest earth substance is diamond. Diamond is all compressed carbon.
  • Air is the hidden name for nitrogen. Our atmosphere has approximately 75% nitrogen.
  • Water is reserved for oxygen. By atomic weight, not by atom count , water is mostly oxygen. It is hydrogen hydroxide.

The alchemical four elements are really the basis of organic chemistry. Their atomic numbers, which define the elements are:

  • Hydrogen-1.
  • Carbon-6.
  • Nitrogen-7.
  • Oxygen-6

Now, let’s parallel the four elements to the four types of triads. Here is their definition by half tones.  These 1/2 tone distances are given from the note before. “X” represents the starting tone. Note: Our basic unit, the “one” is the half tone. Like the hydrogen. The diminished is “6” like the carbon. The major and minor are 7 like the nitrogen. The augmented is 8 like the oxygen.

Four elements, four seaons, four triads. Who's counting?
Classical sets of four really come from the centers of the even numbered number squares used Neolithic times. I blog all about these.


  • Diminished triad:  X-3-3 (total 6 half tones from the starting note). This is like earth or carbon.
  • Minor triad: X-3-4 (Total is 7 half tones from the starting note). These next two are like air or nitrogen
  • Major triad: X -4-3 (Total is 7 half tones from the starting note). Same as above.
  • Augmented triad:  X-4-4 (total is 8 half tones from the starting note). This is like water or  oxygen.
  •  The basic building block is the starting tone. It is the fire or hydrogen.
    image 1 of 23

     Here, I hope, is a treat. Blogger, David, is  playing his own take off on J.S. Bach’s Toccata and Fugue in D minor. I play it  as a Boogie-Woogie. Nobody else has even attempted to  play it. The music is just too difficult. Classical players can’t cut the jazz. Jazz players can’t master its classical aspect. If you are daring enough, I offer it on the product page of Otherwise, simply sit back and enjoy me playing it on the Steinway grand at the Selby Public Library in Sarasota. I also offer piano lessons in Sarasota, Fl. Finally, since I think the Boogie is fun and engages the mind, feel free to share it with your friends.



How, Music is in the Biblical Name, David

How, Music is in the Biblical Name, David: OK, so my name is also David. I’m a composer/pianist. Pure co-incidence. The Hebrew language can lift the fog that lies between the similarities between music and David. In Hebrew letters, David is spelled “dalet, vav, dalet”:  דוד. As a letter and  a number actually share the same symbol in Hebrew, we have:

  • Dalet- the 1st letter equals 4
  • Vav- the 2nd letter equals 6
  • Dalet-the third letter equals 4.

Now, I hope not too many of you will be upset with this quote from Aristotle:”The elements of numbers are the elements of things and therefore, things are numbers.” The most obvious connection of numbers with things are musical intervals. They use set ratios between two number.


The basis of both ancient and modern tuning is the musical fifth. Here is the ratio of the two tones:

  • For every time the higher of the two tones vibrates three times,
  • The lower note vibrates two times
  • To hear these notes just think of the opening 4 tones of “Twinkle, Twinkle Little Star”. The second two are a fifth higher than the first two.

Now let’s look at the numbers behind the name of David:

  • 4 to 6 reduces to 2 to 3. By interval ratios this defines the lower fifth from a starting tone,
  • then 6 to 4 reduces to 3 to 2. This defines the higher fifth from a lower starting  musical tone

David’s power came through his music. He harmonized with the natural plan. This is why the Bible speaks of him as a musician first and and ruler second.


At this point, I must mention another upcoming project (too many projects!). I call the book Music Under the Zodiac. It is based on a unique way to align the 12 key signatures with the 12 signs of the zodiac. It will be used to advance musical therapy. For example, if you have a headache, listen to the music in F# minor.    So much is recorded on Youtube that is free. Most important, pick a pianist with a good touch. Arthur Rubinstein is my favorite in this regard. I also plan to make piano recordings of music that uses my inspired system of therapy. I have several examples of touch in the music of Debussy on my front page of DSOworks,com.  Francois Couperin le Grand wrote a treatise on this subject in 1717. It is called L’Art de Toucher le Clavecin. Then, if you care to, e-mail me about the effect of the music you’ve listened to.

  • Chopin- Polonaise Opus 44 in F# minor
  • Chopin- Nocturne Opus 48 #2
  • Brahms- Sonata in F# minor
  • J.S. Bach- Prelude and Fugue No. 14 Book II of The Well-Tempered Clavier
  • Rachmaninoff- Concerto in F# minor opus 1.
Astrology Signs, Birth Signs, Zodiac, Astrology
The Discovery I Made Between Key Signatures and the Zodiac Can Help the Cause of Musical Therapy. Keep Watching For My Book: Music Under the Zodiac. It’s 3 or 4 months away from publication on this website. I’ll try to hurry!



It’s time to appreciate composer Joachim Raff


It’s time to appreciate composer Joachim Raff. Critics of his day compared the quality of his compositions to his contemporaries, Johannes Brahms and Richard Wagner. I agree. Apparently so did Bernard Herrmann, conductor of the London Symphony Orchestra who featured his Lenore Symphony #5  on May 27-29 1970  in concert. But where is his music now? Why has his music been ignored? I just happened to be sight reading an etude from Schirmer’s Concert Etudes for the Piano edited by Balough.  Raff’s Etude Melodique  Opus 130 No.2 was so well written that I think it’s on a par with the Etude, Un Sospiro, by Franz Liszt. He orchestrated for Liszt for a number of years in the 1850’s.

Raff, 1878 (published in John Knowles Paine‘s Famous Composers, Vol. 2, 1891)

Joseph Joachim Raff (May 27, 1822 – June 24 or June 25, 1882) was a GermanSwiss composer, teacher and pianist.[1]


I feel that, quite bluntly, he went against the male bastion of composers that kept women out of their field. This segregation had been there’s for hundreds of years. In Frankfort Germany Raff was the first director of the Hoch Conservatory of Music. He actually established a class for female composers at a time when women were not taken seriously. Worse yet, Raff hired a woman, Clara Schumann, to instruct composition. Heavens! Does this make him any less of a composer? It just proves that he was secure in his own musical composition.


Felix Mendelssohn was a wonderful supporter of great musicians and composers. He resurrected the music of J.S. Bach in 1829, almost 80 years after Bach passed away, by conducting Bach’s Passion According to St. Matthew.  Mendelssohn also championed the compositions of Raff. In writing this blog, I hope Im doing the same. I feel that music of a romantic nature is about to make a come back. I also think that Rapp has taken a bad wrap for too long a time. Please listen to some of his music and let me know what you think.



The Phantom of the Opera is Now a Boogie?

The Phantom of the Opera  is Now a Boogie?  Yes, and the sheet music is available for purchase on this website. Longevity has come to the  Phantom of the Opera  originally written by Gaston Leroux  as a French magazine series in Le Gaulois.  His first installment appeared September 23, 1909.  Some 106 years later, Andrew Lloyd Webber’s  version is still the longest running musical in the history of Broadway.  As a composer, I have chosen to add to the crest of the Phantom wave with a little help from Bach through his Toccata and Fugue in D minor. I have turned “The Phantom of the Opera” into the “Boogie Man of the Opera” which is available for purchase here.  This work, with its “entertaining version of horror and villainy” not only found its way into the Hollywood film of the Phantom of the Opera (1962) (picture below); but also earlier in Dr. Jekyll and Mr. Hyde (1931); the Black Cat (1934) and later in Disney’s film, Fantasia.

Erik, The Phantom (Lon Chaney) and Christine Daaé (Mary Philbin)

I took Bach’s Toccata and Fugue in D minor  and made it into a boogie-woogie!

The Phantom of the Opera is Now a Boogie? I took Bach’s Toccata and Fugue in D minor  and made it into a boogie-woogie!  Since Bach loved experimentation, most “long-haired”musicians agreed that he would have approved of the project. I was living at the time with my wife and three children in  Toronto in a duplex at 68 Thursfield Cresent.    During cocktail hour I played the piano at the Prince Hotel in Don Mills and at night, I went around the corner and entertained during the dinner hour at the Duncan House.  However, as that winter of ’87  was ferocious, we were often home bound which gave me plenty of time for the project.  I’m including an excerpt for listening.  Until this last year, I have been playing piano in the  summers regularly in New York at Scott’s Oquaga Lake House in Deposit, NY. where my Bach boogie continually receives bravos.  This winter I will begin my 7th year playing the vintage Steinway pianos 6 nights a week at  Gasparilla Inn on Boca Grande in Florida (click on upcoming events).  I frequently close my evenings with the Toccata and Fugue a la boogie for the amusement and enjoyment of  patrons.