Periodic Chart Harmony

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]

pyramiding dots point to the 3 x 3 number square grid and the periodic chart
T-1 is the unison. T-2 is the 2:1 octave ratio. Other harmonies are for future blogs.

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.

 

 

Careless musical editors dominant the works of J.S. Bach

Careless Music Editors Point the Wrong Way

Careless Music Editors Point the Wrong Way. I am a proud graduate of Cass Technical High School in Detroit. The school was a four-year university preparatory high school in Midtown Detroit, United States.[2][3] The school is named in honor of Lewis Cass, an American military officer and politician who served as governor of the Michigan Territory from 1813 until 1831. The school is a part of Detroit Public Schools. In the 1960’s Cass Tech two major musical curriculum. Both were college prep. The school had some 30 college prep courses of study. You could even major in aeronautics. We actually had an airplane in one of the rooms that you could work on for assembly or repair.  In the music courses the  students were wise to editors. We all spoke of a professional frustration cycle. It went from soloist to conductor to editor. Editors, we half-jokingly said, wanted to get revenge on everyone else. Obviously, they couldn’t be successful at the first two professions. Not bad for high school kids!

Careless music editors were bantered about at this High School in Detroit
My High School Alma mater was Cass Technical High School in Detroit

J.S. Bach omitted placing tempo, phrasing or dynamics in his works. Over zealous editors quickly stepped in.  I quote Edward Hughes from G. Schirmer  & Co. I think he is one of the good ones. Edwin Hughes taught at the Ganapol School of Musical Art in Detroit from 1910 to 1912, the Volpe Institute of Music in New York from 1916 to 1917, and the Institute of Musical Art in New York from 1918 to 1923. He lectured at various schools. From 1920 to 1926 he was special editor of piano music for G. Schirmer, Inc. He toured widely in the USA and Europe after the close of World War I; performed duo-recitals with his wife, the pianist Jewel Bethany Hughes, and also gave master-classes. He also had opinions about careless music editors.

Careless Music Editors Over-Edit

I am currently working on the Bach Prelude and Fugue in A minor. It is transcribed for piano by Franz Liszt. Publisher is G. Schirmer Inc. Hughes humbly states about his editing: “The phrasing is to be regarded more as indicative than complete. Of himself he states “There is no desire to appear arbitrary in matters of pedaling, touch and so forth. Also bear in mind: “In the democracy of art there is no final authority on such subjects.” I think these are the words of a great man.

Finally, if anyone is interested I have  I have one or two openings for piano students in Sarasota.

Mischa and I in our Sarasota Home
My instructor, Mischa Kottler, studied with Emil von Sauer- a pupil of Franz Liszt. I acquired a Master of Music degree from Wayne State University under Mischa.

Bach keyboard preference is the harpsichord

Bach Keyboard Preference- Proof is Quite Surprising

Bach Keyboard Preference- Proof is Quite Surprising. We will consider the harpsichord v. the clavichord. All kinds of keyboard falsehoods were spread in the 19th century. Inaccuracies affected keyboard virtuosos, piano teachers and, of course,  instrument builders.

During Bach’s later years,  a new style began brewing.The new style rebelled against counterpoint.  J.S. Bach’s son, Karl Philipp Emanuel, was in favor of change. He advocated the galant style. In music, galant refers to the style which was fashionable from the 1720’s to the 1770’s. The clavichord was well suited to the galant style. This movement featured return to simplicity. It advocated immediacy of appeal.  The style ignored the complexity of the late Baroque era. This meant simpler, more song-like melodies. The sweeter and quieter sound of the clavichord was suited to this style.  The style had decreased use of polyphony.  It favored short, periodic phrases. Harmonic vocabulary was quite limited. It emphasized the tonic and dominant triads. A clear distinction was made between soloist and accompaniment.

Bach Keyboard Preference Favors the Harpsichord

Bach keyboard preference
There is a world of difference between a harpsichord and a clavichord.

No matter how ingrained a style may seem, its life is limited. Of course, that rule applies to today: It holds for popular styles in America as well as the rest of the world. Consider this: In Baroque times  many composers wrote sweet or expressive music for the harpsichord. They included Rameau, Couperin and Frescobaldi. Titles, for example, included: Les Tendres Plaints, La Reine des Coeurs, Canzone, etc. However, Bach also composed music of force and fury. That was more suited to the harpsichord. The harpsichord was flexible. It could be either sweet sounding or furious,

Proof Positive of the Bach Keyboard Preference

After Bach’s death an actual inventory of musical instruments in his home was made.  In the realm of keyboard instruments he had: (1) Five harpsichords. (2) One spinet. (3) He even gave three-pedal harpsichords to Johann Christian before his death. In the inventory not even one clavichord is mentioned. The value of his harpsichords amounted to one-third the value of his entire estate. The entire estate was valued at 1122 rt. 16 gr. My source is Landowska on Music:Collected, edited and translated by Denise Restout assisted by Robert Hawkins. Conclusion: Every keyboard has a personality in the same manner as every person. Incidentally, I have a few openings for piano lessons in Sarasota.

Bach Keyboard Preference:picture of Wanda Landowska on DSOworks
Wanda Landowska
Andante Tempo Chaos

Andante Tempo Chaos as Tempo Lacks Resolution

Andante Tempo Chaos as Tempo Lacks Resolution. I enjoy reading books on music. Landowska on Music is such a book. Wanda Aleksandra Landowska (5 July 1879 – 16 August 1959) was a PolishFrench harpsichordist whose performances, teaching, recordings and writings played a large role in reviving the popularity of the harpsichord in the early 20th century. She was the first person to record Johann Sebastian Bach‘s Goldberg Variations on the harpsichord (1933). She became a naturalized French citizen in 1938.[1]

Landowska we lwowie.jpg

Wanda Landowska in 1937

Her chapter 10 is  entitled “Of Movement and Measure.” I was enthralled by her method of defining the word “andante”. I felt it was necessary to share it with my readers. The differing descriptions of this term can leave a person confused. You might ask, is there even a real answer? She also compares the descriptions of Andante with Andantino. Musicians, read the quotes and decide for yourselves.

Musical Dictionary Andante Tempo Chaos

  1. Le Dictionnaire de l’Academie Française states:  Andante- moderate movement.
  2. Littré: Andante- not too fast or too slow.  Andantino- slower than Andante.
  3. L’Encyclopédie:  “Andante” slow movement.  Andantino – faster than Andante (an obvious contradiction with #2).
  4.  L’Encyclopédie des Gens du Monde: “Andantino”- faster than andante. However, under the word “Movement” we find”Andantino” is slower than andante!
  5. L’Encyclopédie Moderne: “Andantino” means a slower measure and a certain regularity in movement, more in keeping with stiffness than with gravity.
  6. Larousse: “Andante”- moderate movement with a tendency towards slowness. “Andantino” -word indicating a modification of movement (whatever that means).
  7. I’ve saved what I think is the best quote for last:  Le Nouveau Larousse- Andantino- more animated. All musicians agree on this subject!

Well, what source are you going to believe? Perhaps the performer factors into the andante-andantino equation. A most beautiful description of Andante came from the incomparable lady,  George Sand. She was Chopin’s companion and lover. “Autumn is a melancholy and gracious andante which admirably prepares the solemn adagio . Please share this with friends. Perhaps this blog illustrates why most can’t seem to agree on anything- even andante.

George Sand by Charles Louis Gratia (c. 1835)

Changing Music Indicates Changing Times

Changing Music Indicates Changing Times. Welsh music, as recorded in the Welsh Triads, adjusted its music to changing times. Here’s how. In ancient England, changes were foreshadowed by “perpetual choirs.”

Changing Music and Perpetual Choirs?
The Welsh Triads speak of perpetual choirs of saints in the distant past.

How did I discover this? My source is City of Revelaton by the Reverend John Michell. The Welsh Triads are verses of great antiquity. They were written by “prehistoric bardic historians.” Unique choirs are mentioned:

  • One at the now existing site of Glastonbury Abbey.
  • Another operated at the site at which Stonehenge now exists.
  • A third was at Llantwit Major at Glamzorgan.

2,400 saints worked each site. Each kept a perpetual chant going. Each of the 24 hours of the day, at each site, occupied 100 saints with singing.

As the Times Varied, Changing Music Marked Their Song

The character of time changes with the seasons. As light can change by the hour, so could their song. Another aspect of song was planetary. The school of Pythagoras believed that each planet had its own pitch. As their distances from each other changed, so did the music.

We are currently living through times of great change. Music that heralds beautiful melody will lead the way. In all aspects, people will buy what is beautiful. I was taught to play with beautiful tone. Play well-formed two-note phrases are key. Also, how to emphasize the note that is tied over the measure. My instructor was Mischa Kottler.

Image result for picture of Mischa Kottler for the blog on changing music
Mischa Kottler was a pupil of Emil von Sauer, Sauer studied over two years with Liszt.

In looking to this beautiful past, I am helping to lead the way to the future. We all need beautiful things in our lives. When times are difficult, all need the beautiful in art, poetry and music. To this end, I am working full time this year. I will be playing piano from Christmas to Easter. This will be six days weekly. The location is at the Gasparilla Inn on Boca Grande.

Image result for picture of the Gasparilla Inn n the Isle of Boca Grande
I play here on a vintage and newly reconditioned Steinway concert grand from the 1920’s. Parts were shipped directly from Germany.

 

Until Christmas, I am working to bring musical beauty back at the Crab and Fin Restaurant on Saint Armand’s Circle. I play three days weekly. Call for specifics. Wear something comfortable, but beautiful. Enjoy a tasty and well-presented meal  while dining outdoors to my piano music.

 

 

 

New music of the romantic era reflects the times in Beethoven's later music.

New Music Heralds New Ages Like Beethoven’s Music

New Music Heralds a new age. This was a known truth in the past. New music was created by the great composer, Beethoven. At first he wrote in the classical style. By 1810 he became a crucial figure in the transition between the Classical and Romantic eras. In Western art music, he remains one of the most famous and influential of all composers. His best-known compositions include

Image result for picture of Beethoven's piano
Beethoven’s new music included many Masonic principles.

Classical music was often written written for royalty. It needed tp be pleasant and unobtrusive. Romantic emphasized feelings and emotions of the individual. Its range of passion and expression were greater. The power and magnificence of nature was also a subject for Romantic musical expression.

Ludwig von Beethoven was a Mason. A such he knew many Masonic secrets. These secrets heavily figured into Beethoven’s creativity.One such secret was the Fibonacci series of numbers. They grew by successive addition. Nature develops by these numbers. The series goes: 1,1,2,3,5,8,13,21,34,55,55,89,144,233,377,610 etc. Two previous numbers are added to get the next sum.

Related imageLeonardo Fibonacci was born 600 years before Beethoven. The beginning of the Fibonacci series, named after him. are the numbers in red.  It continues to infinity.

Beethoven used this series in his Fifth Symphony. Of course, 5 is the first non-successive Fibonacci number. The series skips from 3 to 5. Here is the proof: 233 measures is the length of Beethoven’s opening section. 377 is the length of Beethoven’s development section).

But Beethoven’s Masonic Use of New Music Goes Even Further

The Masonic tool for engineering par excellence was the 3 x 3 number square. Many of the free blogs on DSOworks.com cover the subject. Look at the composition list above. Beethoven wrote 9 symphonies, 5 piano concertos, and  1 violin concerto. This is a vertical, middle column read across the square of three. I blog about how Solomon’s Temple used this section. The Second Jerusalem Temple used the entire bluprint. Look at the next two numbers of his output:

  • 32 piano sonatas
  • 16 string quartets.

Read my blog about the period chart. The square root of 32 comes from the geometry of the grid. Also, the ratio of 32 to 16 by the sonatas and quartets form a 2:1 ratio. This defines the first fundamental perfect overtone of the octave. Finally look at his crowning 9th symphony. It is all about the brotherhood of man!


Related image

Musical sequences

Musical Sequences are Both Universal and Basic

Musical Sequences are Both Universal and Basic. In music, a sequence is the restatement of a motif or longer melodic (or harmonic) passage at a higher or lower pitch in the same voice.[1] It is one of the most common and simple methods of elaborating a melody in eighteenth and nineteenth century classical music[1](Classical period and Romantic music).  Examples of characteristics of sequences:[1]  

Look at the music of the featured picture: The sequence is well known in America, Canada and England. In the U.S. the music is an excerpt from “My Country Tis’ of Thee.” In England it is “God Save the Queen (King)”. Bars 3 and 4 form a sequence with bars 1 and 2. They use the same pattern, only one tone lower. Just as a refresher, here is the British and American music on youtube. The British words are “Send him victories, Happy and glorious.” In America the corresponding words are “Land where my fathers died, Land of the pilgram’s pride.”

Examples of how Musical Sequences are Universal and Basic

God save the King – The national anthem of the British … – YouTube

My Country, ‘Tis of Thee (with lyrics) – YouTube

Musical Sequences Applies to the Sciences

Let’s look at basic scientific sequences. They work on the same principle as music. In Platonic style, here’s two basic groupings of numbers: 3-4-5 and 6-7-8. We have a true pattern for musical sequence operating in math and the sciences.

  • 3-4-5 has geometrical import.  One is the single line that begins the process. The classic example is the 3-4-5 Pythagorean  right triangle. The formula is 3² + 4² = 5². Of course, with the 5 Platonic solids,  three use triangles (3 sides).These include the tetrahedron, octahedron and icosahedron.  The cube uses squares (4 sides). The dodecahedron uses pentagons (5 sides). Pictures are below.
Image result for picture of the 5 platonic solids on DSOworks
Platonic solids have regular polygons of either 3 4 or 5 sides.
  • 6-7-8 has implications for organic chemistry. Hydrogen begins the count. It is like the single line that begins form in geometry.  Hydrogen’s atomic number is one. Six is carbon’s. Seven is nitrogen’s. Eight is oxygen’s.
Ethanol-structure.svg
An example of an organic compound. Carbon + 6. Hydrogen = 1. Oxygen = 8.

Ethanol-CRC-MW-trans-3D-balls.png  Ethanol-2D-skeletal.svg

 

 

Conclusions: This blog puts forth mathematical Platonism.   Here mathematical entities are abstract They have no spatial, temporal or causal properties.  They are eternal and unchanging.  Numbers represent eternal truths. They are behind everything. Musical sequences, by sound,  express their beaty through sound.

 

 

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Tones plus overtones both come from a number square

Tones Plus Overtones Prove Former Advanced Civilization

Tones Plus Overtones Prove Former Advanced Civilization. This civilization knew the ways  peace. It was a time when “yin” ruled. This is according to Chinese tradition. Also according to Chinese tradition is Feng shui.  Both peace and Feng  shui are based on the 3 x 3 number square. So are two key points of this blog, (1) the primary overtones ratios.  (2) Their vibrations per second  in antiquity.

An overtone is any frequency greater than the fundamental frequency of a sound. Here is the illustration: Play a low “C” on the piano. It is tone “1” in the illustration.  Call this low “C” the fundamental. When played, this tone sets off a series of tones. The strongest are the first five above the fundamental. They also make for the most pleasing ratios in sound. For example 1:2 is the octave.  2 :3 is the fifth. 3:4 is the fourth.

Above is the harmonic series in musical notation.  We see the names of the intervals above the fundamental. . The relative amplitudes (strengths) of the various harmonics primarily determine the timbre of different instruments and sounds.  For example, the clarinet and saxophone have similar mouthpieces and reeds.  Both produce sound through resonance of air inside a chamber.  Each mouthpiece end is considered closed. The clarinet’s resonator is cylindrical. This means even-numbered harmonics are less present. The saxophone’s resonator is conical.  That allows the even-numbered harmonics to sound more strongly.

TONES PLUS OVERTONES PROVE AN ADVANCED, ANCIENT CIVILIZATION

Tones plus overtones of the ancient scale are found here
The simplest of number squares will spearhead a New Golden Age as it did in the past.

Here’s how tones plus overtones work together. Our Neolithic ancestors of this: All “magic square” have characteristic numbers. But this one also has secret number codes. Here are its characteristic numbers:

  • Any two opposite numbers = 10. Examples 4 + 6 or 3 + 7.
  • The single central number is 5.
  • Any straight row of 3 numbers totals 15.
  • The perimeter of 8 numbers totals 40.
  • The perimeter + the center = 45.

Next, here’s how the characteristic numbers relate to fundamental overtones. These are constructed with numbers one thru four. This are expressed by ratios of two consecutive numbers.

  • 1 to 2 is a perfect octave. On the above number square, the ratio of the central 5 to opposite combination on the perimeter of 10 is is 1:2.
  • 3 to 2 is a perfect fifth. On the above square, the ratio of any row of 3 (15) to any 2 opposite numbers (10) is  3:2.
  • 4 to 3 is a perfect fourth. The ratio of the 4 even corner numbers (20) to any row of three (15) is the 4:3 ratio.

Harmonic overtones of fundamental perfect harmonics are defined by these characteristic numbers. They are the octave, fifth and fourth. There are no other Perfect Intervals.

Tones and overtones and number squares.
Knowledge, for me came, from a spiritual presence Oquaga Lake. See products on DSOworks.com.

So Where are the Actual Tones in Terms of V/S on the Number Square?

Go around the perimeter in either direction. Add two numbers at the time as follows.

  • 49 + 92 + 27 + 76 + 61 + 18 + 83 + 34 = 440. Diatonic “A” vibrates 440 times per second.
  • 49 +94 + 35 +53 + 18 + 81 + 92 + 29 + 57 + 75 + 16 + 61 = 660 Diatonic “E” vibrates 660 times per second.
  • 660 to 440 define the 3/2 ratio. These define a section of tones plus overtones.

Other tones of the ancient scale are to found in this number square.  So, the number square holds musical tones.  It has overtones. The number block has interval ratios and their tones. The square of three allows us passage to a lost Golden Age.

 

 

 

Regal Leo the Lionheated

Regal Leo and Audio Musical Preferences

Regal Leo and Audio Musical Preferences. Music Under the Zodiac is the name of my upcoming book. As a musician, I have an interest in the zodiac. There are many parallels, for example:

  • We use the well-tempered scale. It has twelve 12 tones within the octave. There are 12 zodiac signs.
  • We have four types of triads. They are major, minor diminished and augmented.  The zodiac has four elements, They are earth, air, fire and water. Earth is dense. The diminished triad is the most compact. Fire is the most effusive of the signs. An augmented triad is the most expansive of the triads. Water and air parallel minor and major respectively. They fit in their size of 7 half tones from the first note between the earth and fire triads. Earth uses 6 half steps, fire uses eight.

    Types of triadsAbout this sound I About this sound i About this sound io About this sound I+ 

    In music, a triad is a set of three notes (or “pitches“) that can be stacked vertically in thirds.[1] The term “harmonic triad” was coined by Johannes Lippius in his Synopsis musicae novae (1612).

  • Speaking of triads, there are three categories of zodiac signs. They are set by cardinal, fixed and mutable. Cardinal is the month that begins a season. Like the 1st month of Spring under Aries is cardinal. Fixed is the second month of the season. It is Taurus in Spring. The third, a mutable zodiac sign, ends the season.  It is called mutable because it prepares for the next trio of the summer zodiac months. This last month of Spring is Gemini.

What About Regal Leo?

 

 

four aspects of time are cyclic

Four Aspects of the Moon and Four Types of Musical Triads

Four Aspects of the Moon and Four Types of Musical Triads. Time is cyclic. A cycle may be divided into four distinct parts. I call these the four aspects of time. The four aspects of time are continuous. One part of the cycle follows the other in the same order over and over. If we know what point the cycle is at, we can predict the next point.  Just for the sake of starting somewhere in the cycle of time, I listed the up swing of the cycle first.

  1. The winding up of a cycle is the increase of cyclic activity.
  2. The maximum point at which cyclic activity is the greatest is most intense.
  3. After  maximum intensity, the cycle unwinds.
  4. Finally, the point of least activity is reach. Tension disappears. Immediately after this point, the cycle starts another upswing.
Image result for picture of the Moon and its four primary phases
Four aspects of the Moon can be compared to the 4 types of musical triads.

Next we have four types of triads. From smallest to largest they are: Diminished, major and minor, and augmented.

  • Diminished is the most contracted. Counting from the first note, in root position, it has six half steps up to the last note.
  • Major and minor triads are middle of the road. The have 7 half tones from the first note up to the last.
  • Finally, augmented is the largest. It has 8 half tones from the first to the last.
  • Types of triadsAbout this sound I About this sound i About this sound io About this sound I+ 

    In music, a triad is a set of three notes (or “pitches“) that can be stacked vertically in thirds.[1] The term “harmonic triad” was coined by Johannes Lippius in his Synopsis musicae novae (1612).

Here’s how to animate the four phases of the Moon by musical triads:

  1. The new Moon has the least light. The diminished triad is the smallest triad. It has the 6 half tones as described above.
  2. The full Moon has the most light. The augmented triad is the largest triad. It has the 8 half tones.
  3. The waxing and waning Moon are neither the smallest or largest aspect of the Moon. They are in between. They correspond to the major and minor triads respectively. The major would represent the waxing cycle. The minor represents the waning cycle.  Major and minor triads both use 7 half tones from the 1st note.

Four aspects, be they  four elements, the cyclic view of time, or musical triads- all correspond.  The goal is to seek a grand unity of science and art in the same manner as did Neolithic and pre-Neolithic cultures. In unity we find harmony and co-operation.