Wagner Siegfried Idyll

Wagner's Siegfried Idyll, a Symphonic Poem for Chamber Orchestra

German composer Richard Wagner conducts his Siegfried Idyll in his Swiss villa on Christmas morning, December 25, 1870, as a 33rd birthday surprise for his wife, Cosima (daughter of Franz Liszt). It is also a tribute to the birth of their son, Siegfried.  The music lasts approximately twenty minutes.

Mozart in Literature

Mozart in Thomas Hardy's poem and a novel by Chinese author Dai Sijie (trans. by Ina Rilka) Balzac and the Little Chinese Seamstress Literature

The information was sent to me by Terry McIntee, a friend from one of my early Mozart groups way back 2006.  I originally posted his email in my first classical music website CM Lounge. I'm republishing the content to share with Mozarteans and other Mozart enthusiasts. (Thanks a lot, Terry.)

Terry found a couple of things that connects Mozart to literature. He knows that I've always been most interested with any trivia relating to Mozart, including this musical genius's mention in books, movies, to about anything worth knowing.


The first is a poem by Thomas Hardy called: LINES to a movement in Mozart's e-flat symphony

It begins with : Show me again the time

Les Six Composers

Classical Music / Les Six Composers

 

Les Six was a group of early 20th-century composers - five French and one Swiss - who lived and worked in the Montparnasse district of Paris. The group was named in January 1920 by music critic Henri Collet, who drew inspiration from Erik Satie and writer Jean Cocteau. Their music was a conscious reaction against the heavy German Romanticism of Richard Wagner and the lush impressionism of Claude Debussy, favoring clarity, brevity, wit, and contemporary influences like jazz.  

The Members of Les Six:

Darius Milhaud (1892–1974) — Known for bitonality, polytonality, and absorbing jazz and Brazilian rhythms into his work.

Francis Poulenc (1899–1963) — The most famous member, known for his deeply melodic, zany, and poignant vocal, piano, and religious pieces.

Arthur Honegger (1892–1955) — Swiss-born; leaned more toward heavy counterpoint and symphonic structures, keeping some German Romantic influences.

Georges Auric (1899–1983) — Prolific composer of ballets, chamber music, and iconic film scores.

Germaine Tailleferre (1892–1983) — The sole female member of the group, recognized for her delicate, neoclassic grace and dance rhythms.

Louis Durey (1888–1979) — The oldest member and the first to drift away from the collective (in 1921) to pursue a more independent, isolated path.

 

Key Concepts:  

Mentorship: They were strongly guided artistically by writer Jean Cocteau and composer Erik Satie.
Individual Styles: Despite the collective branding, they did not share a single rigid ideology and quickly diverged into distinct, personal careers.

Resources:

Les Siz. Britannica 

Les Six. en.wikipedia.org 

Oxford Companion to Music, Oxford: OUP, 2002

The Grove Concise Dictionary of Music, edited by Stanley Sadie.  London: The Macmillan Press Ltd, 1994

 

(c) December 19, 2012. Tel. Inspired Pen Web. All rights reserved.

Tchaikovsky Ballet The Nutcracker

Classical Music Milestone: Dec 17

The Nutcracker ballet is in two acts and three scenes to a scenario by Marius Petipa and choreographed by Lev Ivanov after Alexandre Dumas Père’s version of E.T.A. Hoffmann’s The Nutcracker and the Mouse King. Tchaikovsky arranged an orchestral suite, op. 71a.

The ballet debuted on December 17, 1892, at the Mariinsky Theatre, St. Petersburg, with a double bill show: Tchaikovsky’s grim opera Iolanta (Iolanthe), followed by the light-hearted ballet The Nutcracker. It was a terrible blow to the composer since The Nutcracker wasn’t warmly received, and the critics, merciless. The composer died less than a year after the ballet’s flop. Interestingly, the ballet was in Mariinsky’s active repertoire for 37 years. It was even performed by other Russian composers, although not that popular.



The complete Nutcracker has enjoyed enormous popularity since the late 1960s and is now performed by countless ballet companies, primarily during the Christmas season, especially in North America. The ballet's score has been used in several film adaptations of Hoffmann's story.
Tchaikovsky's score has become one of his most famous compositions. Among other things, the score is noted for its use of the celesta, an instrument that the composer had already employed in his much lesser known symphonic ballad The Voyevoda.

Suggested Listening:

Tchaikovsky's The Nutcracker without ballet, rather focus is on the orchestra's musicians playing beautifully their parts. Artists: Rotterdams Philharmonisch Orkest. Conductor - Yannick Nézet-Séguin.


Image Credit:

Tchaikovsky's The Nutcracker Ballet  (BalletTheatre)  Kirov Ballet. St Petersburg. Accessed December 17, 2012.


Resource:

Wikipedia. en.wikipedia.org



(c) December 2012. Updated September 29, 2019. Tel. Inspired Pen Web. All rights reserved. 

Robert Schumann Symphony No. 4

Classical Music Milestone:  December 6, 1841.

Robert's Schumann's Symphony No.4 premiered. It was conducted by Ferdinand David at Leipzig's Gewandhaus.   

Symphony No. 4 in D Minor, op. 120, was composed by Robert Schumann.  Although a version of this work was completed in 1841, Schumann heavily revised it in 1851, the version that reached publication.

The 1851 (published) version of the work is in five movements which follow each other without pause:

1. Ziemlich langsam - Lebhaft
2. Romanza: Ziemlich langsam
3. Scherzo: Lebhaft
4. Etwas zurückhaltend - Langsam
5. Lebhaft    

The 1841 version used Italian rather than German tempo indications and had four movements, as follows:

1. Andante con moto - Allegro di molto
2. Romanza: Andante
3. Scherzo: Presto
4. Largo - Finale: Allegro vivace

Schumann's biographer Peter Ostwald comments that this earlier version is "lighter and more transparent in texture" than the revision, but that Clara "always insisted that the later, heavier, and more stately version of 1851 was the better one." Both versions are included on the recent recording of Schumann's complete symphonies by John Eliot Gardiner.


Video Credit:   

 

Schumann: 4. Sinfonie ∙ hr-Sinfonieorchester ∙ Marek Janowski, Conductor. Youtube, uploaded by Frankfurt Radio Symphony. Accessed February 12, 2020. [(Auftritt) 00:00 ∙ I. Ziemlich langsam – Lebhaft 00:26 ∙ II. Romanze. Ziemlich langsam 11:07 ∙ III. Scherzo. Lebhaft 15:04 ∙ IV. Langsam – Lebhaft – Presto 20:33 ∙]

 

Resource:

Robert Schumann Symphony No.4.  en.wikipedia.org. Accessed  Dec 6, 2006.



(c) June 2012. Updated June 12, 2020. Tel. Inspired Pen Web. All rights reserved.

Mozart's Death Anniversary 5 December 2012

A candlelight vigil for Wolfgang Mozart, 2012 Dec 5

Candles up for Mozart! If his music has brought you joy, please consider lighting a candle in his memory.

Light your candle at 12:20am (local time) and extinguish it at 12:55am. This 35 minute duration represents Mozart's 35 years of life and 12:55am represents the time his light left our world on December 5, 1791. This vigil is intended to be a unique and personalized shared experience for Mozart admirers worldwide.

Mozart: Andantino from Concerto in C for Flute and Harp

Mozart's Requiem: The last composition of Wolfgang Amadeus Mozart was the Requiem, K 626, Mass in D minor, one of his masterpieces and most popular works. While ailing and confined to bed, he tirelessly worked on it. He left the Requiem unfinished as he died almost an hour after midnight of December 5, 1791.

In form, the work is in eight parts and contains fourteen musical numbers, as completed by Franz Xaver Süssmayr, Mozart’s pupil.   Check out my related articles:

• Mozart Requiem History (Part 1)

• Mozart Requiem Completed (Part 2)

Mozart - Requiem in D minor (Complete/Full) [HD]


Video Credit from YouTube:

Mozart Andantino from Concerto in C for Flute and Harp. Uploaded by MusicalConcepts.  Renee Siebert, flute; Catherine Michel, harp; Wuttemberg Chamber Orchestra , Jorg Faerber. Mozart set to mesmerizing candles.  Accessed Dec 5, 2012.

Mozart - Requiem in D minor (Complete/Full) [HD]. Uploaded by The Myth of Culturalism. Accessed, Dec 5, 2012.

Something special about Mozart

 Mozart!

(c) By Agnes Selby, Guest Writer-Friend

I can't remember a time when I was not "acquainted" with Mozart. What with the wonderful Mozart biscuits my grandmother baked and the special Viennese chicken coated in breadcrumbs and fried in butter, Mozart came to me first through my stomach. My grandmother's Mozart recipe book is now mine and although we do not fry in butter in a cardiologist's household, the pleasant memories still persist.

As time went on it was his music that engaged my heart. His piano concertos were my staple diet throughout both of my pregnancies for his music was the food I craved.

Later still, when "Amadeus" played in all the theatres around the world, I became alarmed that my Mozart had chosen a silly girl like Constanze for a wife. We lived in Philadelphia at the time and I read all about Constanze in the Curtis Institute's Library. I bought all the books I could find. Then I left for Salzburg where, through the courtesy of the Mozarteum, I spent a month locked up in the Mozarteum archives reading Constanze's letters and her diaries and all I could find about her in that vast library.

Mozart in Novels

Novels that mention Mozart

1. Da Vinci Code

For anyone familiar with Dan Brown’s controversial bestseller The Da Vinci Code, we come across a reference in page 134, well, in some of our own copies. Robert Langdon the Professor is talking to his students about PHI, which he calls the Divine Proportion or 1.618. He says it occurs in nature, in art, in architecture, and “appeared in the organizational structure of Mozart’s sonatas.”  Da Vinci Code by Dan Brown (p.134)

(Contributed by Terry McIntee) 

2. An Angel at my Table

"One evening however, when Karl and Kay brought two records, 'A Little Night Music' and Beethoven's Violin Concerto played by David Oistrach, Frank said, 'We can play them on Janet's radiogram.' Accepting it. I can see that room with the bare wallboard and the wooden floor which Frank oiled each Saturday morning with a mop soaked in linseed oil ('it keeps down the dust'), with the canvas chairs ('the most comfortable type') with their wooden arms, the room that already held all the characters from War and Peace, Anna Karenina, the stories of Tolstoy and Chekhov, from Proust, Flaubert, Olive Schreiner, Doris Lessing, receiving now the music of Mozart and Beethoven while we listen."  An Angel at my Table by Janet Frame (p.152, Vintage Edition)

(Contributed by Terry McIntee)

3.   Snow Falling on Cedars

This is another of those books we read along the way with a mention of Mozart.  Isn't it great when Mozart pops up in literature and other media? I read Snow Falling on Cedars recently and loved the part where Ishmail Chambers sees a recording of the Jupiter on the record player beside his mother's bed, and he imagines her lying there listening to Mozart.  Snow Falling on Cedars is a novel written by David Guterson published by Vintage Books. It's supposed to be inspired by an all-time bestseller, Harper Lee's To Kill a Mockingbird.

(Contributed by Liz Ringrose.)



Note: One of my Mozart groups way back July 2006 planned on listing novels where Mozart is quoted. This list has been revived today, Nov 18, 2012,  intended to be an ongoing post, with latest contribution/s added.

Cousin Marianne: Guardian of Mozart Sacred Works

Mozart's cousin Marianne and his sacred works or How so many Mozart masses came to Augsburg

© by Susanne M. Scholze, Guest Writer-Friend

Wolfgang Amadé Mozart wrote the most wonderful music I can think of. Nowadays, his music can be heard either performed life in concert, or from a CD, privately or through the radio, internet, DVD – however, wherever. Thanks to modern technology it is available at practically any time. I do not know whether all of his known 626 works are currently available on CD, but in this very year 2006, his 250^th anniversary, this might very well be possible. Operas, concertos, divertimenti, arias, chamber music, Lieder, Tänze. And church music. Whatever you wish. This hasn’t been always so. 

During his lifetime, the places where lucky people got to hear, for example, his church music performed were – only churches, of course. At that time, the two churches worldwide that performed his divine music regularly were the Salzburg Cathedral, and the Heilig Kreuz Monastery in Augsburg, Bavaria, Germany. Augsburg? How come? 

Leopold Mozart

Mozart's Father: Leopold Mozart 

German Violinist, Teacher, Composer and Theorist, Wolfgang Mozart's father

While Leopold Mozart (1719-1787), is best known as the devoted father of musical genius Wolfgang Amadeus Mozart, he was a distinguished violinist, a violin teacher, composer and theorist.  Johann Georg Leopold Mozart was born on November 14, 1719 in Augsburg, Germany, to a respectable family of tradesmen. Today he is best known as the father of Wolfgang Amadeus Mozart, and for his violin textbook Versuch einer gründlichen Violinschule.

Bragg's Law a Cornerstone of Crystallography

Bragg's Law: a cornerstone of the science of crystallography

In physics parlance, Bragg's Law gives the angles for coherent and incoherent scattering from a crystal lattice. The law was derived by physicist Sir William Lawrence Bragg in 1912 and first presented on 11 November of the same year to the Cambridge Philosophical Society. In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid.

The Bragg's Law Equation:

Where n is an integer, λ is the wavelength of incident wave, d is the spacing between the planes in the atomic lattice, and θ is the angle between the incident ray and the scattering planes. Note that moving particles, including electrons, protons and neutrons, have an associated De Broglie wavelength.

Verdi Opera La forza del destino

Classical Music Dateline: November 10


November 10, 1862. The opera of Italian composer Giuseppe Verdi, La Forza del destino, which had been commissioned by the Russian Imperial Opera, premiered in Bolshoi Kamenny Theatre of St. Petersburg. The libretto of La forza del destino (The Force of Destiny) was written by Francesco Maria Piave based on a Spanish drama, Don Alvaro o La Fuerza de Sino (1835), by Angel de Saavedra, Duke of Rivas, with a scene adapted from Friedrich Schiller's Wallensteins Lager.



After some revisions, performances were held in Rome and Madrid. Subsequently, the opera travelled to New York, Vienna, Buenos Aires and London. Verdi made other revisions, with additions by Antonio Ghislanzoni, which premiered at La Scala, Milan in 1869. This has become the "standard" performance version. La forza del destino is part of the standard operatic repertoire. There are a number of recordings of it regularly performed.


Video Credit:

Montserrat Caballe "Pace, pace mio Dio" La forza del destino, with Vienna State Opera. Youtube, uploaded by Oneguin65. Accessed October 10, 2017.

Latest update: October 10, 2017. 

Resources:

Verdi La Forza del Destino (English Libretto).

Verdi La Forza del Destino (Italian Libretto). 


(c) 2012-2017. Tel Asiado. Written for Inspired Pen. All rights reserved. 

Marie Skłodowska Curie

Science / Scientist's Datebook: November 7

 

Polish-French Chemist and Physicist, famous for pioneering work on Radioactivity    

      

Marie Curie 

 

Marie Skłodowska Curie (7 November 1867 – 4 July 1934), was born in Warsaw, Poland. She was a chemist and physicist famous for her pioneering work on radioactivity. Although her work brought about her death, it led to the discovery of cancer treatments, saving countless lives.

Marie Curie was married to a fellow scientist, Pierre Curie, and mother of Irène Joliot-Curie and Ève Curie. Despite being barred from higher education due to her sex, Curie pursued her studies at the clandestine "Flying University," where she laid the foundation for her revolutionary discoveries of radium, polonium, and the concept of radioactivity.

Irene followed in her parents' footsteps also becoming a Nobel laureate in Chemistry (1935) with her husband Frédéric Joliot-Curie. Eve (Ève Denise Curie Labouisse) was a writer, journalist and pianist. Ève was the only member of her family who did not choose a career as a scientist, however, her husband Henry Richardson Labouisse, Jr., American diplomat and statesman, collected the Nobel Peace Prize in 1965 on behalf of UNICEF.

Niccolo Paganini

Classical Music / Composer's Datebook

 

Italian virtuoso and composer Niccolo Paganini

Niccolò (or Nicolò) Paganini, (October 27, 1782 - May 27, 1840), was born in Genoa, Italy. He was a violinist, violist, guitarist and composer. He is one of the most famous violin virtuosi, considered one of the greatest violinists of all-time, with perfect intonation and innovative techniques.

Although eighteenth century Europe had seen several extraordinary violinists, Paganini was the preeminent violin virtuoso of the nineteenth century.

The Russian Mighty Five

 Russian Composers

The Russian "Mighty Five" (also known as "The Mighty Handful or Moguchaya kuchka) were a group of five 19th-century Russian composers who collaborated in Saint Petersburg from 1856 to 1870. They forge a distinct national style of clasical music free from Western European conservatory traditions. 

Members of The Five

Mily Balakirev (1837–1910): The dynamic leader, pianist, and mentor who guided the group, collected folk songs, and pushed for a pure Russian musical identity.
Nikolai Rimsky-Korsakov (1844–1908): A naval officer later turned conservatory professor famous for his brilliant orchestration (Scheherazade, The Snow Maiden).
Modest Mussorgsky (1839–1881): A former military officer known for his bold, raw style (Pictures at an Exhibition, Boris Godunov).
Alexander Borodin (1833–1887): A chemistry professor who balanced a scientific career with landmark romantic and nationalist works (Prince Igor).
César Cui (1835–1918): An army fortification engineer and music critic who championed the group's aesthetic through his writings. 

Key Characteristics & Legacy

Nationalist Style: They drew heavily on Russian folk songs, church chants, regional dances, and Russian history rather than standard German or Italian academic forms.
The Name: The term Moguchaya kuchka ("mighty little heap" or "Mighty Handful") was coined in 1867 by music critic Vladimir Stasov.
Impact: Rimsky-Korsakov is considered who has the most enduring role due to his orchestration skills and his mentoring of later figures like Igor Stravinsky. Their work heavily influenced subsequent Russian masters such as Alexander Glazunov, Sergei Prokofiev, and Dmitri Shostakovich.

  

Resources:

Oxford Companion to Music, Oxford: OUP, 2002

The Five. Britannica.com 

The Five (Composers). en.wikipedia.org 

The Grove Concise Dictionary of Music, edited by Stanley Sadie.  London: The Macmillan Press Ltd, 1994

 

 (c) October 27, 2012. Tel. Inspired Pen Web. All rights reserved

Strong and Enduring Tulips in the Snow

On endurance and strength, inspired by tulips in the snow.

The photo "Tulips in the Snow" is a compliment of my Dutch friend Wim Vingerhoed, a Mozart enthusiast from Eindhoven, Holland. Wim has given me numerous wonderful images of Mozart, flowers and nature, but this one, tulips in the snow" has always been a favourite. A lovely sight of yellow-coloured tulips in snow. Ik wens je een prettige dag.

It's spring here in Sydney, although at times we experience the four seasons without snow. On the other side of the hemisphere where other friends live, it is autumn, and perhaps might make more encore after the actual start of winter. Beholding the photo taken by my friend Wim, I wish I'm over where he took it, go out and get snowed on. My mind wanders. In my musings, the cold air seeps through my being while I delightfully witness how the snow clings to the tulips and almost cover some new buds on the trees around.

Tulips, most popular in the Netherlands, don't bend over or resign to the cold. They stand tall against the gusts of winter air, with their bloom, yellow in this photo dusted with snow. Look at the lovely image: they're brave and strong, unresigning to the cold. I love tulips alongside roses and orchids. Spring is the season expected to recover from winter's extreme cold. But winter is not necessarily harsh.

I so admire the fortitude of tulips in the snow, almost in rebellious defiance to the cold winter winds. What endurance and strength amid life's challenges if we let go and let God.



Image credit:

"Tulips in the Snow" by Wim Vingerhoed.

Otto Heinrich Warburg

Science / Scientist Datebook: October 8

 

Biochemist, Medical Doctor, and Nobel Laureate

Otto Heinrich Warburg (October 8, 1883 – August 1, 1970), a German physiologist, medical doctor and Nobel laureate, was the son of physicist Emil Warburg.  One of the 20th century's leading biochemists, his combined work in plant physiology, cell metabolism and oncology made him an integral figure in the later development of systems biology. He also worked with Dean Burk in photosynthesis to discover the I-quantum reaction that splits the carbon dioxide (CO2), activated by the respiration.

He won the Nobel Prize of 1931. An officer in the elite Ulan (cavalry regiment) during the First World War, he won the Iron Cross (1st Class) for bravery.

George Westinghouse

Science / Inventors Datebook: October 6

American engineer, inventor, and pioneer of the electrical company.

George Westinghouse, Jr. (October 6, 1846 – March 12, 1914) was an American engineer and entrepreneur who invented the railway air brake and was a pioneer of the electrical industry. He was also one of Thomas Alva Edison's rivals in the early implementation of the American electricity system. Westinghouse's system, which used alternating current based on the extensive research by Nikola Tesla, eventually prevailed over Edison's insistence on direct Current.

In 1911, Westinghouse received the AIEE's Edison Medal "For meritorious achievement in connection with the development of the alternating current system."

Sacred Geometry in Nature and Culture: The Fibonacci Sequence, Phi, Shapes, and Numbers

For eons, human beings have felt that certain numbers, ratios, and shapes have sacred significance. For instance, the number ‘7’ has had great significance in various aspects of many cultures, geometric shapes have been associated with numbers, and the Fibonacci sequence (discovered by Italian mathematician Fibonacci) and Golden Ratio are still instrumental in everything from Art to Music. 

Sacred Meanings in Geometric Numbers and Shapes

Symbolic and sacred meanings are also ascribed to certain geometric numbers, shapes, and geometric ratios or proportions. Through the ages, especially in the ancient world, some numbers had symbolic meaning has been attached, aside from their ordinary use for counting or calculating. In geometry, figures such as triangles, squares, polygons, hexagons, and so forth are all related to numbers. Triangles, for example, relate to three angles, squares to four, and so on.

As an example of attaching sacred meanings to geometric numbers, the number ‘seven’ occurs consistently in diverse cultures around the world. And more, the religious and mythologies of the world are filled with sevens. Consider some of these:

Pyramids of Giza: Image by Darren Krape

• The shape of the pyramids of Egypt produces the number seven by combining the three-sided triangle and four-sided square.
• In music, the seven musical notes in a scale repeat at the octave.
• There are seven terraces of purgatory in the Roman Catholic beliefs.
• The Christian Church recognizes the seven virtues and seven deadly sins.
• There were seven steps taken by Buddha at his birth.
• There are seven heavens and seven earths in Islamic tradition.
• There are seven worlds in the Hindu universe.
• The seven-branched Jewish menorah is the oldest symbol in Judaism.

The ancient Greek philosopher Pythagoras believed that integers represented fundamental meanings. He regarded seven as the “vehicle” of life. To him, the number seven signified the union of spirit and matter – the union of three (the triple nature of the spirit) combined with the four elements of matter (earth, air, fire, and water). 

The Seven Chakras

The number seven was also associated with growth, whereby a phenomenon tends to be completed in seven stages, such as the “seven stages of man” expressed by Shakespeare in  As You Like It, or the biblical Creation by God in seven days. According to some beliefs, the human body needs seven energy vortices known as chakras to be open for spiritual growth; that is, one has to move focus from the three lower (physical) chakras to the four higher (spiritual) centers. 

The Chakras from bottom to top: 

Root, Sacral, Solar Plexus, 

Heart, Throat,

Crown.

The Fibonacci Sequence (The Pi and the Phi)

In geometry, the symbol Φ or φ (phi) represents the Golden Ratio, also known as the golden mean or divine proportion. This number is approximately equal to 1.61803398875. It appears frequently in geometry, art, architecture, and nature, often in relation to aesthetically pleasing proportions.

Aryabhata, in the 5th century CE (refers to "Common Era", the same years as AD does, but in a more secular way), calculated Pi to four decimal places (3.1416), while Brahmagupta introduced the symbol for zero and developed formulas to approximate Pi. With these contributions, Indian mathematicians were able to utilize Pi in a wide array of fields, including astronomy, geometry, and trigonometry.

Pi (π) and Phi (Φ), also known as the Golden Ratio, are two fundamental mathematical constants. Pi is the ratio of a circle's circumference to its diameter, approximately 3.14159. The Golden Ratio, approximately 1.618, is found by dividing a line into two segments such that the ratio of the whole line to the longer segment is equal to the ratio of the longer segment to the shorter segment.

Fibonacci Blocks

The Sacred Geometry

How then is the Fibonacci sequence related to Sacred Geometry? The Fibonacci sequence, discovered by Fibonacci, is a series of numbers in which each number is the sum of the previous two. It starts with 0 and 1,which equals 1. Then 1 plus 2 equals 3, 2 plus 3 equals 5, 3 plus 5 equals 8, and so on. Why are these numbers significant? Simply, they are nature’s numbering system and they give rise to the mystical Phi, referred to as the “golden section” or “golden ratio.” It should be noted that the ratio of successive pairs from the Fibonacci series tends toward Phi or 1.618 and out of this ratio comes the golden rectangle and the spiral shape, which is the most widespread shape in the universe.

The Fibonacci numbers are represented practically everywhere. In the petals on a flower, or the arrangement of leaves along a stem, we find this sequence of numbers. The petals on most flowers display one of the Fibonacci numbers. The numbers also appear in certain parts of sea shell formations. Parts of the human body also reveal these ratios, including the five fingers, and a thumb on each hand. Fibonacci can also be seen in a piano that produces harmony through a beautiful music. A piano has one keyboard with five black keys (sharps and flats) arranged in groups of two and three, and eight white keys (whole tones) for the 13 chromatic musical octaves.

The Phi or 1.618 was described in the past as a divine number because it signifies beauty and harmony. Egyptian architects made use of Phi relationships in the construction of temples and the Great Pyramid, and so did the Greeks in their Parthenon in Athens, and the Europeans, for their Gothic cathedrals.

Simply described, the Sacred Geometry arises out of the set of numbers from the Fibonacci series or the “golden ratio.”  Through the years since ancient times, it has been significantly used in the planning and construction of religious structures (churches, temples, mosques, tabernacles, altars and monuments), as well as sacred spaces (like holy wells and sacred groves), and the creation of religious art.

Consciously or not, humans seem to be genetically programmed to respond to these sacred numbers, ratios, and shapes. Thanks to Italian mathematician Leonardo Fibonacci for introducing his famous Fibonacci sequence, its associated mystical ratio, the Phi, and paving the way for the shapes that greatly defined the world’s magnificent structures and amazing wonders.

 

Fibonacci numbers, ratios and shapes have been used to explain creation, growth and harmony – from a number of petals on a flower and grandiose architecture, to a spiraling galaxy. To music lovers, it’s one beautiful harmony of musical scale that pleases the ear and ultimately the spirit.  

 

Mandalas and How they relate to Sacred Geometry

  

Mandalas are circular designs deeply rooted in history and spiritual practices, particularly Hinduism and Buddhism. It is said to have originated in India. The term "mandala" is derived from Sanskrit, meaning "circle".  While their earliest appearance is linked to religious texts like the Rig Veda around 1500-1100 BCE, mandalas have transcended geographical and cultural boundaries, appearing in various forms across different periods and regions. 

 

Mandalas are linked to sacred geometry as they are visual representations of geometric patterns found in nature. They are used to explore spiritual and cosmological concepts. The circular form of a mandala often symbolizes the universe, while the geometric shapes within it (like circles, squares, and triangles) represent different aspects of other consciousness   The circular form of a mandala often symbolizes the universe, while the geometric shapes within it, such as circles, squares, and triangles, represent different aspects of creation, the divine, and consciousness, and the individual's place within it.   

 

 

Mandala (Flower of Life) 

 

  

TRIVIA:

 

After 13 years, I'm revisiting this post.  My longtime interest in Sacred Geometry has been greatly rekindled after a  course in 'Neurographic Art for Inner Balance and Flow' under my engaging instructor with professional knowledge, Alina Smolyansky. She is a neurographica certified instructor & artist at NeurographicArt and Life. We drew the  "Flower of Life" (Mandala) during our final class session.  A versatile and powerful tool, I find mandala art therapeutic, calming, a great benefit for well-being, from stress reduction to self expression.  (Tel / August 4, 2025.) 

 

 

Resources:

Bradley, P.  Great Mysteries. New Holland (2010).

Corbalan, Fernando. The Golden Ratio. RBA Coleccionables, S.A. (2012)

Devlin, Keith. The Man of Numbers. Bloomsbury (2011)

Livio, Mario. The Golden Ratio. Broadway Books (2002)

Sacred Geometry. Wikipedia. Accessed  September 23, 2011.

"The Parthenon and Phi". The Golden Ratio. By Gary Meisner. Accessed September 23, 2014 

"Phi: The Golden Ratio". What is the Golden Ratio. Live Science. 

 

 

(c) September 23, 2012. Updated August 4, 2025. Tel Asiado. Inspired Pen Web. All rights reserved.