Music - Highest Form of Worship - Page 2

Leo Tolstoy.

😊 😊 😊

Composer Profile - Leo Tolstoy

It is not widely known that Tolstoy was a composer. A waltz for piano, the one musical work of his that survives, is posted on this site as a result of an interview that took place between Humphrey Carpenter and Isaiah Berlin, near the end of Berlin's life. This interview came to the attention of Berlin's editor, Henry Hardy, who followed up the clue about Tolstoy's waltz that it contains. Carpenter was working on The Envy of the World, his history of the BBC's Third Programme/Radio 3, and during his discussion with Berlin (a prominent figure on the Third Programme in its early days) happened to raise the subject of Tolstoy's The Kreutzer Sonata, the story of a man so obsessively jealous of his wife's music-making with a male violinist that he kills her for her supposed infidelity. Apropos this musical background Berlin observes: 'He was very musical, Tolstoy. He wrote a waltz - [...] I've heard it played. It's printed in a book. My wife played it to me, it's very simple.' Hardy followed up these remarks and, to cut a long story short, found the waltz in a Russian book published in 1953 by N. Gusev and A. Goldenveizer, Leo Tolstoy and Music. In his contribution, Goldenveizer writes: 'In his youth Lev Nikolaevich composed a waltz for the piano. When, in 1906, I was at Yasnaya Polyana with Taneev, Lev Nikolaevich played it to us, and we noted it down. This was the only time that we heard Lev Nikolaevich play.' The waltz (in F) is printed in manuscript as an appendix to the book. It was recorded for the National Sound Archive by Imogen Cooper on 17 October 1997 and has been played on Radio 3 by Brian Kay. It lasts less than a minute, and has a great charm .

 

Here's the link to Tolstoy's waltz (only a minute's recording) :

http://berlin.wolf.ox.ac.uk/writings_on_ib/hhonib/BerlinHarv ard5.mp3

That's all that remains of his compositions today ....

Pythagorus

------------------------------------------------------------ -------------------------------

Pythagoras: Music and Space

"We shall therefore borrow all our Rules for the Finishing our Proportions, from the Musicians, who are the greatest Masters of this Sort of Numbers, and from those Things wherein Nature shows herself most excellent and compleat." Leon Battista Alberti (1407-1472)

 

Pythagoras
&
Music of the Spheres

 

There is geometry in the humming of the strings
... there is music in the spacing of the spheres.

Pythagoras. The History of Philosophy (c.1660) by Thomas Stanley.

Outline:	Pythagoras
	The Pythagoreans
	Pythagorean Number Symbolism
	Music of the Spheres
	Summary
Reading

---

Pythagoras

From Egypt we move across the Mediterranean Sea to the Greek island of Samos, the birthplace of Pythagoras, whose ideas dominate most of the material in this course. We'll introduce Pythagoras and his secret society of the Pythagoreans.

We'll look at the Pythagoreans' ideas about numbers, as a prelude to our next unit on number symbolism. Finally, we'll introduce a new idea that will be recurring theme throughout this course, the musical ratios, which will reappear in discussions of the architecture of the Renaissance.

Our main link between Egypt and Greece seems to be Thales c 640-550 BC, father of Greek mathematics, astronomy, and Philosophy, and was one of the Seven Sages of Greece. A rich merchant, his duties as a merchant took him to Egypt, and so became one of the main sources of Egyptian mathematical information in Greece. It was Thales advised his student to visit Egypt, and that student was Pythagoras.

---

Raphael's School of Athens

Slide 3-1: Raphael's School of Athens 1510-11.

Janson, H. W. History of Art. Fifth Edition. NY: Abrams, 1995. p.497

 

Pythagoras is shown in this famous painting, done by Raphael in 1510-11, which also shows most of the Greek philosophers.

Socrates sprawls on the steps at their feet, the hemlock cup nearby.

His student Plato the idealist is on the left, pointing upwards to divine inspiration. He holds his Timaeus, a book we'll talk about soon.

Plato's student Aristotle, the man of good sense, stands next to him. He is holding his Ethics in one hand and holding out the other in a gesture of moderation, the golden mean.

Euclid is shown with compass, lower right. He is the Greek mathematician whose Elements we'll mention often.

Slide 3-2: Pythagoras in Raphael's School of Athens Janson, H. W. History of Art. Fifth Edition. NY: Abrams, 1995. p.497

Finally, we see Pythagoras (582?-500? BC), Greek philosopher and mathematician, in the lower-left corner.

---

The Pythagoreans

Pythagoras was born in Ionia on the island of Smos, and eventually settled in Crotone, a Dorian Greek colony in southern Italy, in 529 B.C.E. There he lectured in philosophy and mathematics.

He started an academy which gradually formed into a society or brotherhood called the Order of the Pythagoreans.

---

Disciplines of the Pythagoreans included:

silence	music	incenses	physical and moral purifications
rigid cleanliness	a mild ascetisicm	utter loyalty	common possessions
secrecy	daily self-examinations (whatever that means)
pure linen clothes

We see here the roots of later monastic orders.

For badges and symbols, the Pythagoreans had the Sacred Tetractys and the Star Pentagram, both of which we'll talk about later.

There were three degrees of membership:

1. novices or "Politics"
2. Nomothets, or first degree of initiation
3. Mathematicians

The Pythagoreans relied on oral teaching, perhaps due to their pledge of secrecy, but their ideas were eventually committed to writing. Pythagoras' philosophy is known only through the work of his disciples, and it's impossible to know how much of the "Pythagorean" discoveries were made by Pythagoras himself. It was the tradition of later Pythagoreans to ascribe everything to the Master himself.

---

Pythagorean Number Symbolism

The Pythagoreans adored numbers. Aristotle, in his Metaphysica, sums up the Pythagorean's attitude towards numbers.

"The (Pythagoreans were) ... the first to take up mathematics ... (and) thought its principles were the principles of all things. Since, of these principles, numbers ... are the first, ... in numbers they seemed to see many resemblances to things that exist ... more than [just] air, fire and earth and water, (but things such as) justice, soul, reason, opportunity ..."

 

The Pythagoreans knew just the positive whole numbers. Zero, negative numbers, and irrational numbers didn't exist in their system. Here are some Pythagorean ideas about numbers.

---

Masculine and Feminine Numbers

Odd numbers were considered masculine; even numbers feminine because they are weaker than the odd. When divided they have, unlike the odd, nothing in the center. Further, the odds are the master, because odd + even always give odd. And two evens can never produce an odd, while two odds produce an even.

Since the birth of a son was considered more fortunate than birth of a daughter, odd numbers became associated with good luck. "The gods delight in odd numbers," wrote Virgil.

---

1   Monad. Point. The source of all numbers. Good, desirable, essential, indivisible.

2   Dyad. Line. Diversity, a loss of unity, the number of excess and defect. The first feminine number. Duality.

3   Triad. Plane. By virtue of the triad, unity and diversity of which it is composed are restored to harmony. The first odd, masculine number.

4   Tetrad. Solid. The first feminine square. Justice, steadfast and square. The number of the square, the elements, the seasons, ages of man, lunar phases, virtues.

5   Pentad. The masculine marriage number, uniting the first female number and the first male number by addition.

The number of fingers or toes on each limb.

• The number of regular solids or polyhedra.
  

Incorruptible: Multiples of 5 end in 5.

6   The first feminine marriage number, uniting 2 and 3 by multiplication.
The first perfect number (One equal to the sum of its aliquot parts, IE, exact divisors or factors, except itself. Thus, (1 + 2 + 3 = 6).
The area of a 3-4-5 triangle

7   Heptad. The maiden goddess Athene, the virgin number, because 7 alone has neither factors or product. Also, a circle cannot be divided into seven parts by any known construction).

8   The first cube.

9   The first masculine square.
Incorruptible - however often multiplied, reproduces itself.

10   Decad. Number of fingers or toes.
Contains all the numbers, because after 10 the numbers merely repeat themselves.
The sum of the archetypal numbers (1 + 2 + 3 + 4 = 10)

27   The first masculine cube.

28   Astrologically significant as the lunar cycle.
It's the second perfect number (1 + 2 + 4 + 7 + 14 = 28).
It's also the sum of the first 7 numbers (1 + 2 + 3 + 4 + 5 + 6 + 7 = 28)!

35   Sum of the first feminine and masculine cubes (8+27)

36   Product of the first square numbers (4 x 9)
Sum of the first three cubes (1 + 8 + 27)
Sum of the first 8 numbers (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8)

---

Figured Numbers

The Pythagoreans represented numbers by patterns of dots, probably a result of arranging pebbles into patterns. The resulting figures have given us the present word figures.

Thus 9 pebbles can be arranged into 3 rows with 3 pebbles per row, forming a square.

Similarly, 10 pebbles can be arranged into four rows, containing 1, 2, 3, and 4 pebbles per row, forming a triangle.

From these they derived relationships between numbers. For example, noting that a square number can be subdivided by a diagonal line into two triangular numbers, we can say that a square number is always the sum of two triangular numbers.

Thus the square number 25 is the sum of the triangular number 10 and the triangular number 15.

---

Sacred Tetractys

One particular triangular number that they especially liked was the number ten. It was called a Tetractys, meaning a set of four things, a word attributed to the Greek Mathematician and astronomer Theon (c. 100 CE). The Pythagoreans identified ten such sets.

Ten Sets of Four Things

---

Gnomons

Gnomon means carpenter's square in Greek. Its the name given to the upright stick on a sundial. For the Pythagoreans, the gnomons were the odd integers, the masculine numbers. Starting with the monad, a square number could be obtained by adding an L-shaped border, called a gnomon.

Thus, the sum of the monad and any consecutive number of gnomons is a square number.

 

1 + 3 = 4

1 + 3 + 5 = 9

1 + 3 + 5 + 7 = 16

 

and so on.

---

The Quadrivium

While speaking of groups of four, we owe another one to the Pythagoreans, the division of mathematics into four groups,

giving the famous Quadrivium of knowledge, the four subjects needed for a bachelor's degree in the Middle Ages.

---

Music of the Spheres

Jubal and Pythagoras

Slide 3-4: Theorica Musica F. Gaffurio, Milan, 1492 Lawlor, Robert. Sacred Geometry. NY: Thames & Hudson, 1982. p.7

So the Pythagoreans in their love of numbers built up this elaborate number lore, but it may be that the numbers that impressed them most were those found in the musical ratios.

Lets start with this frontispiece from a 1492 book on music theory.

The upper left frame shows Lubal or Jubal, from the Old Testament, "father of all who play the lyre and the pipe" and 6 guys whacking on an anvil with hammers numbered 4, 6, 8, 9, 12, 16.

The frames in the upper right and lower left show Pithagoras hitting bells, plucking strings under different tensions, tapping glasses filled to different lengths with water, all marked 4, 6, 8, 9, 12, 16. In each frame he sounds the ones marked 8 and 16, an interval of 1:2 called the octave, or diapason.

In the lower right, he and Philolaos, another Pythagorean, blow pipes of lengths 8 and 16, again giving the octave, but Pythagoras holds pipes 9 and 12, giving the ratio 3:4, called the fourth or diatesseron while Philolaos holds 4 and 6, giving the ratio 2:3, called the fifth or diapente.

They are:

These were the only intervals considered harmonious by the Greeks. The Pythagoreans supposedly found them by experimenting with a single string with a moveable bridge, and found these pleasant intervals could be expressed as the ratio of whole numbers.

---

Pythagoras in the School of Athens

Slide 3-3: Closeup of Tablet Bouleau Janson, H. W. History of Art. Fifth Edition. NY: Abrams, 1995. p.497

Raphael's School of Athens shows Pythagoras is explaining the musical ratios to a pupil.

Notice the tablet. It shows:

The words diatessaron, diapente, diapason.
The roman numerals for 6, 8, 9, and 12, showing the ratio of the intervals, same as in the music book frontispiece.

The word for the tone, EPOGLOWN, at the top.

Under the tablet is a triangular number 10 called the sacred tetractys, that we mentioned earlier.

---

The Harmonic Scale

Slide 3-5: Gafurio Lecturing F. Gafurio, De Harmonia musicorum instrumentorum, 1518, Wittkower, Rudolf. Architectural Principles in the Age of Humanism. NY: Random, 1965. 43a.

This diagram from a book written in 1518 shows the famous Renaissance musical theorist Franchino Gafurio with three organ pipes and 3 strings marked 3 , 4, 6. This indicates the octave, 3 : 6 divided by the harmonic mean 4, into the fourth, 3 : 4, and the fifth, 4 : 6 or 2 : 3.

The banner reads, "Harmonia est discordia concors" or Harmony is discordant concord, propounding the thesis that harmony results from two unequal intervals drawn from dissimilar proportions. The diagram shows compasses, suggesting a link between geometry and music.

---

So What?

So after experimenting with plucked strings the Pythagoreans discovered that the intervals that pleased people's ears were

and we can add the two Greek composite consonances, not mentioned before . . .

Now bear in mind that we're dealing with people that were so nuts about numbers that they made up little stories about them and arranged pebbles to make little pictures of them. Then they discovered that all the musical intervals they felt was beautiful, these five sets of ratios, were all contained in the simple numbers

1, 2, 3, 4

and that these were the very numbers in their beloved sacred tetractys that added up to the number of fingers. They must have felt they had discovered some basic laws of the universe.

Quoting Aristotle again ... "[the Pythagoreans] saw that the ... ratios of musical scales were expressible in numbers [and that] .. all things seemed to be modeled on numbers, and numbers seemed to be the first things in the whole of nature, they supposed the elements of number to be the elements of all things, and the whole heaven to be a musical scale and a number."

---

Music of the Spheres

Slide 3-6: Kepler's Model of the Universe Lawlor, Robert. Sacred Geometry. NY: Thames & Hudson, 1982. p. 106

"... and the whole heaven to be a musical scale and a number... "

It seemed clear to the Pythagoreans that the distances between the planets would have the same ratios as produced harmonious sounds in a plucked string. To them, the solar system consisted of ten spheres revolving in circles about a central fire, each sphere giving off a sound the way a projectile makes a sound as it swished through the air; the closer spheres gave lower tones while the farther moved faster and gave higher pitched sounds. All combined into a beautiful harmony, the music of the spheres.

This idea was picked up by Plato, who in his Republic says of the cosmos; ". . . Upon each of its circles stood a siren who was carried round with its movements, uttering the concords of a single scale," and who, in his Timaeus, describes the circles of heaven subdivided according to the musical ratios.

Kepler, 20 centuries later, wrote in his Harmonice Munde (1619) says that he wishes "to erect the magnificent edifice of the harmonic system of the musical scale . . . as God, the Creator Himself, has expressed it in harmonizing the heavenly motions."

And later, "I grant you that no sounds are given forth, but I affirm . . . that the movements of the planets are modulated according to harmonic proportions."

---

Systems of Proportions based on the Musical Ratios

Slide 17-1: Villa Capra Rotunda
citatation

What does this have to do with art or architecture? The idea that the same ratios that are pleasing to the ear would also be pleasing to the eye appears in the writings of Plato, Plotinus, St. Augustine, and St. Aquinas. But the most direct statement comes from the renaissance architect Leone Battista Alberti (1404-1472), "[I am] convinced of the truth of Pythagoras' saying, that Nature is sure to act consistently . . . I conclude that the same numbers by means of which the agreement of sounds affect our ears with delight are the very same which please our eyes and our minds."

Alberti then gives a list of ratios permissible, which include those found by Pythagoras. We'll encounter Alberti again for he is a central figure in the development of perspective in painting.

We'll also discuss another architect who used musical ratios, Andrea Palladio (1518-1580), who designed the Villa Capra Rotunda shown here.

---

Summary

Slide 3-7: Correspondence School in Crotone W. S. Anglin. Mathematical Intelligence V19, No. 1, 1997

I always wanted to make a pilgrimage to Crotone, site of the Pythagorean cult, but this is all that's there to mark their presence. Pythagoras and his followers died when their meetinghouse was torched. We'll have more on the Pythagoreans later, in particular their fondness for the star pentagram.

In this unit we've had some Pythagorean number lore and soon we'll add to it by talking about number symbolism in general, especially numbers in astrology and the Old Testament. Somewhere I had read that one answer to the question, Why study history? was To keep Pythagoras alive! I've forgotten where I read that, but anyway, it makes a nice goal for this course.

Nietzsche. 😊 😊 😊 SCULPTING IN MUSIC Friedrich Nietzsche's music has long held an unusual place in his works, considered by many in the philosophical world as an amateurish indulgence and almost completely ignored by those in the musical world. Publicly available only through the efforts of Curt Paul Janz, the music is difficult to find and even more difficult to properly evaluate. Additionally, members of the discipline best suited to evaluating his compositions - music - frequently harbor preexisting prejudices against the writer who so bitterly attacked the revered (if not always beloved) Richard Wagner. Even in Frederick Love's short work, Young Nietzsche and the Wagnerian Experience - the most substantial analysis of Nietzsche's music to date - the compositions are examined only in reference to Nietzsche's relationship with Wagner. By ignoring the music itself, the musical world has deprived itself of several pieces worthy of admittance to the standard performing repertoire and the philosophical world has missed an opportunity to observe an important facet of Nietzsche's inherently interdisciplinary philosophy.

Nietzsche's musical output - concentrated in his early years - provided him with a medium in which to experiment and refine ideas that would later reappear in more finished forms in his mature works. When specific instances of musical experimentation are examined, a pattern of musical 'prototypes' emerges in which Nietzsche utilizes musical composition to extrapolate the effects of altering accepted concepts.

Friedrich Nietzsche, Hymnus An Das Leben

It is not well known that Friedrich Nietzsche wrote music, and among those who do know it, he has a reputation as having been a terrible composer. This is a little unfair. It is true that he never developed a personal style, and his few attempts at longer forms are mostly unfinished and awkward. The bulk of his pieces, however, were written before the age of twenty; a handful of longer attempts were made in the early 1870s, and Nietzsche composed virtually nothing new after 1874, discouraged by sharp criticism from his friends Richard Wagner and Hans von Bulow. With friends like these, his music didn't need enemies.

By common consent, Nietzsche's most successful works were his songs, about 16 in number, most of which he wrote as a teenager, between the years 1861 and 1864. Some of these are quite lovely, with a stirring sense of melodicism that hews closely to the texts. In addition, the Musikalische Nachlass published for Nietzsche in 1976 contains about a dozen completed piano works, most of them brief character pieces of the albumbltter variety, and many more unfinished; fragments of a mass and the beginning of a Christmas Oratorio (it will be remembered that Nietzsche came from a family of Lutheran clergymen); a piece for violin and piano; several choral songs; and an 1872 tone poem, written for two pianos and never orchestrated, based on Byron's supernatural poem Manfred.

Most of this music was written before Nietzsche was converted to the Wagnerian cause, which happened around 1868; his early hero was Robert Schumann, whose melodicism leaves its mark on the piano pieces especially. And yet, while there are Schubertian touches in the lieder, Nietzsche's style also shows some influence of the Wagner-Liszt "Music of the Future" school, and often resembles Liszt's in its poignantly leaping melodies and tonal ambiguities. Remarkable in this regard is the Manfred-Meditation, Nietzsche's most developed large composition, which he reportedly wrote because he found Schumann's Manfred music unsatisfactory and felt he could do better. The middle development section of this piece is undeniably over-repetitious, but I leave it to those less generous to argue whether this work's often ambiguous harmonies reveal an attachment to the Weimar-centered avant-garde of the time, or are merely the result of incompetence.

The Hymnus an das Leben (Hymn to Life) represents one of Nietzsche's final musical thoughts. The original song, under the title Gebet an das Leben, was written for voice and piano in 1882 to a poem by Lou Salom, using music from a piano piece Nietzsche had earlier written in 1874, Hymnus an die Freundschaft. Part of the impetus for setting the poem was no doubt to draw closer to Salom, whom Nietzsche had met in April of 1882 in Rome. He proposed to her twice, through their mutual friend Paul Re, and was twice rejected. In August or September he set her poem to music, but in October Lou and Re left together, causing Nietzsche considerable jealousy. Much later, in 1897, Salom would go on to become the mistress of the poet Rainer Maria Rilke, and still later a close disciple of Freud.

Nietzsche had an amenuensis, Peter Gast (real name: Heinrich Kselitz) who had first come to hear the great philosopher lecture in 1875, and to whom Nietzsche, plagued by eye trouble, subsequently dictated several of his books. It was Gast who, in 1887, arranged Gebet an das Leben for chorus and orchestra, the version heard tonight. Where Nietzsche had set only the first verse of Salom's poem, Gast repeated the musical setting to include a second. The poem apostrophizes both the joy and bitterness of life in a way reminiscent of what has become one of Nietzsche's most widely quoted phrases, "Whatever doesn't kill me makes me stronger":

Whether you gave me suffering or pleasure,
I love you with your happiness and harm,
And even if you must destroy me,
I tear myself painfully out of your arms
Like a friend tearing himself away from the breast
of a friend...

If you have no more happiness to give me,
Well, then, you still have your pain.

Despite the rather dark stoicism of the poem's sentiments, Nietzsche's setting is triumphal and full of light, if also marked by abrupt changes of key. Nietzsche never managed an imaginative use of musical texture, but the chromatic harmonies do show that he was attuned to the more musically progressive currents of his day, and the stirring melody has the air of a nationalistic German anthem.

Thanks, Abhi. You can stop saving the articles. Have linked the articles to the proper page on the first post of the thread. Makes for an easy reference for anyone interested in someone particular.

Hope the mods make the thread sticky. More than that, would love everyone else to contribute here as well.

😊 😊 😊

Hi SimplySkud
This thread is Simply Marvellous. Shows your high IQ. 😊

Since you've asked us to talk about people whose profession was not music, yet they excelled in it, I thought about Charlie Chaplin, one of my idols. Sheer genius.

I just adored the music he composed for his last film "Limelight" Has anyone heard it?

Don't have time to do much research but this is an excerpt from an article I have:
Chaplin proved to be a prolific composer. He could not read a note of music but could play it for those who could write it down. Some of his music has gained widespread recognition, such as "Smile", from Modern Times and "This is my Song" from one of his lesser known films, A Countess from Hong Kong. The most beautiful is "Eternally", the opening theme of Limelight. It became so widely known as one of the great Chaplin compositions that it was played at many of his professional appearances, including his Academy Award acceptance in 1972.

Incidentally, when I was hearing the songs of the Dev Anand starrer "Maya" the other day, I was startled to hear a complete copy of Chaplin's Limelight music in the song "zindagi hai kya, o meri jaan, pyaar bhara dil, meethi zubaan".

Skudbhai - So far I was keeping a distance from this thread - because it's depth and vastness - If I start, I won't be able to emerge from it. But now I am helpless - give me little time - to read the posts and come up with my own 2 cent worth contribution.

Punjini - not only IQ can do all the magic, Skud bahi got balanced amount of EQ too. Let me stand up for our dear Skud bhai and 👏