Musical Pi

 

March 14 (3/14) is Pi Day: celebrating the number pi: 3.14159…..   Pi is a numerical constant that stands for the diameter of a circle to its circumference, no matter the size of the circle.

What does that have to do with music? Several individuals have tried to transform the number pi into music. So for something different in this blog, here are some videos that illustrate that effort.

Here’s a scientific explanation of pi in terms of musical notes: https://www.youtube.com/watch?v=YOQb_mtkEEE

Here’s how a composer wrote a song with the number pi: https://www.youtube.com/watch?v=z7vovDiPjW4

Here’s a song where the composer takes pi and assigns each number to a note on the A harmonic minor scale: https://www.youtube.com/watch?v=OMq9he-5HUU  At this website you can access its sheet music and read about the story behind this song.

Listen to the ruse Performance Movement 1 of the Pi Symphony at https://www.youtube.com/watch?v=CGK2i2BaWW8

Who says music isn’t intellectual while being creative?

The Mathematical Harmony in Music

 

“Music is the mathematics of one who does not know that he is counting.” Gottfried Wilhelm Leibniz (1646-1716)

 Tomoko realizes the preciseness and patterns of music. Not surprisingly then, math helps in reading music. The simplest task such as counting the beats uses math. Each time signature codes the number of beats per measure, and the notes represent fractions of a measure and beat – such as whole notes, quarter notes, eighth notes and so on. In turn, reading these rhythmic notations can help one read and solve math equations. 

In fact, mathematics lies underneath much musical composition and reflects the very nature of music itself. Even the concept of octaves is mathematical. An octave is the distance between a given note with a set sound frequency (that is, the string’s vibration) with another note with double that frequency. A perfect fifth is 1.5 times the frequency of the octave’s base note. Ratios help make music harmonious.

Music compositions reflect patterns, just as math does: symmetry, repetition, transposition, inversion.  The process for perceiving and generating those patterns mirrors mathematical processes. Johann Sebastian Bach very consciously incorporated mathematical principles into his keyboard compositions. His work “Musical Offering” is comprised of ten canons, in which each canon is a mathematical transformation of the principal musical line. In fact, a mathematical breakthrough enabled Bach to write “The Well-Tempered Clavier.” Keyboard instruments used to be tuned using a just-toned scale, which made shifting to keys other than the tonic sounded “off.” The equal (even)-tempered scale, popularized by Bach, evened out the frequency ratios between all 12 notes of the chromic scale so that shifts of harmonies to other keys would sound the same.

Tomoko rightly asserts that reading and playing music require good discipline, improve listening and collaborative skills, and strengthens mental and muscle memory.  Those practices can also build math skills and recall of math details. A harmonious blend!

 

The Secret Facts of Composers

Piano teachers need to know their music, and it’s useful to know about the composers themselves. Tomoko likes to read biographies – especially those of composers. And she relates stories about them to her students, providing context for the compositions as well as making those composers more human. Here are some of the lesser known facts about some of them.

Vivaldi became a priest when he was 25, and served as a master of violin at an orphanage. Vivaldi suffered from bronchial asthma throughout his life, which kept him from playing wind instruments.

Liszt was very popular when young, and he was quite the playboy. One of his illegitimate daughters become Richard Wagner’s wife. Nevertheless, throughout his life he considered becoming a priest, and took four minor religious orders when 54.

Schubert was famous for his musical parties, which sometimes lasted until dawn. Yet he was very prolific; he wrote more than 20,000 bars of music, including 600 songs. He wrote 8 songs in one day. 

Rachmaninoff's fingers could span 12 keys.  On the other hand 😉, Schumann ruined his performing career by practicing with a homemade finger-stretching device; then he would plunge his hands into slaughtered animals’ entrails to heal himself.

Frederic Handel loved rich food and wine. He would order enough food for three people – for himself. The food caused him gout, and the wine may have caused him lead poisoning. 

Johann Sebastian Bach frequented Leipzig’s Café Zimmermann where he would drink several cups of coffee (which was a luxury beverage at the time). He liked coffee so much he wrote the Coffee Cantata about a woman who was trying to stop her coffee drinking habit.  Bach was also an amateur mathematician, which is evident in his compositions, especially his canons.

Speaking of coffee, Beethoven was so meticulous that he would measure exactly 60 beans when making coffee.

Mozart’s life included many interesting facts. He could write music before he could write words. He could listen to a piece of music just once and be able to write it down from memory perfectly. He wrote half of his symphonies between the age of 8 and 19. was a big cat fan. He would imitate cats when bored during rehearsals. In fact, he liked cats so much that he wrote a song called "The Cat Duet,” in which the husband asks his wife questions and she answers back in meows.

The Harmony of Music and Mathematics

There is a long connection between music and mathematics, asserts Tomoko. Both require precision and order. Both deal with proportion and harmony. Both use pattern creatively. Music is very measured, and mathematics has its own kind of rhythm.

Likewise, composers and mathematicians have connections. Bach is known for his mathematical counterpoint.  Bach wrote his crab canon such that it can be played backwards and forwards at the same time. Bach also used musical numerology. For instance, he would incorporate his name into compositions: B, A, C, and H (B is B natural in German, and B is H).

Mozart was a super mathematician, and his composition papers sometimes had algebra notes on them.  Mozart also used musical numerology, weaving masonic numerical symbols in his open The Magic Flute, such as the number three (such as three-part haromy, characters in sets of three, and  key E flat major, which has three flats.

On the flip side, Einstein played the violin for his own pleasure, and would even perform at benefit concerts. He loved Mozart because of the composer’s expression of universal harmony, and he revered Bach for his structure.

How does this fit into learning the piano? Tomoko says, “At the beginning, the child needs to learn the basics, like arithmetic tables.” She points out the importance of understanding a composition’s structure and patterns, just like mathematics. “And we strive for harmony.”