The Measure of Music

 

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.

Every measurement has a unit of measure: one second, one inch, one pound. And for music it is literally one measure: one bar of music. That measure is the basis for the rhythm, the meter, of the piece, particularly when accented. Without measures, the music could become, in a way, unmusical, just meandering notes.

Nevertheless, the use of barlines, indicating a measure, is a relatively recent invention. The first use of barlines, in the 15^th and 16^th century, sometimes marked off a section and other times marked individual beats. Todays’ use of barlines, a consistent measure unit, dates back to the 17^th century.

Even with this measured scoring, music is ultimately measured in its performance – and the experience of the listener can sometimes be measureless, transcending any mathematical unit.

 

 

 

European Influence on Japanese Music

Tomoko’s favorite piano music continues to be European classical compositions. That taste was started early in her life as she heard European classical music on the radio and the organ pieces that her brother played. These habits reflected the earlier Japanese interests in Western   (generally European) music.

Traditional Japanese musical tonality differed from its Western counterparts; it uses a Phyrgian scale of E-F-A-B-C-E instead of C-D-F-G-A. The Phyrgian scale is also used in modern blues minor keys. The oldest forms of Japanese music include Buddhist chant and orchestral court music. Traditional folk music included religious songs and songs for gatherings, work songs, and children’s songs. Typical instruments were stringed instruments, drums, flutes, bells. The first piano wasn’t heard until the opening of Japan, but by 1875 the Japanese were manufacturing their own pianos and other Western musical instruments.

Emperor Mutsuhito, who adopted the title Meiji – or Enlightened Rule – in 1867, pushed for modernization with an eye to the West to avoid becoming dominated by other countries. In 1868, the government issued the Charter Oath: a five-article document outlining the principles of the Meiji administration. It declared that “knowledge shall be sought throughout the world.” Meiji curiosity about Western culture included absorbing foreign classical and religious music. On the bureaucratic side, the Meiji government created the Music Study Committee, which encouraged Western music. They wanted Japanese composers to write in the Western style, and the committee required the German model of music instruction for all students. The committee also led to the founding of the Tokyo National University of Fine Arts and Music, which Tomoko attended. 

Combining Western and Japanese music could be challenging though. For instance, Christian religious tended to be Western based, which was sometimes hard for Japanese to intonate. And when missionaries tried to translate their hymns into Japanese, they found it hard to match the rhythm to Japanese text. 

The tension between Western and Japanese music and their currents continued to flow through Tomoko’s families. During World War II at school Tomoko’s class sang nationalistic music with Japanese lyrics set to European music. Tomoko’s mother played and sang Christian songs, and Tomoko’s brother became a composer in the more Japanese mode. 

Nevertheless, Tomoko brings her Japanese sensibility as she performs music from around the world.

Harmony in Life

“Harmony is important,” asserts Tomoko. It is certainly a core sensibility in her life.

Tomoko remembers taking music theory when in secondary school, which included harmony. She and her classmates would sing in harmony in front of the classroom. The girls would perform in duets and quartets, personifying the core of musical harmony.

In turn, Tomoko weaves in music theory in her piano lessons. She 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.”

Tomoko also notes the link between harmony and mathematics. Both require precision and order. Both deal with proportion and use pattern creatively. Music is very measured, and mathematics has a certain rhythm. Einstein, who played the violin for his own pleasure, loved Mozart because of the composer’s expression of universal harmony,

Tomoko says of harmony: “There is something creative about harmony: it is stimulating.” Tomoko continues, “Art is supposed to have a sense of a group; it is communication.”

When people are in harmony with music, they are at peace and yet energized.  Tomoko talks about culture’s impact on music. “I have a student from India. Each country has a traditional music. The people in each country meet for a unique reason. During their gatherings a special harmony is produced, and even the way to perform that ritual music is unique.”

The saying “to make beautiful music together” is a sure sign of harmony, a sign that should be heard around the world.

The Reality of Music Theory

“Piano reading skills is most important,” asserts Tomoko. But this reading goes beyond just following the notes, just as cooking transcends reading the recipe. Cooking follows certain protocols based on the science of food; so too does music follows the theory of music.  

Music reveals patterns of sound, and music theory codifies those patterns. Music theory covers not just the elements of composition, but also studies the writing of music. Over the ages, composers create new patterns, which shape music theory and makes it truly dynamic.

When Tomoko studied music, she had to take music theory along with instrumentation and composition. Her own students also complement piano lessons with music theory. Furthermore, Tomoko incorporates music theory into her lesson. “Students need to know the vocabulary of music and the inner workings of music in order to perform knowledgeably.” Tomoko says, “It’s like an English teacher explaining grammar.”

Tomoko also talks about composers and their music, including how they manifest music theory. How are composers identified by their musical forms? How does Bach’s compositions reflect mathematical knowledge? Why was Schoenberg’s twelve-tone technique so revolutionary? How does music theory inform Bartok’s use of folk melodies?

Like the master chef, the master pianist knows and appreciates the theory behind of music, and applies that knowledge to enrich the performance – and the listener’s experience.