Reece’s session, at 2:30 p.m. April 23 in the Campus Center auditorium, will include playing Bach selections on an authentic harpsichord while incorporating music theory, mathematics, physics and history. It is one of about 180 contributions to the annual celebration of the campus community’s scholarly and creative pursuits.
“On all musical instruments, the space between different notes in the scale are based on mathematical ratios,” Reece said. Unfortunately, he added, it is mathematically impossible to space all the notes over the scale and make them absolutely true.
“We can try to make certain intervals more pure than others, but that’s going to make some intervals more impure,” Reece said. “The system by which we choose which interval to favor when tuning is called a temperament. There are a great variety of temperaments produced by music theorists and used by performers throughout history.”
Much like trying to tweak the calendar by adding a day every leap year, temperaments seek to solve a mathematical problem that can never be perfectly reconciled. Tuning instruments involves tradeoffs among intervals—octaves, fifths, fourths or other relationships—to account for this mathematical imperfection.
Over the years, renowned philosophers including Pythagoras, Leonardo Da Vinci, Isaac Newton and Christiaan Huygens have also been captivated by and explored this mathematical riddle, Reece explained.
Until Johann Sebastian Bach’s time, composers tended to write in keys calling for purer sounds at their intervals to the detriment of more remote, less-used keys. Bach decided to create a challenging conundrum by composing the first single song cycle to use all 24 major and minor keys, “The Well-Tempered Clavier,” in the early 18th century.
“Bach is the kind of composer who enjoyed intellectual challenges and I think you can clearly see that in his music,” Reece said.
But the exact temperament that Bach used for “The Well-Tempered Clavier” has never been solved, as he left no specific instructions how to tune a harpsichord or other instrument for that piece, Reece said. Scholars have tried to explore it using everything from biographical information to statistical analysis.
“An intriguing theory holds that Bach encoded his temperament in the ornamental squiggle on the title page of ‘The Well-Tempered Clavier,’ a series of 11 loops with different numbers of spirals inside,” Reece said (see photo; click on image for greater detail).
The 18th century harpsichord reconstruction will allow him “to try to closely mirror the sort of instrument Bach might have used,” while exploring possible temperaments, Reece said. “Through these examples, I hope to give a sense of how these theories influence composers and have a dramatic impact on the musical sound.”
His session will be followed by another performance/presentation, “The Notion of Free Time as Developed by Percy Granger,” by student Zachary Parchomenko.
For more information, visit www.oswego.edu/quest.
- END -
(Posted: Apr 09, 2008)