Before Spring Break, SMUS welcomed mathematics historian Glen Van Brummelen, who spoke to students about the interplay of music and mathematics. As part of the Scholar in Residence program, the Quest university professor visited classes and gave an open lecture during lunch.
“You hear a lot about how mathematics and music are related, but few people actually get into the details,” says Mr. Van Brummelen, author of The Mathematics of the Heavens and the Earth: The Early History of Trigonometry.
The shared history of music and math goes back to the mathematician Pythagorus (570-500 BC), who is often called the father of numbers and is best known for the Pythagorean theorem. “His interest in music was at least as important as his interest in mathematics,” says Mr. Van Brummelen.
To demonstrate how the human ear detects mathematics in music, Mr. van Brummelen used a monochord to play three pairs of notes and asked the audience to identify which pairing was most pleasing. All agreed that the two notes that had a ratio of 1:2 were the most pleasing to hear and notably different from notes that had ratios of 1:1.93 and 1:1.98.
“It was the Greeks who decided there should be 12 notes in each octave,” says Mr. Van Brummer. Though the decision was essentially arbitrary, the 12-note system means that the fifth and seventh notes hit the most ear-pleasing ratios (4:3 and 3:2). When we describe a note as being sharper or flatter, we are commenting on whether the note has a bigger or smaller ratio than the note it is being compared to.
“Musical notes work best when arranged in proportion,” says Mr. Van Brummelen. Though scales can range from the Polynesian 5-note scale to an 88-note scale, our preference for certain ratios is a universal quality that is not affected by culture. Eventually, we may come to prefer music in whichever scale to which we are most exposed, but as we listen to more music in different scales, we begin to perceive the differences less and less.
“There is no perfect scale,” says Van Brummelen.