Elkies addressed how much a piece of music needs to change before it is a different piece, rather than a variation on the original. He also talked about how much information remains when the redundancy of repeated themes in a piece is accounted for.
.. But his lecture ended with an impressive performance, from memory, of a piece made from a baroque-style repeating arpeggiation where the root of the chord changed from measure to measure based not on a conventional harmonic progression, but on the digits of π. The result was an intriguingly disorienting congress of order with randomness, evoking something like an inebriated Buxtehude.
.. Tymoczko’s objective, data-driven approach to musical practice seems to have the power to reveal other significant insights. His love and deep understanding of music was evident in the joy with which he shared his discovery of hidden canons (or rounds, as in “Row, Row, Row Your Boat”) in pieces by Bach and Marenzio.
.. As the Pythagoreans discovered, harmonious intervals in music are formed from frequencies that are the ratios of small whole numbers.
.. The highlight here was a recording of a barbershop quartet in which Wright discovered a subtle use of microtonics during a chord change. In shifting from one chord to another, three of the singers changed notes, while the fourth held on to his note across the chord change—or should have, based on the notes on paper. In practice, the sustained note shifted frequency by a small fraction of a semitone to maintain just intervals with the notes of the second chord.
These types of microtonal manipulations are part of what give barbershop quartet performances their intensely harmonious quality.
Why Are So Many Singers Suffering From Vocal-Cord Injuries? A Leading Surgeon Explains
Vocal-cord issues have always been around, says Dr. Zeitels, but singers used to keep them secret. Nowadays, “the minute somebody is not going to go on, it’s all over the internet. Fifteen years ago, that didn’t happen. People would cancel the show in Kansas, but you didn’t know about it in New York.” As a result, singers today are more willing to acknowledge when vocal injuries have occurred, and feel less shame about admitting it.