The McGovern Center for Humanities and Ethics’ Arts & Resilience program kicked off the 2019 schedule with “Music by the Numbers,” featuring Mark Vogel on Sept. 19 in the Fifth Floor Gallery.
Vogel, the artistic director, conductor, and pianist for International Voices Houston performed for the Arts & Resilience program for the third consecutive year. He treated students, faculty, and staff at the Medical School to classic piano pieces while explaining some of the key roles that mathematics plays in music.
Vogel, who refers to himself as a piano nerd, opened the show with Wolfgang Amadeus Mozart’s Sonata No. 19 in B-Flat Major. Vogel explained that the piece written in 1789 is in 3/4 time and contains 209 measures, 627 total beats, and roughly 2009 notes.
Following the piece, Vogel explained the Fibonacci Sequence to the audience, which is a series of numbers where the next number is found by adding up the two previous numbers. For instance, 0+1=1; 1+1=2; 1+2=3; and so on. The Fibonacci Sequence creates a consistent ratio from pairing to paring that is 1.618 times from one digit to the next.
Vogel noted that the 13 notes in an octave contain five black keys and eight white keys, and how the numbers five, eight, and 13 all appear on the Fibonacci Sequence. He also pointed out that Mozart’s Sonata No. 19 follows the Fibonacci Sequence as 79 measures are in the exposition, or primary thematic material for the piece, while 130 measures fall in the development and recapitulation phases of the sonatas. The numbers 79, 130 and 209, while not on the Fibonacci Sequence, still follow the 1.6 times ratio.
Vogel’s next song was from a Johann Sebastian Bach piece called “The Well-Tempered Clavier.” The clavier has divided octaves, however they are not equal, which causes each key to sound different. For this set, Bach wrote 24 different songs to explore each of the 24 keys of the clavier.
Vogel’s next pieces centered around meter, or how many beats there are in the pattern for a particular piece of music. Vogel started with the song “Happy Birthday” which is metered in 3/4 time before moving on to Dave Brubeck’s “Blue Rondo A La Turk.” The song from Brubeck was written in 9/8 meter, which can be common in Eastern Europe.
Vogel then introduced the audience to 12-tone serialism and “Suite of Dances” by Arnold Schoenberg. The technique of 12-tone serialism requires that all 12 notes of the chromatic scale are played once before a note can be repeated.
Vogel’s next two pieces centered on the length of time it takes to play each. The first, Eric Satie’s “Vexations” has to be played 840 times in succession, which requires roughly 18 hours to perform live. The piece, written in the 1890s, was unpublished by Satie, and was not played live until 1963, when John Cage and Lewis Lloyd organized a concert at the Pocket Theatre in New York.
Cage also wrote Vogel’s next featured piece 4’33, in which the performer approaches their instrument, prepares to play, and then sits in silence for four minutes and 33 seconds. The piece is designed to highlight the sounds of the environment around the listeners.
The final two songs Vogel shared with the audience were Arvo Pärt’s “Fur Alina” and Fredrick Chopin’s “Fantaisie-Impromptu.” Pärt’s piece is perfectly mathematical until the final note, while Chopin invited conflict into his piece by having the left hand played in triple time, while the right hand is played in duple.
The next installment of the Arts & Resilience program is called “Violin” and features Chloe Trevor with Michael Zuraw. The performance will be held at noon Oct. 10 in the Fifth Floor Gallery. The program is sponsored by the Dean’s Office in collaboration with the McGovern Center for Humanities and Ethics. For more information and a schedule, visit the program’s website here.