Mathematics for Musicians
- Armando is the dynamic new conductor of an orchestra and has increased the ticket sales for the classical series 95%. If the concert hall holds 3200 people, and the concerts begin promptly at 8:05 P.M., how many digital watch alarms will go off within one minute of 9 P.M.? Within 5 minutes?
- Richard has been a professional timpanist for 35 years. In his personal kit he owns 32 different yarn mallets, 12 different wool mallets, 5 different rubber mallets, and 2 different polished brass tack hammers. What are the odds that a conductor will ask him to use different mallets at the first rehearsal of a Haydn symphony? A Mahler symphony?
- Julinda's orchestra performs Dvorak's "New World" symphony every 6 years, Sibelius' Swan of Tuoneola every 4 years, and Berlioz's Overture to Benvenuto Cellini every 3 years. What are the odds that, in any given year, the program notes will include the sentence, "The English Horn is neither English nor a horn"?
- Wilma is tired of paying for clarinet reeds. If she adopts a policy of playing only on rejected reeds from her colleagues will she be able to retire on the money she has saved if she invests it in mutual bonds, yielding 8.7%, before she is fired from her job? If not, calculate the probability of her ever working in a professional symphony orchestra again.
- Jethro has been playing the double bass in a symphony orchestra for twelve years, three months and seven days. Each day, his inclination to practice decreases by the equation: (Total days in the orchestra) x 0.000976 Assuming he stopped practicing altogether four years, six months and three days ago, how long will it be before he is completely unable to play the double bass?
- Wilma plays in the second violin section, but specializes in making disparaging remarks about conductors and other musicians. The probability of her making a negative comment about any given musician is 4 chances in 7, and for conductors is 16 chances in 17. If there are 103 musicians in the orchestra and the orchestra sees 26 different conductors a year, how many negative comments does Wilma make in a two-year period? How does this change if five of the musicians are also conductors? What if six of the conductors are also musicians?
- Horace is the General Manager of an important symphony orchestra. He tries to hear at least four concerts a year. Assuming that at each concert the orchestra plays a minimum of three pieces per concert, what are the chances that Horacecan avoid hearing a single work by Mozart, Beethoven or Brahms in the next ten years?
- Betty plays in the viola section. Despite her best efforts she is unable to play with the rest of the orchestra and, on average, plays 0.3528 seconds behind the rest of the viola section, which is already 0.16485 seconds behind the rest of the orchestra. If the orchestra is moving into a new concert hall with a reverberation time of 2.7 seconds, will she be able to continue playing this way undetected?
- Ralph loves to drink coffee. Each week he drinks three more cups of coffee than Harold, who drinks exactly one third the amount that the entire brass section consumes in beer. How much longer is Ralph going to live?
- Rosemary is unable to play in keys with more than three sharps or flats without making an inordinate number of mistakes. Because her colleagues in the cello section are also struggling in these passages she has so far been able to escape detection. What is the total number of hours they would all have to practice to play the complete works of Richard Strauss?