The Mathematics of a Note: teacher key

Music and Instruments, grade 11 edition, written for 11th grade. Half wavelengths, ratios and the number 1.059: how modes, tubes and tuning turn vibrations into notes, and how instruments have been built to follow them.

Read the book. Print this page for the key.

Questions and answers

1. What does a standing wave on a string need at its ends?
   • Frets
   • Nodes (answer)
   • Pickups
2. Which harmonics does a closed tube have?
   • Only even multiples
   • None at all
   • Only odd multiples (answer)
3. What is the frequency ratio of an octave?
   • 2:1 (answer)
   • 3:1
   • 12:1
4. How many of the 21 players chose an old violin?
   • 3
   • 15
   • 8 (answer)
5. What is true of a drumhead's overtones?
   • They are all whole multiples
   • They are inharmonic (answer)
   • They do not exist
6. What was found at Ur?
   • A great lyre with a bull's head (answer)
   • A steel pan
   • A piano

Words

• harmonics: overtone family
• octave: a 2:1 jump
• temperament: tuning system
• inharmonic: not whole multiples
• electrophones: electric instruments
• aerophone: air instrument