Important Announcements and Exam Information for the Week

1. Announcements 3/2/11 • Prayer • Term projects • Proposals under review • You can change your idea, but need to send me a new proposal • My office hours this week: I’ll likely be in my lab, room U130, just down the hall from normal office hour location. Find me there. • Exam 2 starts on Saturday • Exam review session, results of voting: • Friday 3:30 – 5 pm. Room: C261 • Next week: I’ll be out of town on Mon. You’ll have Dr. Gus Hart as a substitute.

2. Tone “quality” • Why does a trumpet playing 440 Hz sounddifferent than when I whistle the same frequency? • The wave: Spectrum Lab as oscilloscope • The sounds have different ____________ … but both sounds have the same ____________ • What does that imply about their Fourier frequency components?

3. Tone quality, cont. • Spectrum Lab as frequency analyzer From unknown website

4. Tone quality, cont. • Odd-sounding instruments (“tonal percussion”: bells, xylophone, tympani, etc.) From http://web.telia.com/~u57011259/Bellspectra.htm

5. Piano keyboard layout Image: http://www.music-for-music-teachers.com/piano-keyboard.html • Half step: C to C-sharp (or, e.g. E to F) • Whole step (C to D): ___ half steps • Octave (C to C): ___ half steps • Fifth (C to G): ___ half steps • Fourth (C to F): ___ half steps • Major Third (C to E): ___ half steps • Minor Third (C to E-flat): ___ half steps C E G B C-sharp/D-flat D F A C 2 12 7 5 4 3

6. Chords Image: http://www.music-for-music-teachers.com/piano-keyboard.html • Why does this sound “good”? • Because they are all harmonics (aka overtones) of the same note!  Their fundamental frequencies are all integer multiples of the same number  What happens when you add frequencies that are multiples of the same number? • What is the note? • It’s actually a C, two octaves below the C that’s being played! • The frequencies of the three notes are 4:5:6 C E G

7. Chords, cont. • Consonant chords: simple frequency ratios (small integers), many harmonics of each note overlap • Dissonant chords: not many harmonics match

8. Trumpets (Lets suppose a “C trumpet” instead of a regular “B-flat” trumpet, so we don’t have to worry about the usual whole-step shift between piano and trumpet scales.) • The notes you can play with no valves pushed in: B-flat on piano = 932.3 Hz

9. Back to Pianos • Why is a high B-flat on a piano 932.3 Hz? • How many half steps is it? • How many half steps in an octave? • How much frequency change in an octave? • Each half step = increase freq by a factor of ______ high B-flat A = 440 Hz (defined as reference) (middle C)

10. So, why are there 12 half-steps in an octave? • Smallest number of tones that can give you close to the right ratios needed for harmonics and chords  Fewer equally-spaced tones in a scale wouldn’t get close enough  More equally-spaced tones in a scale adds unnecessary complexity

11. Which is better? The debate Disclaimer: In actuality, piano tuners don’t use a strict equal-tempered scale

12. The Exam • “What’s on the exam?” (you ask)

13. Light • Textbook: “Sometimes light acts like a wave, and other times it acts like a particle.” • Colton: Light is made up of quantum-mechanical particles. (Same with electrons, protons, etc.) Quantum-mechanical particles are neither waves nor particles in the macroscopic sense, but rather we should think of the converse: “waves” and “particles” as we typically use the words are based on our observations of large-scale effects of these quantum-mechanical particles. Advertisement for grad school. 

14. The wave nature of light • What is “waving”? http://stokes.byu.edu/emwave_flash.html • Medium?