Announcements 10/24/11

1. Announcements 10/24/11 • Prayer • Term project proposals under review, I’ve responded to about 2/3 of them. I’ll send an email when I’m done, and when scores should show up in computer. • You can change your project idea, but if so you’ll need to send me a new proposal • Due today: HW 22 and HW 23 • Exam 2 review session: Tuesday 5-6 pm. Room: C255 (not C460 where we were last time) • Exam 2 starts on Thursday morning, goes until next Tuesday evening Frank & Ernest

2. Tone “quality” • Why does a trumpet playing 440 Hz sounddifferent than when I whistle or sing 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 of the same note! 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 (plus higher harmonics of each term)

7. C, E, G

8. G combined with G#

9. Chords, cont. • “nice” chords: simple frequency ratios (small integers), many harmonics of each note overlap • “ugly” chords: not many harmonics match

10. 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

11. 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)

12. 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

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

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

15. 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, called “photons”. Electrons, protons, etc., are also quantum mechanical particles. 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. • Colloquium speaker a few weeks ago: “Photons don’t exist. They are only quantized oscillations of electro-magnetic fields.” Advertisement for grad school. 

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