Announcements 10/22/12 Prayer Term project proposals: I responded to all I received, and everyone should have a score. a. a.You can change your project idea, but if so you’ll need to send me a new proposal Careful: Lab 6 due Wed night Exam 2 starts Thurs morning, goes until next Tues evening a. a.Review session: this Tues, 5:30 – 7 pm, C255 Frank & Ernest

Demos f(x,t) tests with Slinky (results from last lecture)

From warmup Extra time on? a. a.(nothing in particular) Other comments? a. a.Liked it! b. b.If i did the lab on time but forgot to turn it in...is it still late?

From warmup Why does a trumpet playing a 440 Hz note sound qualitatively different than when a violin plays the same note? Both are producing 440 Hz waves, aren't they? a. a.Yes they are, but they have different timbres- meaning that they are both playing the fundamental and then certain levels of the harmonics above the fundamental. Due to the different levels of harmonics played there is a different feel to the final tone. wave shape

Tone “quality” Why does a trumpet playing 440 Hz sound different 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?

Tone quality, cont. Frequency analysis From unknown website

Tone quality, cont. Odd-sounding instruments (“tonal percussion”: bells, xylophone, tympani, etc. ) From

From warmup What is a chapter on musical scales doing in a physics textbook? What's the connection to physics? a. a.It is acoustics and AWESOME. b. b.Relation between notes of frequencies. Types of scales used were mathematical relations between frequencies. c. c.Everything's connected to physics. Physics defines how things happen. Music created by sound waves of certain frequencies, and as we've been learning in class, waves, frequencies, and harmonics have a lot of physics applications. d. d.Just cause we are physicists doesnt mean we are incapable of doing anything else...like art or music. This statement is not reflexive however, If you are a musician....you probably cant do physics.

Piano keyboard layout 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 D E F G A B C Image: C-sharp/D-flat

Chords 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 CEG Image: (plus higher harmonics of each term)

C, E, G

G combined with G#

Chords, cont. “nice” chords: simple frequency ratios (small integers), many harmonics of each note overlap “ugly” chords: not many harmonics match ChordFreq. Ratios Octave (C-C)2:1 Major triad (C-E-G)4:5:6 Minor triad (C-E flat -G)10:12:15 Major 7 th (C-E-G-B)8:10:12:15 Major-minor, aka “dominant 7 th ” (C-E-G-B flat ) 4:5:6:7 Minor-minor, aka “minor 7 th ” (C-E flat -G-B flat ) 10:12:15:18

Trumpets The notes you can play with no valves pushed in: (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.) NoteFrequencyRatio to Fundamental 1 st harmonic: Low C (with difficulty) Hz (fundamental) 1:1 2 nd harm: Middle C261.62:1 3 rd harm: G392.43:1 4 th harm: C above middle C :1 5 th harm: E654.15:1 6 th harm: G784.96:1 7 th harm: B-flat??915.77:1 8 th harm: High C Hz8:1 B-flat on piano = Hz

Back to Pianos Why is a high B-flat on a piano 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 ______ A = 440 Hz (defined as reference) high B-flat (middle C)

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 Note on pianoFrequencyHow calculatedRatio to Fundamental Start with Low C130.8 Hzf 1 = 21 half steps below A (440 Hz) 1:1 Middle C261.6 f 1  2 12/12 2:1 G392.0 f 1  2 19/ :1 C above middle C523.3 f 1  2 24/12 4:1 E659.3 f 1  2 28/ :1 G783.9 f 1  2 31/ :1 B-flat932.3 f 1  2 34/ :1 High C f 1  2 36/12 8:1

Which is better? The debate “Equal-tempered”“Just-intonation” Advocated by Galileo’s father, 1581; Extremely influential work by J.S. Bach, 1782: “The Well- Tempered Clavier” Still used in many instruments, without even thinking about it (just not piano) Same ratio between successive notes: all halfsteps are the same. C to D flat = same as B flat to B All halfsteps are not equal. In fact, what’s a halfstep? Makes key changes possible without retuning instrument Key changes sound very bad unless you re-tune Chords are a little off (not exact integer ratios), e.g. C-E-G = : : Creates beats (see PpP Fig 7.1) Chords are precise (integer ratios exact), e.g. C-E-G = 4:5:6 No beats Disclaimer: In actuality, piano tuners don’t use a strict equal-tempered scale

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

The wave nature of light What is “waving”? Medium? Polarization: quick definition