Transcript Slides
Final Review 1. Same interval means the same ratio of frequencies 2. Doubling the frequency gives the same pitch sensation In Western music the pitch range from f to 2f is split in 12 steps (entirely cultural) f f0 semitone 2 f0 C, C#/Db, D, D#/Eb, E, E#, Fb, F, F#/Gb, G, G#/Ab, A, A#/Bb, B C C# D D# E F F# minor major minor major 4th tritone 2nd 2nd 3rd 3rd G G# A A# B C 5th minor major minor major 6th 6th 7th 7th Consonances: sensation of calm and repose Frequency ratios 2/1 3/2 4/3 5/4 name octave (7 tones) fifth (3 ½ tones) forth (2 ½ tones) major third (2 tones) Dissonances: sensation of tension Frequency ratios name 729/512 tritone 243/128 minor second Equal temperament C C# D D# E F F# G G# A A# r r2 r12=2 r12 2 r 12 2 1.05946... B C Room Acoustics Reverberation direct sound reflected sounds Acoustics characteristics of auditoriums “liveness” : reverberation time “intimacy”: time to the first reflected sound to arrive “fullness/clarity”: direct sound versus reflected sound volume “warmth/brilliance”: reverberation time for low frequencies larger/smaller than for high frequencies s nnn i o ### resonances, n1 2 3 We want lots of evenly spread in the W1 1 1 frequencies) frequency (no favored i . . . d1 2 6 t 4 8 0 h xxx HHH e e e i i i ggg hhh t t t L1 e. n3 g9 t hx 1 . 5 4 2 . 3 3 xx 10.89-ft high, 12.4-ft wide, and 15.14 ft long 8-ft high, 16-ft wide, and 16 ft long Calculation of reverberation time (engineer style) V V TR 55.2 0.050 vs A A volume (ft3) absorption (ft2) reverberation time (s) A is the sum over all absorbing surfaces Example: 13ft by 20ft by 8ft room 4 walls of plaster (absorption coefficient 0.1) carpet floor (absorption coefficient 0.3) absorptive tile ceiling (absorption coefficient 0.6) walls floor ceiling A 2 (20 8) 2 (13 8) 0.1 (13 20) 0.3 (13 20) 0.6 286 sabins Loudspeakers http://electronics.howstuffworks.com/speaker5.htm Digital recording sampling precision sampling time Larger sampling rate and sampling precision improves fidelity What are the sampling rates we need for high fidelity ? A sampling rate equal to the twice the maximum frequency 20.000 Hz 40.000 samples per second Discretization (digitalization) Pressure level at one instant represented by 1’s and 0’s Two levels: 0 or 1 1 bit Four levels: 00, 01, 10 or 11 2 bits Eight levels: 000, 001, 010, 100, 011, 101, 110 or 111 3 bits … 65536 levels: 0000000000000000, 000000000000001, … 16 bits = 8 bytes Strategies for compression used in MP3 • masking • more precision in sounds we hear better How to read a cd/dvd? depth = ¼ wavelength constructive interference destructive interference This is a cartoon, real systems involve several mirrors, etc, … The main problem with all string instruments is: How to make a skinny string move a large amount of air (impedance matching) ? Solution: The string moves a board, the board moves the air Acoustic guitar, violins, cellos, … String vibration body vibration Resonances of the body (and air inside) help transfer the energy from the strings to sound at some frequencies, like the formants in the voice The sound of the piano is loud AND sustained change in decay rate one single string, overtones filtered out One reason for the two decay rates vertical mode excited initially by the hammer sounding board “gives” faster dumping horizontal mode not initially present sounding board is rigid slower dumping How to generate oscillation (sound) from continuous blowing ? • fipple • reed • lips recorder: fipple Reeds Brass Pressure antinodes (displacement nodes) appear at the position of the holes what changes the wavelength (frequency) of the note played