1. Final Review

2. 1. Same interval means the same ratio of frequencies 2. Doubling the frequency gives the same pitch sensation

3. In Western music the pitch range from f to 2f is split in 12 steps (entirely cultural) f f0f0f0f0 2 f 0 C, C#/Db, D, D#/Eb, E, E#, Fb, F, F#/Gb, G, G#/Ab, A, A#/Bb, B semitone

4. C C# D D# E F F# G G# A A# B C minor 2 nd major 2 nd minor 3 rd major 3 rd 4 th tritone tritone 5 th minor 6 th major 6 th minor 7 th major 7 th

5. Consonances: sensation of calm and repose Frequency ratios name 2/1 octave (7 tones) 2/1 octave (7 tones) 3/2 fifth (3 ½ tones) 3/2 fifth (3 ½ tones) 4/3 forth (2 ½ tones) 4/3 forth (2 ½ tones) 5/4 major third (2 tones) 5/4 major third (2 tones) Dissonances: sensation of tension Frequency ratios name 729/512 tritone 729/512 tritone 243/128 minor second 243/128 minor second

6. Equal temperament C C# D D# E F F# G G# A A# B C r r2r2r2r2 r 12 =2

7. Reverberation direct sound reflected sounds Room Acoustics

8. 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

9. We want lots of resonances, evenly spread in the frequency (no favored frequencies) DimensionDimension Design #1Design #1 Design #2Design #2 Design #3Design #3 WidthWidth 1.14 x Height1.14 x Height 1.28 x Height1.28 x Height 1.60 x Height1.60 x Height LengthLength 1.39 x Height1.39 x Height 1.54 x Height1.54 x Height 2.33 x Height2.33 x Height DimensionDimension Design #1Design #1 Design #2Design #2 Design #3Design #3 WidthWidth 1.14 x Height1.14 x Height 1.28 x Height1.28 x Height 1.60 x Height1.60 x Height LengthLength 1.39 x Height1.39 x Height 1.54 x Height1.54 x Height 2.33 x Height2.33 x Height 8-ft high, 16-ft wide, and 16 ft long 10.89-ft high, 12.4-ft wide, and 15.14 ft long

10. Calculation of reverberation time (engineer style) volume (ft 3 ) absorption (ft 2 ) A is the sum over all absorbing surfaces reverberation time (s)

11. 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) wallsfloorceiling

12. Loudspeakers http://electronics.howstuffworks.com/speaker5.htm

13. sampling time sampling precision Digital recording

14. Larger sampling rate and sampling precision improves fidelity

15. 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

16. 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

17. Strategies for compression used in MP3 masking masking more precision in sounds we hear better more precision in sounds we hear better

18. How to read a cd/dvd? This is a cartoon, real systems involve several mirrors, etc, … constructive interference destructive interference depth = ¼ wavelength

19. 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

20. 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

21. The sound of the piano is loud AND sustained one single string, overtones filtered out change in decay rate

22. vertical mode excited initially by the hammer sounding board “gives” faster dumping horizontal mode not initially present sounding board is rigid slower dumping One reason for the two decay rates

23. How to generate oscillation (sound) from continuous blowing ? fipple fipple reed reed lips lips

24. recorder: fipple

25. Reeds

26. Brass

27. Pressure antinodes (displacement nodes) appear at the position of the holes what changes the wavelength (frequency) of the note played what changes the wavelength (frequency) of the note played