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Final Review

Explore the fundamentals of music theory, room acoustics, and instrument mechanics to gain a deeper understanding of sound and music production. Learn about pitch intervals, consonances, and dissonances, as well as room reverberation and instrument mechanics.

michaelarnold
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Final Review

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  1. Final Review

  2. Same interval means the same ratio of frequencies • 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 f0 2 f0 semitone C, C#/Db, D, D#/Eb, E, E#, Fb, F, F#/Gb, G, G#/Ab, A, A#/Bb, B

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

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

  6. Equal temperament C C# D D# E F F# G G# A A# B C r r2 r12=2

  7. Room Acoustics Reverberation direct sound reflected sounds

  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) 10.89-ft high, 12.4-ft wide, and 15.14 ft long 8-ft high, 16-ft wide, and 16 ft long

  10. Calculation of reverberation time (engineer style) volume (ft3) absorption (ft2) reverberation time (s) A is the sum over all absorbing surfaces

  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) walls floor ceiling

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

  13. Digital recording sampling precision sampling time

  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 • more precision in sounds we hear better

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

  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 change in decay rate one single string, overtones filtered out

  22. 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

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

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