final review. 1. same interval means the same ratio of frequencies 2. doubling the frequency gives...
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Final ReviewFinal Review
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1.1. Same interval means the same ratio of Same interval means the same ratio of frequenciesfrequencies
2.2. Doubling the frequency gives the same Doubling the frequency gives the same pitch sensationpitch sensation
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In Western music the pitch range from f to 2f is In Western music the pitch range from f to 2f is split in 12 stepssplit in 12 steps
(entirely cultural)(entirely cultural)
ff
ff00 2 f2 f00
C, C#/Db, D, D#/Eb, E, E#, Fb, F, F#/Gb, G, G#/Ab, A, C, C#/Db, D, D#/Eb, E, E#, Fb, F, F#/Gb, G, G#/Ab, A, A#/Bb, BA#/Bb, B
semitone
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CC
C# D D# E F F# G G# A A# B CC# D D# E F F# G G# A A# B Cminor minor
22ndnd major major
22ndnd minor minor
33rdrd major major
33rdrd 44thth tritonetritone 55thth minor minor
66thth major major
66thth minor minor
77thth major major
77thth
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Consonances: sensation of calm and reposeConsonances: sensation of calm and repose
Frequency ratios nameFrequency 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 tensionDissonances: sensation of tension
Frequency ratios nameFrequency ratios name
729/512 tritone729/512 tritone
243/128 minor second243/128 minor second
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Equal temperamentEqual temperament
C C# D D# E F F# G G# A A# B CC C# D D# E F F# G G# A A# B C
rr
12 122 2 1.05946...r r
rr22
rr1212=2=2
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ReverberationReverberation
direct direct soundsound
reflected reflected soundssounds
Room AcousticsRoom Acoustics
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Acoustics characteristics of auditoriumsAcoustics characteristics of auditoriums
““liveness” : liveness” : reverberation timereverberation time
““intimacy”: intimacy”: time to the first reflected sound to arrivetime to the first reflected sound to arrive
““fullness/clarity”: fullness/clarity”: direct sound versus reflected sound direct sound versus reflected sound volumevolume
““warmth/brilliance”:warmth/brilliance”: reverberation time for low reverberation time for low frequencies larger/smaller than for high frequenciesfrequencies larger/smaller than for high frequencies
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We want lots of resonances, evenly spread in the We want lots of resonances, evenly spread in the frequency (no favored frequencies)frequency (no favored frequencies)
Dimension
Design #1
Design #2
Design #3
Width
1.14 x Height
1.28 x Height
1.60 x Height
Length
1.39 x Height
1.54 x Height
2.33 x Height
Dimension
Design #1
Design #2
Design #3
Width
1.14 x Height
1.28 x Height
1.60 x Height
Length
1.39 x Height
1.54 x Height
2.33 x Height
8-ft high, 16-ft wide, 8-ft high, 16-ft wide, and 16 ft long and 16 ft long
10.89-ft high, 12.4-ft 10.89-ft high, 12.4-ft wide, and 15.14 ft long wide, and 15.14 ft long
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Calculation of reverberation time (engineer style)Calculation of reverberation time (engineer style)
55.2 0.050Rs
V VT
v A A
volume (ftvolume (ft33))
absorption (ftabsorption (ft22))
A is the sum over all absorbing surfacesA is the sum over all absorbing surfaces
reverberation time (s)reverberation time (s)
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Example:Example:
13ft by 20ft by 8ft room13ft by 20ft by 8ft room
4 walls of plaster (absorption coefficient 0.1)4 walls of plaster (absorption coefficient 0.1)
carpet floor (absorption coefficient 0.3)carpet floor (absorption coefficient 0.3)
absorptive tile ceiling (absorption coefficient 0.6)absorptive tile ceiling (absorption coefficient 0.6)
2 (20 8) 2 (13 8) 0.1 (13 20) 0.3 (13 20) 0.6
286 sabins
A
wallswalls floorfloor ceilingceiling
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LoudspeakersLoudspeakers
http://electronics.howstuffworks.com/speaker5.htm
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sampling time
sampling sampling precisionprecision
Digital recordingDigital recording
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Larger sampling rate and sampling precision Larger sampling rate and sampling precision improves fidelityimproves fidelity
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What are the sampling rates we need for high 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
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Discretization (digitalization)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
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Strategies for compression used in MP3Strategies for compression used in MP3
• maskingmasking
• more precision in sounds we hear bettermore precision in sounds we hear better
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How to read a cd/dvd?How to read a cd/dvd?
This is a cartoon, real systems involve This is a cartoon, real systems involve several mirrors, etc, …several mirrors, etc, …
constructive constructive interferenceinterference
destructive destructive interferenceinterference
depth = ¼ wavelengthdepth = ¼ wavelength
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The main problem with all string instruments is:The main problem with all string instruments is:
How to make a skinny string move a large amount How to make a skinny string move a large amount of air (impedance matching) ?of air (impedance matching) ?
Solution:Solution:
The string moves a board, the board moves the airThe string moves a board, the board moves the air
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Acoustic guitar, violins, cellos, …Acoustic guitar, violins, cellos, …
String vibration body vibrationString vibration body vibration
Resonances of the body (and air inside) Resonances of the body (and air inside) help transfer the energy from the strings help transfer the energy from the strings
to sound at some frequencies,to sound at some frequencies,like the formants in the voicelike the formants in the voice
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The sound of the piano is loud AND sustainedThe sound of the piano is loud AND sustained
one single string, overtones filtered outone single string, overtones filtered out
change in change in decay ratedecay rate
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vertical modevertical mode
excited initially by the excited initially by the hammerhammer
sounding board “gives”sounding board “gives”
faster dumpingfaster dumping
horizontal modehorizontal mode
not initially presentnot initially present
sounding board is rigidsounding board is rigid
slower dumpingslower dumping
One reason for the two decay ratesOne reason for the two decay rates
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How to generate oscillation (sound) How to generate oscillation (sound) from continuous blowing ?from continuous blowing ?
• fipplefipple
• reedreed
• lipslips
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recorder: fipplerecorder: fipple
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ReedsReeds
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BrassBrass
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Pressure antinodes (displacement nodes) appear at the Pressure antinodes (displacement nodes) appear at the position of the holesposition of the holes
what changes the wavelength (frequency) of the what changes the wavelength (frequency) of the note playednote played