Week 1 Homework Notes Part 1 (Ch.1 & 2)
Week 1 Homework Notes Part 1 (Ch.1 & 2) MUSC 80C - 01
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Date Created: 09/28/15
Music 80C History Literature amp Technology of Electronic Music Week 1 Homework Notes Prof Polansky DISCLAIMER THESE NOTES WERE UPLOADED WITH PERMISSION BY THE PROFESSOR WHO IS A COAUTHOR OF THIS EBOOK FROM WHICH THE NOTES WERE TAKEN FROM THE NOTES HERE ARE SIMPLE IMPORTANT CHUNKS OF THE TEXT TAKEN OUT REWORDED AS BEST AS POSSIBLE amp FURTHER EXPLAINED FOR COPYRIGHT REASONS I AM IUST GOING TO SITE THE ENTIRE PAGE AS A PARAPRHASEQUOTED TEXT HERE IS THE LINK FROM WHICH THE INFORMATION IS TAKEN httpmusiccolumbiaeducmcMusicAndComputers Chapter 1 The Digital Representation of Sound Part One Sound amp Timbre What is Sound sound involves at least physics amp perception sound involves at least 3 things 1 something moving 2 something transmitting the results of that movement 3 something someone hearing the result of that movement All things that make sound move and all things that move make sound That is if they are not moving too fast or too slow What we hear sound waves that are created by compression amp rarefactions when things move pushing amp pulling at the surrounding airwater whatever medium the movement is occurring in Amplitude amp Pressure Functions are graphs that show the amplitude of sound over time Sampling the recording of the value of a displacement in time Amplitude represents the amount of air compression above zero or rarefication below zero zero rest silence Amplitude shape corresponds to 1 the actual vibrations of the object 2 the changes in pressure of the air water or other medium 3 the deformation in or out of the eardrum Frequency a repeating pattern amp how quickly it repeats the rate at which air pressure uctuates How our ears work Eardrums are transducers in that they turn one form of info Or energy into another High frequencies cause peaks toward the front of the cochlea and low frequencies cause peaks toward the back The basilar membrane serves as a timetofrequency converter Amplitude amp loudness Frame average amplitude over a number of samples Psychosocial anything that we perceive about the physical world Frequency how fast something vibrates Pitch how high or low sound is perceived FREQUENCY TRANSLATES TO PICTCH IN OTHER WORDS HOW FAST SOMETHING VIBRATES TRANSLATES TO HOW HIGH OR LOW WE HEAR SOUND Amplitude how much something vibrates wave shape attack decay modulation spectral characteristic spectral pitch amp loudness trajectory Intensity how much the medium is displaced how much it is moved loudness how loud we perceive sound affected by pitch amp timbre pitch and loudness are independent of each other AMPLITUDE TRANSLATES TO INTENSITY WHICH TRANSLATES TO LOUDNESS IN OTHER WORDS HOW MUCH SOMETHING VIBRATES TRANSLATES TO HOW LOUD WE HEAR THE SOUND envelope the average or smoothed amplitude of the sound wave phase cancellation when one wave form goes negative it will counteract another positive Logarithmic perception it takes more of change in the amplitude to produce the same perceived change in loudness we ll cover more of this later on Decibel dB describes how loud a sound is perceived ANY CHANGE OF 10dB CORRESPONDS TO A DOUBLING OF PERCIEVED LOUDNESS Frequency Pitch amp Intervals Frequency a measurement of how often a given event repeats in time measured in hertz Hz Hertz Hz cycles per second Period the length of time it takes for frequency to go on one cycle Distance of wave wave length Fletcher Munson Curves equal loudness contours tell us how much intensity is needed at a certain frequency in order to produce the same perceived loudness as a tone at a different frequency 3 20 50 ICO 200 500 1000 5000 20000 Frequency Hz Sound Pressure Level dB Timbre Timbre the qualities of sound that aren t just frequency or amplitude Some of these qualities are 1 spectra the aggregate of simpler waveforms that make up what we recognize as a particular sound 2 envelope the attack sustain amp decay portion of a sound Here s a example Think of a section of a choir let s say the Alto 1 group All people in the Alto 1 group are assigned the same part of music they must sing the same notes with the goal of making their group sound unified as if they were one voice However if you tell each person in the Alto 1 group to sing individually one after another you will here the individuality of their voices the timbre also known as tone color The differences in timbre in a choir may be slight but many famous singers use timbre their advantage to make their sound unique Spectrum defined by a waveform distribution of energy Chapter 2 The Digital Representation of Sound Part Two Playing by the Numbers Digital Representation of Sound Analog function continuous function in which at every instance of time we could write down a number that is the value of the function at that instant 1 HI I I I I amp it udc ti me Analog to Digital Converter ADC records sound fast grabs instantaneous amplitudes at rapid audio rates Continuous functions are sampled amp stored as numerical values Digital to Analog Converter DAC converts numbers back to sound takes discrete functions amp returns a list of smooth values Spectrum of sound the complete description of how much of each of the frequencies is used Analog Versus Digital Sampling rate the rate at which samples are retained Analog information is continuous while digital information is not Analog waveforms are nice amp smooth while the digital waveform is chunky due to quantization or staircasing Sampling Theory Nyquist Sampling Theorem states that to well represent a signal the sampling rate needs to be at least twice the highest frequency contained in the sound of the signal With this theorem in mind remember that since the human ear only responds to sound up to about 20000 Hz we need to sample sound at a rate of 40000 Hz Nyquist frequency 22056 Hz half of the most common standard sampling rate for digital audio FoldoverAliasing undesirable artifacts in the signal Antialiasing Filters LowPass Filters make sure that the signal doesn t contain any frequencies above the Nyquist frequency Binary Numbers Base2 Representation all digital information is stored as binary numbers 2 to the power of the bit number Here s an example a Let s take the digital number 0101 and treat it as a binary numbers which has 5 bits each numeral in that makes up the number is considered a bit b Let s transform this binary number to a bit number Think about it like this each binary number is in place starting with zero Because there are four places the bit numbers range from zero to three There is a 3rd bit number a 2nd bit number a 1St bit number amp a 0 bit number c So the binary number 0 is the bit number 3 the binary number 1 is the bit number 2 the binary number 0 is the bit number 1 the binary number 1 is the bit number 0 These bit numbers are used as the exponents for the base of 2 numbers d Next you re going to multiply each binary number by the base 2 number which has the bit number as the exponent You add each of these values to get your bit value 0962312209 2119 2 0 4 0 1 5 Binary Bit Becomes the Binary Number Bit Number Number exponent of 936 Base 2 Number Value the Base 2 Number 0 3 9 23 0 96 23 0 1 2 9 22 1 96 22 4 0 1 9 21 0 96 21 0 1 0 9 20 1 96 2 1 See I told you it had 5bits Total 5 Bits How many numbers can be represented by bits Here s a chart Number of Bits Base 2 Number Number of Numbers Represented by Bits 8 28 256 16 216 65536 24 224 16777216 32 232 4294967296 Bit Width The more bits that are used the more hard disk space or memory size is needed Same with sampling rates the higher the sampling rate the more space will be used The more bits used the higher resolution and more accurate recording there will be Digital Copying Each copy is less pure than the first Noise any information that is added by the imperfection of the recording or playback technology Generations copies of copies Copyright is difficult to maintain since it is hard to say what is the original amp what is the copy where it comes from who owns it etc Storage Concerns The Size of Sound Bits can be stored on CDs which is a standard of 74 minutes One can have more than 6 million pits on which the bits are stored 8 bits 1 byte Let s find out just how much memory can be stored in a CD if we re using 16bit samples at a sampling rate of 44100 times second in stereo mode Stereo mode is made up of 2 independent channels so we need to double the amount of samples we re recording 32 bits 16 bits 936 2 32 bits 4 bytes So now we have 44100 4byte stereo samples second 44100 936 4 176400 bytes 176400 bytes 1764 kilobytes KB There are 60 seconds in a minute so 1764 KB 96 60 10584 KB 10584 KB 10584 megabytes MB There are 60 minutes in an hour so 10584 MB 96 60 about 600 MB 600 MB is the amount of information that can be stored on a standard CD Compression Data compression ways to express the same information in a shorter string of symbols storing the most information in the smallest amount of space without compromising the quality of the signal As the amount of information on a medium increases so does the importance of data compression Ways to compress data 1 Eliminate Redundancy take redundant information out amp put it back in later Here s an example with taking vowels out of words YNK DDL WNT T TWN RDING N PNY This is understood as Yankee doodle went to town riding on a ponyquot This works because this information is familiar to us which is why we re able to reconstruct information to what it really means 2 Grouping Information group information in order and short hand it to the simplest form Here s an example Bluebluebluebluegreengreengreenredblueredblueyellow This can be shortened to 4blue 3green red blue red blue yellow Which can be further shortened 4blue 3green 2red blue yellow Which can be finally abbreviated to 4b 3g 2 rb y Note that data would most likely be entered without the hyphens Also note that this works if there is a key for what each letter means that way it doesn t get confused with other meanings like b standing for brown instead of blue 3 Perceptual Encoding getting rid of data that does not have much value to the overall perception of sound by the receiver Some types of perceptual encoding include MP3 Compression Algorithm u law MuLawquot based on the principle that our ears are far more sensitive to low ample changes than to high ones change in sound is more noticeable with soft sounds than loud sounds u law table O 8 16 24 32 4O 48 56 64 72 8O 88 96 104 112 120 132 148 164 180 196 212 228 244 260 276 292 308 324 340 356 372 How to encode a u law sample a Start with a 16bit sample like 330 b Find an entry in the table above that is closest to the sample value Let s go with 324 c Count what entry number the entry value 324 is In this case the entry value s entry number is 28 It is the 28th entry in the chart count it d When decoding 28 is the index to the entry value which is 324 Yes some accuracy was lost since our initial value was 330 but it s a better sound quality than having used regular 8 bit samples p law offers near 16bit sound quality in an 8bit storage format 4 Prediction Algorithms making a prediction on what a signal is going to do frequency wise amp store the difference between the prediction amp the actual value The pros and cons of compression techniques some are time consuming but accurate others are simple to do but less accurate
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