| Lesson 1: Sound... and by association: Music |
Lesson 1: Sound
So were going to start at the very, very beginning and talk a bit about what sound (and by association music) is.
So without getting too heavy, sound is the production of longitudinal waves in a medium. In short, you sing or drop a book or your dog barks, the air vibrates and sends pulses to your ear. These pulses whirl they're way into your inner ear and tap on a membrane known as your ear drum. You hear.
Now discussing sound does mean we have to delve into a little bit of physics and talk about waves.
Waves are the propagation of energy through a medium (which is why in space no one can hear you scream). In simpler terms, think of the atmosphere as a system of very tiny little balls in contact with one another (like those tricolor ball playpens you used to love and probably still do), when you push one, it collides with another which hits another and so forth, transferring energy and propagating a wave.
Waves have three very important properties that help to define them. They are frequency (f), wavelength (λ), and speed (v), related by the equation v=fλ. Sound travels at a somewhat constant speed through air (though it is dependent on temperature and humidity) so if we consider it to be constant we can relate frequency directly to wavelength. This is helpful because it helps define the size and properties of instruments.
Waves are composed of repeating concave (troughs) and convex (crests) segments in alternation (like a sine or cosine function). The distance between the peaks of two adjacent crests or troughs is the wavelength usually measured in meters. The number of cycles (1 crest, 1 trough) that the wave can undergo in 1 second is the frequency measured in Hertz (1 Hz = 1 1/s). We usually differentiate notes by their frequencies. Getting back to music, the frequency of a note an octave above another note is has twice frequency of the lower pitched note.
Consider now a guitar string. When we pluck a string that is unstopped at a fret, the string vibrates. The wavelength of the string's vibration is the full length of the string. To play higher notes, we shorten the wavelength by stopping the string, reducing its effective length and thus raising the frequency of the string's vibration. Note though that the air may not vibrate at the same wavelength as the string does. If this was true, different strings would not produce different pitches at the same fret.
Most, if not all, pitched instruments create different pitches by altering the effective wavelength of whatever it is that vibrates.
Waves also have another important property, amplitude. Amplitude measures the length of the peaks of the wave's crests or troughs and is proportional to the loudness of a sound. High amplitude, high volume. But the relationship is not perceived linearly. Interestingly, our ears interpret sound logarithmically at base 10. This means that if you wanted to hear a particular sound twice as loudly, you would need ten times the energy. Twice the volume of one instrument is perceived by having ten of them.
Lastly, we need to discuss overtones. Let's go back to the guitar string. If you pluck it unstopped, it will vibrate between the two points where that string is fixed. But there are other ways that it can vibrate between these two points. The string could vibrate so that it is essentially stationary at various points along it's length. In physics, these points are called nodes. Different patterns of vibration are called different modes of vibration and the number of nodes plus one in the pattern give the mode number. For example a string that vibrates but is stationary a midspan is vibrating in it's second mode. Hitting harmonics on instruments is done by isolating these modes of vibration. We'll talk more about modes of vibrations when we talk about the harmonic overtone series.
Now to music. What differentiates music from noise is distinct and recognizable pitches. This isn't to say that non-pitched instruments and music that is purely rhythmic isn't music, it just isn't from a very scientific perspective. What makes a pitch recognizable and different from noise is a discernible wave pattern. We'll get more into it when we discuss the harmonic overtone series but the main difference between music and noise is that noise is composed of a disorganized combination of waves that don't produce any distinguishable tone. Music has a distinguishable frequency.
For more info see:
http://www.lukestark.com/blog/2009/01/04/sharing-music-theory-noise-music-and-patterns/
http://en.wikipedia.org/wiki/Wave
http://en.wikipedia.org/wiki/Sound
So were going to start at the very, very beginning and talk a bit about what sound (and by association music) is.
So without getting too heavy, sound is the production of longitudinal waves in a medium. In short, you sing or drop a book or your dog barks, the air vibrates and sends pulses to your ear. These pulses whirl they're way into your inner ear and tap on a membrane known as your ear drum. You hear.
Now discussing sound does mean we have to delve into a little bit of physics and talk about waves.
Waves are the propagation of energy through a medium (which is why in space no one can hear you scream). In simpler terms, think of the atmosphere as a system of very tiny little balls in contact with one another (like those tricolor ball playpens you used to love and probably still do), when you push one, it collides with another which hits another and so forth, transferring energy and propagating a wave.
Waves have three very important properties that help to define them. They are frequency (f), wavelength (λ), and speed (v), related by the equation v=fλ. Sound travels at a somewhat constant speed through air (though it is dependent on temperature and humidity) so if we consider it to be constant we can relate frequency directly to wavelength. This is helpful because it helps define the size and properties of instruments.
Waves are composed of repeating concave (troughs) and convex (crests) segments in alternation (like a sine or cosine function). The distance between the peaks of two adjacent crests or troughs is the wavelength usually measured in meters. The number of cycles (1 crest, 1 trough) that the wave can undergo in 1 second is the frequency measured in Hertz (1 Hz = 1 1/s). We usually differentiate notes by their frequencies. Getting back to music, the frequency of a note an octave above another note is has twice frequency of the lower pitched note.
Consider now a guitar string. When we pluck a string that is unstopped at a fret, the string vibrates. The wavelength of the string's vibration is the full length of the string. To play higher notes, we shorten the wavelength by stopping the string, reducing its effective length and thus raising the frequency of the string's vibration. Note though that the air may not vibrate at the same wavelength as the string does. If this was true, different strings would not produce different pitches at the same fret.
Most, if not all, pitched instruments create different pitches by altering the effective wavelength of whatever it is that vibrates.
Waves also have another important property, amplitude. Amplitude measures the length of the peaks of the wave's crests or troughs and is proportional to the loudness of a sound. High amplitude, high volume. But the relationship is not perceived linearly. Interestingly, our ears interpret sound logarithmically at base 10. This means that if you wanted to hear a particular sound twice as loudly, you would need ten times the energy. Twice the volume of one instrument is perceived by having ten of them.
Lastly, we need to discuss overtones. Let's go back to the guitar string. If you pluck it unstopped, it will vibrate between the two points where that string is fixed. But there are other ways that it can vibrate between these two points. The string could vibrate so that it is essentially stationary at various points along it's length. In physics, these points are called nodes. Different patterns of vibration are called different modes of vibration and the number of nodes plus one in the pattern give the mode number. For example a string that vibrates but is stationary a midspan is vibrating in it's second mode. Hitting harmonics on instruments is done by isolating these modes of vibration. We'll talk more about modes of vibrations when we talk about the harmonic overtone series.
Now to music. What differentiates music from noise is distinct and recognizable pitches. This isn't to say that non-pitched instruments and music that is purely rhythmic isn't music, it just isn't from a very scientific perspective. What makes a pitch recognizable and different from noise is a discernible wave pattern. We'll get more into it when we discuss the harmonic overtone series but the main difference between music and noise is that noise is composed of a disorganized combination of waves that don't produce any distinguishable tone. Music has a distinguishable frequency.
For more info see:
http://www.lukestark.com/blog/2009/01/04/sharing-music-theory-noise-music-and-patterns/
http://en.wikipedia.org/wiki/Wave
http://en.wikipedia.org/wiki/Sound
Just one note..Most percussion instruments that I know do have a low pitch to them..So when you say rhythmic Im assuming you mean nothing that creates a pitch note like sticks,guiro and such?Congas deyembe ,drum toms and all of the sort do emit a very low pith note which is often tuned to fit the space were used in oder to avoid room overtones and more commonly used to also give music a tighter feel....Even cymbals bell have a pith to them wich I often have found with feedback on the guitar..Then on the other hand what about that loud hurting feedback when your to close to the speakers,that has a pitch(Not the good guitar pick up controllable feedback), would science consider that music?hmm confused here...
Percussion instruments typically divide into three categories:
Definite Pitch
Indefinite Pitch
Non-Pitched
Definite pitched percussion instruments are things like pianos and xylophones and timpanis. Indefinite pitched instruments like a lot of percussion instruments and most cymbals, don't have a definite pitch in that you'd have a really hard time picking out which one note the cymbal plays but do have a pitch range, generally low, middle, or high. Especially if you're playing big drums, you're going to hear a low sound, but you'll probably have a hard time pinpointing what note it is. A lot of this has to do with the overtone series and the fact that many of these instruments contain too many that are very scattered. In reality there's no way to make something non-pitched. If it makes sound it has to do it at some frequency and therefore some pitch, but these frequencies aren't often constant for percussion instruments and hence you hear a garbled mess of notes. You get the same thing on an instrument we just accept it as vibrato.
I don't know much about tuning drums, but a friend who plays told me they often tune the toms and bass to a minor triad or something like that. I don't know why.
Hope that helps. We'll discuss this sort of thing more when we get to the harmonic overtone series.
Definite Pitch
Indefinite Pitch
Non-Pitched
Definite pitched percussion instruments are things like pianos and xylophones and timpanis. Indefinite pitched instruments like a lot of percussion instruments and most cymbals, don't have a definite pitch in that you'd have a really hard time picking out which one note the cymbal plays but do have a pitch range, generally low, middle, or high. Especially if you're playing big drums, you're going to hear a low sound, but you'll probably have a hard time pinpointing what note it is. A lot of this has to do with the overtone series and the fact that many of these instruments contain too many that are very scattered. In reality there's no way to make something non-pitched. If it makes sound it has to do it at some frequency and therefore some pitch, but these frequencies aren't often constant for percussion instruments and hence you hear a garbled mess of notes. You get the same thing on an instrument we just accept it as vibrato.
I don't know much about tuning drums, but a friend who plays told me they often tune the toms and bass to a minor triad or something like that. I don't know why.
Hope that helps. We'll discuss this sort of thing more when we get to the harmonic overtone series.
I did forget to say tx for taking the time to do this..Thats the first thing I should have said...Sorry...
Ill wait for the overtone thread to see If I can put the picture together..I might be confusing overtones with what I hear as a pitch on the percussion instrument...I do hear a pitch but it might be the creation of overtones once the waves get organized..Not sure..Ill wait and read..Tx again
One thing you could mention for pitch when talking about vibration is reaction due to length ..For the guitar you could say 440 vibrations would give you a perfect A so 880 vibrations would give you and octave higher A....So that would represent and Open 5 string as your 440 vibrations and as you press on the 5th stg 12 frt you double the vibrations when your shorten the length...
Ill wait for the overtone thread to see If I can put the picture together..I might be confusing overtones with what I hear as a pitch on the percussion instrument...I do hear a pitch but it might be the creation of overtones once the waves get organized..Not sure..Ill wait and read..Tx again
One thing you could mention for pitch when talking about vibration is reaction due to length ..For the guitar you could say 440 vibrations would give you a perfect A so 880 vibrations would give you and octave higher A....So that would represent and Open 5 string as your 440 vibrations and as you press on the 5th stg 12 frt you double the vibrations when your shorten the length...
Marino brings up a good point that my use some more clarity.
Frequency is related to pitch. If the speed of sound is constant where you're playing (which it should be unless you're in some odd control room) then frequency and wavelength are related by the equation v=fλ which means that the wavelength (λ) is inversely proportional to the frequency, i.e. f = v/λ. Now getting a little harrier, frequency can be most easily related to pitch using the cent system, i.e. this equation:
n = 1200log2(a/b) where n is the interval between two pitches in cents (100 cents = 1 semitone) and a and b are the frequencies of those two pitches that are on either ends of the interval. Now for an octave, the ratio of the lower to higher frequencies is 2:1, so A4 (440 Hz) is an octave lower than A5 (880 Hz) and two octaves lower than A6 (1760 Hz). Using the cent system, an octave is equal to 1200 cents. If the ratio of the two frequencies is 2:1 then plugging that ratio in the the above equation for a/b proves the result
1200 = 1200log2(2/1). For the frequencies a and b we can show with the first equation on this post that a = v/λa and b = v/λb. Taking the ratio a/b = 2 then we can show that an octave means twice the frequency and correspondingly half the wavelength. This is why the twelfth fret is located at half the length of your string. If we wanted we could say that for a string on a guitar of length L, if you wanted to play n octaves above that pitch you'd need to stop the string at L/(2^n).
This will all become very important when we discuss the harmonic overtone series. Apologies to those who hate physics.
Frequency is related to pitch. If the speed of sound is constant where you're playing (which it should be unless you're in some odd control room) then frequency and wavelength are related by the equation v=fλ which means that the wavelength (λ) is inversely proportional to the frequency, i.e. f = v/λ. Now getting a little harrier, frequency can be most easily related to pitch using the cent system, i.e. this equation:
n = 1200log2(a/b) where n is the interval between two pitches in cents (100 cents = 1 semitone) and a and b are the frequencies of those two pitches that are on either ends of the interval. Now for an octave, the ratio of the lower to higher frequencies is 2:1, so A4 (440 Hz) is an octave lower than A5 (880 Hz) and two octaves lower than A6 (1760 Hz). Using the cent system, an octave is equal to 1200 cents. If the ratio of the two frequencies is 2:1 then plugging that ratio in the the above equation for a/b proves the result
1200 = 1200log2(2/1). For the frequencies a and b we can show with the first equation on this post that a = v/λa and b = v/λb. Taking the ratio a/b = 2 then we can show that an octave means twice the frequency and correspondingly half the wavelength. This is why the twelfth fret is located at half the length of your string. If we wanted we could say that for a string on a guitar of length L, if you wanted to play n octaves above that pitch you'd need to stop the string at L/(2^n).
This will all become very important when we discuss the harmonic overtone series. Apologies to those who hate physics.
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