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Sound waves in different octaves
Why do I hear beats through headphones only at low frequencies?The definition of “frequency” in different contextsSound Wave Propagation: Why HF are more specular while LF are more omniHow are complex sound waves combined?Frequency dependance of sound wave reflectionWhy is a single string's vibration very weak but on the other hand, a guitar's string can be very loud?Is it possible to estimate the speed of a passing vehicle using a musical ear and the doppler effect?Intensity of sound and pitch perceptionWhere do pure tones occur in nature, besides harmonics?Why can we distinguish different pitches in a chord but not different hues of light?
$begingroup$
How do the sound waves compare between different octaves? Why is it that you can play a low c and a c, and they are at different frequencies, but the same tone? An octave above a note is the fourth overtone, I'm assuming, so would the slopes of the waves align? You can still tune to these notes between octaves, and the beats can still be heard if out of tune. My AP physics teacher was unable to answer why.
waves acoustics frequency
edited 4 hours ago
Ben Crowell
53k6164310
asked 6 hours ago
Ava Miller Ava Miller
112
New contributor
Ava Miller is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
How do the sound waves compare between different octaves? Why is it that you can play a low c and a c, and they are at different frequencies, but the same tone? An octave above a note is the fourth overtone, I'm assuming, so would the slopes of the waves align? You can still tune to these notes between octaves, and the beats can still be heard if out of tune. My AP physics teacher was unable to answer why.
waves acoustics frequency
edited 4 hours ago
Ben Crowell
53k6164310
asked 6 hours ago
Ava Miller Ava Miller
112
New contributor
Ava Miller is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
The word tone refers to a sound or note, or even an out of tune note. The higher c is a different tone than the middle c. Octaves are double (or half) the frequency of any note. Middle c is 440Hz, its octave is 880Hz ( another c). Also 220Hz, see wikipedia.
$endgroup$
– PhysicsDave
5 hours ago
$begingroup$
I feel like this a question more about human perception rather than physics. The physics just says that (what we call) octaves are at different frequencies. The similarity, pleasantness, etc. of sounds when compared is purely based on our perception.
$endgroup$
– Aaron Stevens
5 hours ago
1
$begingroup$
@PhysicsDave Middle c is at 262 hertz (in current standard tuning where a' is att 440 hertz).
$endgroup$
– Pieter
4 hours ago
add a comment |
$begingroup$
How do the sound waves compare between different octaves? Why is it that you can play a low c and a c, and they are at different frequencies, but the same tone? An octave above a note is the fourth overtone, I'm assuming, so would the slopes of the waves align? You can still tune to these notes between octaves, and the beats can still be heard if out of tune. My AP physics teacher was unable to answer why.
waves acoustics frequency
edited 4 hours ago
Ben Crowell
53k6164310
asked 6 hours ago
Ava Miller Ava Miller
112
New contributor
Ava Miller is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
How do the sound waves compare between different octaves? Why is it that you can play a low c and a c, and they are at different frequencies, but the same tone? An octave above a note is the fourth overtone, I'm assuming, so would the slopes of the waves align? You can still tune to these notes between octaves, and the beats can still be heard if out of tune. My AP physics teacher was unable to answer why.
waves acoustics frequency
waves acoustics frequency
edited 4 hours ago
Ben Crowell
53k6164310
asked 6 hours ago
Ava Miller Ava Miller
112
New contributor
Ava Miller is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 4 hours ago
Ben Crowell
53k6164310
asked 6 hours ago
Ava Miller Ava Miller
112
New contributor
Ava Miller is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 4 hours ago
Ben Crowell
53k6164310
edited 4 hours ago
Ben Crowell
53k6164310
edited 4 hours ago
Ben Crowell
53k6164310
53k6164310
asked 6 hours ago
Ava Miller Ava Miller
112
New contributor
Ava Miller is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 hours ago
Ava Miller Ava Miller
112
asked 6 hours ago
Ava Miller Ava Miller
112
112
New contributor
Ava Miller is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Ava Miller is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Ava Miller is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
$begingroup$
The word tone refers to a sound or note, or even an out of tune note. The higher c is a different tone than the middle c. Octaves are double (or half) the frequency of any note. Middle c is 440Hz, its octave is 880Hz ( another c). Also 220Hz, see wikipedia.
$endgroup$
– PhysicsDave
5 hours ago
$begingroup$
I feel like this a question more about human perception rather than physics. The physics just says that (what we call) octaves are at different frequencies. The similarity, pleasantness, etc. of sounds when compared is purely based on our perception.
$endgroup$
– Aaron Stevens
5 hours ago
1
$begingroup$
@PhysicsDave Middle c is at 262 hertz (in current standard tuning where a' is att 440 hertz).
$endgroup$
– Pieter
4 hours ago
add a comment |
1
$begingroup$
The word tone refers to a sound or note, or even an out of tune note. The higher c is a different tone than the middle c. Octaves are double (or half) the frequency of any note. Middle c is 440Hz, its octave is 880Hz ( another c). Also 220Hz, see wikipedia.
$endgroup$
– PhysicsDave
5 hours ago
$begingroup$
I feel like this a question more about human perception rather than physics. The physics just says that (what we call) octaves are at different frequencies. The similarity, pleasantness, etc. of sounds when compared is purely based on our perception.
$endgroup$
– Aaron Stevens
5 hours ago
1
$begingroup$
@PhysicsDave Middle c is at 262 hertz (in current standard tuning where a' is att 440 hertz).
$endgroup$
– Pieter
4 hours ago
1
1
$begingroup$
The word tone refers to a sound or note, or even an out of tune note. The higher c is a different tone than the middle c. Octaves are double (or half) the frequency of any note. Middle c is 440Hz, its octave is 880Hz ( another c). Also 220Hz, see wikipedia.
$endgroup$
– PhysicsDave
5 hours ago
$begingroup$
The word tone refers to a sound or note, or even an out of tune note. The higher c is a different tone than the middle c. Octaves are double (or half) the frequency of any note. Middle c is 440Hz, its octave is 880Hz ( another c). Also 220Hz, see wikipedia.
$endgroup$
– PhysicsDave
5 hours ago
$begingroup$
I feel like this a question more about human perception rather than physics. The physics just says that (what we call) octaves are at different frequencies. The similarity, pleasantness, etc. of sounds when compared is purely based on our perception.
$endgroup$
– Aaron Stevens
5 hours ago
$begingroup$
I feel like this a question more about human perception rather than physics. The physics just says that (what we call) octaves are at different frequencies. The similarity, pleasantness, etc. of sounds when compared is purely based on our perception.
$endgroup$
– Aaron Stevens
5 hours ago
1
1
$begingroup$
@PhysicsDave Middle c is at 262 hertz (in current standard tuning where a' is att 440 hertz).
$endgroup$
– Pieter
4 hours ago
$begingroup$
@PhysicsDave Middle c is at 262 hertz (in current standard tuning where a' is att 440 hertz).
$endgroup$
– Pieter
4 hours ago
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
The phenomenon you're asking about is known as octave equivalence. It's a hard-wired thing in the human ear-brain system. (We know it's hard-wired because it's present without musical training and is true cross-culturally.) Notes that differ in frequency by a factor of 2 (or a power of 2) are perceptually similar, and may be mistaken for one another, even by trained musicians. So this is really a fact about the ear-brain system (i.e., psychology and physiology) rather than physics, although it does relate to a physical property.
Looking through the index entries on this topic in Diana Deutsch, The psychology of music, 3rd ed., 2013, I don't see anything about any physical, neurological, or evolutionary explanation of octave equivalence. That may mean that nobody has such an explanation, or just that it wasn't something that Deutsch wanted to get into in this anthology of articles. It seems likely that it has at least some physical basis, because periodic tones usually have their first two frequencies (fundamental and first harmonic) in the ratio of two to one.
An octave above a note is the fourth overtone, I'm assuming
No, it's the first overtone.
How do the sound waves compare between different octaves?
Pitch perception can be complicated in some cases, but essentially our sense of pitch is normally based on the period of the wave. So notes differing by an octave in pitch have waveforms that are related by the fact that their periods are in a 2 to 1 ratio.
You can still tune to these notes between octaves, and the beats can still be heard if out of tune.
The beats would be beats between the first harmonic of the lower note and the fundamental of the higher note.
answered 4 hours ago
Ben CrowellBen Crowell
53k6164310
$endgroup$
$begingroup$
If you think about it, the human ear contains thousands (if not millions) of tiny hairs which vibrate at different frequencies. The nervous system detects the vibration as "sound". But, as with guitar strings, a hair that is "tuned" to a given frequency will tend to vibrate at frequencies twice as high, or, to a lesser extent, half as high. To avoid befuddling the poor human, the nervous system somehow combines the various related harmonics into a single sensation, with high or low being a separate sensation.
$endgroup$
– Hot Licks
1 hour ago
$begingroup$
@HotLicks: Normally a resonator does not respond strongly to a driving force at twice its resonant frequency, so it's far from obvious that the mechanism you propose should occur.
$endgroup$
– Ben Crowell
1 hour ago
$begingroup$
You're assuming linearity.
$endgroup$
– Hot Licks
1 hour ago
add a comment |
$begingroup$
I basically agree with the answers of Ben Crowell and of Pieter. The fact that we hear the octave as a pleasant pure interval is hard-wired in the human hearing system. As Pieter explained, musical instruments produce tones with many overtones of different intensities, where usually the frequency assigned to the tone is the lowest, and the overtones are integer multiples of it.
The point I can add to these previous answers gives a hint, why the octave is a very special interval sounding most pure. The point is that if you produce a perfect octave on a musical instrument, the frequencies of all the overtones of the higher note will exactly line up with frequencies of the overtones of the lower note. This means that any beating in the resulting sound is reduced to a minimum.
The situation is already different for a perfect fifth. In this case only every second overtone of the higher note lines up with an overtone of the lower note.
The situation gets even worse for the other intervals. For example, for the minor third, only every fifth overtone lines up, and other overtones start to generate beatings. For dissonances, like the minor second, none of the overtones line up, and severe beatings arise from the overtones, resulting in a 'rough' perceived sound.
answered 1 hour ago
flaudemusflaudemus
1,853313
$endgroup$
add a comment |
$begingroup$
The human voice and most musical instruments produce tones with many overtones. The sound pressure is periodic with a period $T$, but does not vary like a sine wave at all. Instead, it can be described by a Fourier series. That is the sum of sines that are integer multiples of the fundamental frequency $f=1/T$.
So when a singer sings with a fundamental at 220 hertz (an a), that note includes overtones at 440 hertz (a'), 660 hertz (e"), 880 hertz (a") etcetera. This is why beats can be heard between two instruments that play an a and an a' slightly out of tune.
would the slopes of the waves align?
The ear does a kind of Fourier analysis of the input waveform, where different frequencies are mapped to different parts of the cochlea and to different nerves going to the brain. Our hearing is almost insensitive to the relative phase between the frequency components.
One can look at the frequency content of sounds with spectrogram apps on mobile phones or on https://musiclab.chromeexperiments.com/
edited 1 hour ago
flaudemus
1,853313
answered 5 hours ago
PieterPieter
9,03331536
$endgroup$
$begingroup$
This doesn't answer the question, which is about octave identification.
$endgroup$
– Ben Crowell
4 hours ago
$begingroup$
@BenCrowell The OP also wrote something about beats.
$endgroup$
– Pieter
4 hours ago
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The phenomenon you're asking about is known as octave equivalence. It's a hard-wired thing in the human ear-brain system. (We know it's hard-wired because it's present without musical training and is true cross-culturally.) Notes that differ in frequency by a factor of 2 (or a power of 2) are perceptually similar, and may be mistaken for one another, even by trained musicians. So this is really a fact about the ear-brain system (i.e., psychology and physiology) rather than physics, although it does relate to a physical property.
Looking through the index entries on this topic in Diana Deutsch, The psychology of music, 3rd ed., 2013, I don't see anything about any physical, neurological, or evolutionary explanation of octave equivalence. That may mean that nobody has such an explanation, or just that it wasn't something that Deutsch wanted to get into in this anthology of articles. It seems likely that it has at least some physical basis, because periodic tones usually have their first two frequencies (fundamental and first harmonic) in the ratio of two to one.
An octave above a note is the fourth overtone, I'm assuming
No, it's the first overtone.
How do the sound waves compare between different octaves?
Pitch perception can be complicated in some cases, but essentially our sense of pitch is normally based on the period of the wave. So notes differing by an octave in pitch have waveforms that are related by the fact that their periods are in a 2 to 1 ratio.
You can still tune to these notes between octaves, and the beats can still be heard if out of tune.
The beats would be beats between the first harmonic of the lower note and the fundamental of the higher note.
answered 4 hours ago
Ben CrowellBen Crowell
53k6164310
$endgroup$
$begingroup$
If you think about it, the human ear contains thousands (if not millions) of tiny hairs which vibrate at different frequencies. The nervous system detects the vibration as "sound". But, as with guitar strings, a hair that is "tuned" to a given frequency will tend to vibrate at frequencies twice as high, or, to a lesser extent, half as high. To avoid befuddling the poor human, the nervous system somehow combines the various related harmonics into a single sensation, with high or low being a separate sensation.
$endgroup$
– Hot Licks
1 hour ago
$begingroup$
@HotLicks: Normally a resonator does not respond strongly to a driving force at twice its resonant frequency, so it's far from obvious that the mechanism you propose should occur.
$endgroup$
– Ben Crowell
1 hour ago
$begingroup$
You're assuming linearity.
$endgroup$
– Hot Licks
1 hour ago
add a comment |
$begingroup$
The phenomenon you're asking about is known as octave equivalence. It's a hard-wired thing in the human ear-brain system. (We know it's hard-wired because it's present without musical training and is true cross-culturally.) Notes that differ in frequency by a factor of 2 (or a power of 2) are perceptually similar, and may be mistaken for one another, even by trained musicians. So this is really a fact about the ear-brain system (i.e., psychology and physiology) rather than physics, although it does relate to a physical property.
Looking through the index entries on this topic in Diana Deutsch, The psychology of music, 3rd ed., 2013, I don't see anything about any physical, neurological, or evolutionary explanation of octave equivalence. That may mean that nobody has such an explanation, or just that it wasn't something that Deutsch wanted to get into in this anthology of articles. It seems likely that it has at least some physical basis, because periodic tones usually have their first two frequencies (fundamental and first harmonic) in the ratio of two to one.
An octave above a note is the fourth overtone, I'm assuming
No, it's the first overtone.
How do the sound waves compare between different octaves?
Pitch perception can be complicated in some cases, but essentially our sense of pitch is normally based on the period of the wave. So notes differing by an octave in pitch have waveforms that are related by the fact that their periods are in a 2 to 1 ratio.
You can still tune to these notes between octaves, and the beats can still be heard if out of tune.
The beats would be beats between the first harmonic of the lower note and the fundamental of the higher note.
answered 4 hours ago
Ben CrowellBen Crowell
53k6164310
$endgroup$
$begingroup$
If you think about it, the human ear contains thousands (if not millions) of tiny hairs which vibrate at different frequencies. The nervous system detects the vibration as "sound". But, as with guitar strings, a hair that is "tuned" to a given frequency will tend to vibrate at frequencies twice as high, or, to a lesser extent, half as high. To avoid befuddling the poor human, the nervous system somehow combines the various related harmonics into a single sensation, with high or low being a separate sensation.
$endgroup$
– Hot Licks
1 hour ago
$begingroup$
@HotLicks: Normally a resonator does not respond strongly to a driving force at twice its resonant frequency, so it's far from obvious that the mechanism you propose should occur.
$endgroup$
– Ben Crowell
1 hour ago
$begingroup$
You're assuming linearity.
$endgroup$
– Hot Licks
1 hour ago
add a comment |
$begingroup$
The phenomenon you're asking about is known as octave equivalence. It's a hard-wired thing in the human ear-brain system. (We know it's hard-wired because it's present without musical training and is true cross-culturally.) Notes that differ in frequency by a factor of 2 (or a power of 2) are perceptually similar, and may be mistaken for one another, even by trained musicians. So this is really a fact about the ear-brain system (i.e., psychology and physiology) rather than physics, although it does relate to a physical property.
Looking through the index entries on this topic in Diana Deutsch, The psychology of music, 3rd ed., 2013, I don't see anything about any physical, neurological, or evolutionary explanation of octave equivalence. That may mean that nobody has such an explanation, or just that it wasn't something that Deutsch wanted to get into in this anthology of articles. It seems likely that it has at least some physical basis, because periodic tones usually have their first two frequencies (fundamental and first harmonic) in the ratio of two to one.
An octave above a note is the fourth overtone, I'm assuming
No, it's the first overtone.
How do the sound waves compare between different octaves?
Pitch perception can be complicated in some cases, but essentially our sense of pitch is normally based on the period of the wave. So notes differing by an octave in pitch have waveforms that are related by the fact that their periods are in a 2 to 1 ratio.
You can still tune to these notes between octaves, and the beats can still be heard if out of tune.
The beats would be beats between the first harmonic of the lower note and the fundamental of the higher note.
answered 4 hours ago
Ben CrowellBen Crowell
53k6164310
$endgroup$
The phenomenon you're asking about is known as octave equivalence. It's a hard-wired thing in the human ear-brain system. (We know it's hard-wired because it's present without musical training and is true cross-culturally.) Notes that differ in frequency by a factor of 2 (or a power of 2) are perceptually similar, and may be mistaken for one another, even by trained musicians. So this is really a fact about the ear-brain system (i.e., psychology and physiology) rather than physics, although it does relate to a physical property.
Looking through the index entries on this topic in Diana Deutsch, The psychology of music, 3rd ed., 2013, I don't see anything about any physical, neurological, or evolutionary explanation of octave equivalence. That may mean that nobody has such an explanation, or just that it wasn't something that Deutsch wanted to get into in this anthology of articles. It seems likely that it has at least some physical basis, because periodic tones usually have their first two frequencies (fundamental and first harmonic) in the ratio of two to one.
An octave above a note is the fourth overtone, I'm assuming
No, it's the first overtone.
How do the sound waves compare between different octaves?
Pitch perception can be complicated in some cases, but essentially our sense of pitch is normally based on the period of the wave. So notes differing by an octave in pitch have waveforms that are related by the fact that their periods are in a 2 to 1 ratio.
You can still tune to these notes between octaves, and the beats can still be heard if out of tune.
The beats would be beats between the first harmonic of the lower note and the fundamental of the higher note.
answered 4 hours ago
Ben CrowellBen Crowell
53k6164310
edited 4 hours ago
answered 4 hours ago
Ben CrowellBen Crowell
53k6164310
answered 4 hours ago
Ben CrowellBen Crowell
53k6164310
answered 4 hours ago
Ben CrowellBen Crowell
53k6164310
53k6164310
$begingroup$
If you think about it, the human ear contains thousands (if not millions) of tiny hairs which vibrate at different frequencies. The nervous system detects the vibration as "sound". But, as with guitar strings, a hair that is "tuned" to a given frequency will tend to vibrate at frequencies twice as high, or, to a lesser extent, half as high. To avoid befuddling the poor human, the nervous system somehow combines the various related harmonics into a single sensation, with high or low being a separate sensation.
$endgroup$
– Hot Licks
1 hour ago
$begingroup$
@HotLicks: Normally a resonator does not respond strongly to a driving force at twice its resonant frequency, so it's far from obvious that the mechanism you propose should occur.
$endgroup$
– Ben Crowell
1 hour ago
$begingroup$
You're assuming linearity.
$endgroup$
– Hot Licks
1 hour ago
add a comment |
$begingroup$
If you think about it, the human ear contains thousands (if not millions) of tiny hairs which vibrate at different frequencies. The nervous system detects the vibration as "sound". But, as with guitar strings, a hair that is "tuned" to a given frequency will tend to vibrate at frequencies twice as high, or, to a lesser extent, half as high. To avoid befuddling the poor human, the nervous system somehow combines the various related harmonics into a single sensation, with high or low being a separate sensation.
$endgroup$
– Hot Licks
1 hour ago
$begingroup$
@HotLicks: Normally a resonator does not respond strongly to a driving force at twice its resonant frequency, so it's far from obvious that the mechanism you propose should occur.
$endgroup$
– Ben Crowell
1 hour ago
$begingroup$
You're assuming linearity.
$endgroup$
– Hot Licks
1 hour ago
$begingroup$
If you think about it, the human ear contains thousands (if not millions) of tiny hairs which vibrate at different frequencies. The nervous system detects the vibration as "sound". But, as with guitar strings, a hair that is "tuned" to a given frequency will tend to vibrate at frequencies twice as high, or, to a lesser extent, half as high. To avoid befuddling the poor human, the nervous system somehow combines the various related harmonics into a single sensation, with high or low being a separate sensation.
$endgroup$
– Hot Licks
1 hour ago
$begingroup$
If you think about it, the human ear contains thousands (if not millions) of tiny hairs which vibrate at different frequencies. The nervous system detects the vibration as "sound". But, as with guitar strings, a hair that is "tuned" to a given frequency will tend to vibrate at frequencies twice as high, or, to a lesser extent, half as high. To avoid befuddling the poor human, the nervous system somehow combines the various related harmonics into a single sensation, with high or low being a separate sensation.
$endgroup$
– Hot Licks
1 hour ago
$begingroup$
@HotLicks: Normally a resonator does not respond strongly to a driving force at twice its resonant frequency, so it's far from obvious that the mechanism you propose should occur.
$endgroup$
– Ben Crowell
1 hour ago
$begingroup$
@HotLicks: Normally a resonator does not respond strongly to a driving force at twice its resonant frequency, so it's far from obvious that the mechanism you propose should occur.
$endgroup$
– Ben Crowell
1 hour ago
$begingroup$
You're assuming linearity.
$endgroup$
– Hot Licks
1 hour ago
$begingroup$
You're assuming linearity.
$endgroup$
– Hot Licks
1 hour ago
add a comment |
$begingroup$
I basically agree with the answers of Ben Crowell and of Pieter. The fact that we hear the octave as a pleasant pure interval is hard-wired in the human hearing system. As Pieter explained, musical instruments produce tones with many overtones of different intensities, where usually the frequency assigned to the tone is the lowest, and the overtones are integer multiples of it.
The point I can add to these previous answers gives a hint, why the octave is a very special interval sounding most pure. The point is that if you produce a perfect octave on a musical instrument, the frequencies of all the overtones of the higher note will exactly line up with frequencies of the overtones of the lower note. This means that any beating in the resulting sound is reduced to a minimum.
The situation is already different for a perfect fifth. In this case only every second overtone of the higher note lines up with an overtone of the lower note.
The situation gets even worse for the other intervals. For example, for the minor third, only every fifth overtone lines up, and other overtones start to generate beatings. For dissonances, like the minor second, none of the overtones line up, and severe beatings arise from the overtones, resulting in a 'rough' perceived sound.
answered 1 hour ago
flaudemusflaudemus
1,853313
$endgroup$
add a comment |
$begingroup$
I basically agree with the answers of Ben Crowell and of Pieter. The fact that we hear the octave as a pleasant pure interval is hard-wired in the human hearing system. As Pieter explained, musical instruments produce tones with many overtones of different intensities, where usually the frequency assigned to the tone is the lowest, and the overtones are integer multiples of it.
The point I can add to these previous answers gives a hint, why the octave is a very special interval sounding most pure. The point is that if you produce a perfect octave on a musical instrument, the frequencies of all the overtones of the higher note will exactly line up with frequencies of the overtones of the lower note. This means that any beating in the resulting sound is reduced to a minimum.
The situation is already different for a perfect fifth. In this case only every second overtone of the higher note lines up with an overtone of the lower note.
The situation gets even worse for the other intervals. For example, for the minor third, only every fifth overtone lines up, and other overtones start to generate beatings. For dissonances, like the minor second, none of the overtones line up, and severe beatings arise from the overtones, resulting in a 'rough' perceived sound.
answered 1 hour ago
flaudemusflaudemus
1,853313
$endgroup$
add a comment |
$begingroup$
I basically agree with the answers of Ben Crowell and of Pieter. The fact that we hear the octave as a pleasant pure interval is hard-wired in the human hearing system. As Pieter explained, musical instruments produce tones with many overtones of different intensities, where usually the frequency assigned to the tone is the lowest, and the overtones are integer multiples of it.
The point I can add to these previous answers gives a hint, why the octave is a very special interval sounding most pure. The point is that if you produce a perfect octave on a musical instrument, the frequencies of all the overtones of the higher note will exactly line up with frequencies of the overtones of the lower note. This means that any beating in the resulting sound is reduced to a minimum.
The situation is already different for a perfect fifth. In this case only every second overtone of the higher note lines up with an overtone of the lower note.
The situation gets even worse for the other intervals. For example, for the minor third, only every fifth overtone lines up, and other overtones start to generate beatings. For dissonances, like the minor second, none of the overtones line up, and severe beatings arise from the overtones, resulting in a 'rough' perceived sound.
answered 1 hour ago
flaudemusflaudemus
1,853313
$endgroup$
I basically agree with the answers of Ben Crowell and of Pieter. The fact that we hear the octave as a pleasant pure interval is hard-wired in the human hearing system. As Pieter explained, musical instruments produce tones with many overtones of different intensities, where usually the frequency assigned to the tone is the lowest, and the overtones are integer multiples of it.
The point I can add to these previous answers gives a hint, why the octave is a very special interval sounding most pure. The point is that if you produce a perfect octave on a musical instrument, the frequencies of all the overtones of the higher note will exactly line up with frequencies of the overtones of the lower note. This means that any beating in the resulting sound is reduced to a minimum.
The situation is already different for a perfect fifth. In this case only every second overtone of the higher note lines up with an overtone of the lower note.
The situation gets even worse for the other intervals. For example, for the minor third, only every fifth overtone lines up, and other overtones start to generate beatings. For dissonances, like the minor second, none of the overtones line up, and severe beatings arise from the overtones, resulting in a 'rough' perceived sound.
answered 1 hour ago
flaudemusflaudemus
1,853313
edited 1 hour ago
answered 1 hour ago
flaudemusflaudemus
1,853313
answered 1 hour ago
flaudemusflaudemus
1,853313
answered 1 hour ago
flaudemusflaudemus
1,853313
1,853313
add a comment |
add a comment |
$begingroup$
The human voice and most musical instruments produce tones with many overtones. The sound pressure is periodic with a period $T$, but does not vary like a sine wave at all. Instead, it can be described by a Fourier series. That is the sum of sines that are integer multiples of the fundamental frequency $f=1/T$.
So when a singer sings with a fundamental at 220 hertz (an a), that note includes overtones at 440 hertz (a'), 660 hertz (e"), 880 hertz (a") etcetera. This is why beats can be heard between two instruments that play an a and an a' slightly out of tune.
would the slopes of the waves align?
The ear does a kind of Fourier analysis of the input waveform, where different frequencies are mapped to different parts of the cochlea and to different nerves going to the brain. Our hearing is almost insensitive to the relative phase between the frequency components.
One can look at the frequency content of sounds with spectrogram apps on mobile phones or on https://musiclab.chromeexperiments.com/
edited 1 hour ago
flaudemus
1,853313
answered 5 hours ago
PieterPieter
9,03331536
$endgroup$
$begingroup$
This doesn't answer the question, which is about octave identification.
$endgroup$
– Ben Crowell
4 hours ago
$begingroup$
@BenCrowell The OP also wrote something about beats.
$endgroup$
– Pieter
4 hours ago
add a comment |
$begingroup$
The human voice and most musical instruments produce tones with many overtones. The sound pressure is periodic with a period $T$, but does not vary like a sine wave at all. Instead, it can be described by a Fourier series. That is the sum of sines that are integer multiples of the fundamental frequency $f=1/T$.
So when a singer sings with a fundamental at 220 hertz (an a), that note includes overtones at 440 hertz (a'), 660 hertz (e"), 880 hertz (a") etcetera. This is why beats can be heard between two instruments that play an a and an a' slightly out of tune.
would the slopes of the waves align?
The ear does a kind of Fourier analysis of the input waveform, where different frequencies are mapped to different parts of the cochlea and to different nerves going to the brain. Our hearing is almost insensitive to the relative phase between the frequency components.
One can look at the frequency content of sounds with spectrogram apps on mobile phones or on https://musiclab.chromeexperiments.com/
edited 1 hour ago
flaudemus
1,853313
answered 5 hours ago
PieterPieter
9,03331536
$endgroup$
$begingroup$
This doesn't answer the question, which is about octave identification.
$endgroup$
– Ben Crowell
4 hours ago
$begingroup$
@BenCrowell The OP also wrote something about beats.
$endgroup$
– Pieter
4 hours ago
add a comment |
$begingroup$
The human voice and most musical instruments produce tones with many overtones. The sound pressure is periodic with a period $T$, but does not vary like a sine wave at all. Instead, it can be described by a Fourier series. That is the sum of sines that are integer multiples of the fundamental frequency $f=1/T$.
So when a singer sings with a fundamental at 220 hertz (an a), that note includes overtones at 440 hertz (a'), 660 hertz (e"), 880 hertz (a") etcetera. This is why beats can be heard between two instruments that play an a and an a' slightly out of tune.
would the slopes of the waves align?
The ear does a kind of Fourier analysis of the input waveform, where different frequencies are mapped to different parts of the cochlea and to different nerves going to the brain. Our hearing is almost insensitive to the relative phase between the frequency components.
One can look at the frequency content of sounds with spectrogram apps on mobile phones or on https://musiclab.chromeexperiments.com/
edited 1 hour ago
flaudemus
1,853313
answered 5 hours ago
PieterPieter
9,03331536
$endgroup$
The human voice and most musical instruments produce tones with many overtones. The sound pressure is periodic with a period $T$, but does not vary like a sine wave at all. Instead, it can be described by a Fourier series. That is the sum of sines that are integer multiples of the fundamental frequency $f=1/T$.
So when a singer sings with a fundamental at 220 hertz (an a), that note includes overtones at 440 hertz (a'), 660 hertz (e"), 880 hertz (a") etcetera. This is why beats can be heard between two instruments that play an a and an a' slightly out of tune.
would the slopes of the waves align?
The ear does a kind of Fourier analysis of the input waveform, where different frequencies are mapped to different parts of the cochlea and to different nerves going to the brain. Our hearing is almost insensitive to the relative phase between the frequency components.
One can look at the frequency content of sounds with spectrogram apps on mobile phones or on https://musiclab.chromeexperiments.com/
edited 1 hour ago
flaudemus
1,853313
answered 5 hours ago
PieterPieter
9,03331536
edited 1 hour ago
flaudemus
1,853313
edited 1 hour ago
flaudemus
1,853313
edited 1 hour ago
flaudemus
1,853313
1,853313
answered 5 hours ago
PieterPieter
9,03331536
answered 5 hours ago
PieterPieter
9,03331536
answered 5 hours ago
PieterPieter
9,03331536
9,03331536
$begingroup$
This doesn't answer the question, which is about octave identification.
$endgroup$
– Ben Crowell
4 hours ago
$begingroup$
@BenCrowell The OP also wrote something about beats.
$endgroup$
– Pieter
4 hours ago
add a comment |
$begingroup$
This doesn't answer the question, which is about octave identification.
$endgroup$
– Ben Crowell
4 hours ago
$begingroup$
@BenCrowell The OP also wrote something about beats.
$endgroup$
– Pieter
4 hours ago
$begingroup$
This doesn't answer the question, which is about octave identification.
$endgroup$
– Ben Crowell
4 hours ago
$begingroup$
This doesn't answer the question, which is about octave identification.
$endgroup$
– Ben Crowell
4 hours ago
$begingroup$
@BenCrowell The OP also wrote something about beats.
$endgroup$
– Pieter
4 hours ago
$begingroup$
@BenCrowell The OP also wrote something about beats.
$endgroup$
– Pieter
4 hours ago
add a comment |
Ava Miller is a new contributor. Be nice, and check out our Code of Conduct.
Ava Miller is a new contributor. Be nice, and check out our Code of Conduct.
Ava Miller is a new contributor. Be nice, and check out our Code of Conduct.
Ava Miller is a new contributor. Be nice, and check out our Code of Conduct.
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$begingroup$
The word tone refers to a sound or note, or even an out of tune note. The higher c is a different tone than the middle c. Octaves are double (or half) the frequency of any note. Middle c is 440Hz, its octave is 880Hz ( another c). Also 220Hz, see wikipedia.
$endgroup$
– PhysicsDave
5 hours ago
$begingroup$
I feel like this a question more about human perception rather than physics. The physics just says that (what we call) octaves are at different frequencies. The similarity, pleasantness, etc. of sounds when compared is purely based on our perception.
$endgroup$
– Aaron Stevens
5 hours ago
1
$begingroup$
@PhysicsDave Middle c is at 262 hertz (in current standard tuning where a' is att 440 hertz).
$endgroup$
– Pieter
4 hours ago