Sound waves in different octaves The Next CEO of Stack OverflowWhy 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?
Why did CATV standarize in 75 ohms and everyone else in 50?
Are there any unintended negative consequences to allowing PCs to gain multiple levels at once in a short milestone-XP game?
Beveled cylinder cutout
What is the difference between 翼 and 翅膀?
I believe this to be a fraud - hired, then asked to cash check and send cash as Bitcoin
Would a completely good Muggle be able to use a wand?
Why is the US ranked as #45 in Press Freedom ratings, despite its extremely permissive free speech laws?
Why does standard notation not preserve intervals (visually)
Would this house-rule that treats advantage as a +1 to the roll instead (and disadvantage as -1) and allows them to stack be balanced?
In excess I'm lethal
Unreliable Magic - Is it worth it?
Is this "being" usage is essential?
Ubuntu shell scripting
Is it professional to write unrelated content in an almost-empty email?
Can we say or write : "No, it'sn't"?
Is wanting to ask what to write an indication that you need to change your story?
What did we know about the Kessel run before the prologues?
Rotate a column
Do I need to write [sic] when a number is less than 10 but isn't written out?
WOW air has ceased operation, can I get my tickets refunded?
Why, when going from special to general relativity, do we just replace partial derivatives with covariant derivatives?
How to place nodes around a circle from some initial angle?
How to get from Geneva Airport to Metabief?
How to get the end in algorithm2e
Sound waves in different octaves
The Next CEO of Stack OverflowWhy 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
$endgroup$
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
$endgroup$
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
Mar 20 at 17:44
1
$begingroup$
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
Mar 20 at 18:06
5
$begingroup$
@PhysicsDave Middle c is at 262 hertz (in current standard tuning where a' is att 440 hertz).
$endgroup$
– Pieter
Mar 20 at 19:11
1
$begingroup$
Heavily related is music.stackexchange.com/q/44783/45266, which I believe answers the question pretty well.
$endgroup$
– user45266
Mar 21 at 1:19
1
$begingroup$
And certainly music.stackexchange.com/q/43335/45266, specifically the answers. Check these out, guys!
$endgroup$
– user45266
Mar 21 at 1:25
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
$endgroup$
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 Mar 20 at 19:21
Ben Crowell
53.5k6165313
53.5k6165313
asked Mar 20 at 17:34
Ava Miller Ava Miller
312
312
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
Mar 20 at 17:44
1
$begingroup$
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
Mar 20 at 18:06
5
$begingroup$
@PhysicsDave Middle c is at 262 hertz (in current standard tuning where a' is att 440 hertz).
$endgroup$
– Pieter
Mar 20 at 19:11
1
$begingroup$
Heavily related is music.stackexchange.com/q/44783/45266, which I believe answers the question pretty well.
$endgroup$
– user45266
Mar 21 at 1:19
1
$begingroup$
And certainly music.stackexchange.com/q/43335/45266, specifically the answers. Check these out, guys!
$endgroup$
– user45266
Mar 21 at 1:25
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
Mar 20 at 17:44
1
$begingroup$
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
Mar 20 at 18:06
5
$begingroup$
@PhysicsDave Middle c is at 262 hertz (in current standard tuning where a' is att 440 hertz).
$endgroup$
– Pieter
Mar 20 at 19:11
1
$begingroup$
Heavily related is music.stackexchange.com/q/44783/45266, which I believe answers the question pretty well.
$endgroup$
– user45266
Mar 21 at 1:19
1
$begingroup$
And certainly music.stackexchange.com/q/43335/45266, specifically the answers. Check these out, guys!
$endgroup$
– user45266
Mar 21 at 1:25
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
Mar 20 at 17:44
$begingroup$
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
Mar 20 at 17:44
1
1
$begingroup$
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
Mar 20 at 18:06
$begingroup$
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
Mar 20 at 18:06
5
5
$begingroup$
@PhysicsDave Middle c is at 262 hertz (in current standard tuning where a' is att 440 hertz).
$endgroup$
– Pieter
Mar 20 at 19:11
$begingroup$
@PhysicsDave Middle c is at 262 hertz (in current standard tuning where a' is att 440 hertz).
$endgroup$
– Pieter
Mar 20 at 19:11
1
1
$begingroup$
Heavily related is music.stackexchange.com/q/44783/45266, which I believe answers the question pretty well.
$endgroup$
– user45266
Mar 21 at 1:19
$begingroup$
Heavily related is music.stackexchange.com/q/44783/45266, which I believe answers the question pretty well.
$endgroup$
– user45266
Mar 21 at 1:19
1
1
$begingroup$
And certainly music.stackexchange.com/q/43335/45266, specifically the answers. Check these out, guys!
$endgroup$
– user45266
Mar 21 at 1:25
$begingroup$
And certainly music.stackexchange.com/q/43335/45266, specifically the answers. Check these out, guys!
$endgroup$
– user45266
Mar 21 at 1:25
add a comment |
4 Answers
4
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.
$endgroup$
$begingroup$
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
Mar 20 at 22:23
$begingroup$
@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
Mar 20 at 22:30
$begingroup$
You're assuming linearity.
$endgroup$
– Hot Licks
Mar 20 at 22:32
$begingroup$
@HotLicks: it can hardly boil down to a "single sensation". We can also perceive the spectral content of a sound. Just like our vision system, our hearing has some very sophisticated signal processing capabilities.
$endgroup$
– whatsisname
Mar 21 at 1:53
4
$begingroup$
@HotLicks- it is a common misconception that the 'hairs' vibrate at different frequencies -- they are all identical (and far too small for audible frequencies). They are positioned along the sides of a long (coiled) tube and detect frequencies as the locations where the reflection from the end of the tube matches the incoming wave.
$endgroup$
– amI
Mar 21 at 5:03
|
show 2 more comments
$begingroup$
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 (fundamental frequency $f_0$), and the overtones are integer multiples $nf_0$ 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.
However, one should not believe that this spectral line-up is a definitive explanation for the particularly pure perception of the octave by most people. Let me give the following reasons (citing from the answer of topo morto on Music SE) to a similar question:
- a higher note with a fundamental frequency that is the same as that of one of the lower note's higher (>2) harmonics will also have a subset of the lower note's harmonics
- a sound with only the first, third, and fifth harmonics (as produced, e.g., by some woodwind instruments) won't share any component pitches with the same timbre sounded an octave up
$endgroup$
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/
$endgroup$
$begingroup$
This doesn't answer the question, which is about octave identification.
$endgroup$
– Ben Crowell
Mar 20 at 18:49
add a comment |
$begingroup$
Your ear recognizes different frequencies because hairs in the cochlea vibrate at certain frequencies, and they send a message to your brain telling you that you're hearing a particular frequency. Let's take the pitch A=440hz. That sets off the A440 receptor most strongly, but also sets off the A880 receptor less strongly. A880 is an octave higher than A440, and obviously the A880 receptor is expecting to be "pushed" 880 times per second, but A440 "pushes" the A880 receptor every other time it is expecting, so it sends a weaker signal to the brain, and our brain picks this multiples of frequencies up as an octave.
There's a vihart video on this topic that I think probably answers the question more clearly than I did, but this is the cliffnotes version.
$endgroup$
$begingroup$
Sorry, but Vi Hart is wrong there about how the cochlea works.
$endgroup$
– Pieter
Mar 21 at 8:44
add a comment |
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "151"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphysics.stackexchange.com%2fquestions%2f467666%2fsound-waves-in-different-octaves%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
4 Answers
4
active
oldest
votes
4 Answers
4
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.
$endgroup$
$begingroup$
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
Mar 20 at 22:23
$begingroup$
@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
Mar 20 at 22:30
$begingroup$
You're assuming linearity.
$endgroup$
– Hot Licks
Mar 20 at 22:32
$begingroup$
@HotLicks: it can hardly boil down to a "single sensation". We can also perceive the spectral content of a sound. Just like our vision system, our hearing has some very sophisticated signal processing capabilities.
$endgroup$
– whatsisname
Mar 21 at 1:53
4
$begingroup$
@HotLicks- it is a common misconception that the 'hairs' vibrate at different frequencies -- they are all identical (and far too small for audible frequencies). They are positioned along the sides of a long (coiled) tube and detect frequencies as the locations where the reflection from the end of the tube matches the incoming wave.
$endgroup$
– amI
Mar 21 at 5:03
|
show 2 more comments
$begingroup$
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.
$endgroup$
$begingroup$
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
Mar 20 at 22:23
$begingroup$
@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
Mar 20 at 22:30
$begingroup$
You're assuming linearity.
$endgroup$
– Hot Licks
Mar 20 at 22:32
$begingroup$
@HotLicks: it can hardly boil down to a "single sensation". We can also perceive the spectral content of a sound. Just like our vision system, our hearing has some very sophisticated signal processing capabilities.
$endgroup$
– whatsisname
Mar 21 at 1:53
4
$begingroup$
@HotLicks- it is a common misconception that the 'hairs' vibrate at different frequencies -- they are all identical (and far too small for audible frequencies). They are positioned along the sides of a long (coiled) tube and detect frequencies as the locations where the reflection from the end of the tube matches the incoming wave.
$endgroup$
– amI
Mar 21 at 5:03
|
show 2 more comments
$begingroup$
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.
$endgroup$
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.
edited Mar 20 at 19:23
answered Mar 20 at 18:51
Ben CrowellBen Crowell
53.5k6165313
53.5k6165313
$begingroup$
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
Mar 20 at 22:23
$begingroup$
@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
Mar 20 at 22:30
$begingroup$
You're assuming linearity.
$endgroup$
– Hot Licks
Mar 20 at 22:32
$begingroup$
@HotLicks: it can hardly boil down to a "single sensation". We can also perceive the spectral content of a sound. Just like our vision system, our hearing has some very sophisticated signal processing capabilities.
$endgroup$
– whatsisname
Mar 21 at 1:53
4
$begingroup$
@HotLicks- it is a common misconception that the 'hairs' vibrate at different frequencies -- they are all identical (and far too small for audible frequencies). They are positioned along the sides of a long (coiled) tube and detect frequencies as the locations where the reflection from the end of the tube matches the incoming wave.
$endgroup$
– amI
Mar 21 at 5:03
|
show 2 more comments
$begingroup$
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
Mar 20 at 22:23
$begingroup$
@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
Mar 20 at 22:30
$begingroup$
You're assuming linearity.
$endgroup$
– Hot Licks
Mar 20 at 22:32
$begingroup$
@HotLicks: it can hardly boil down to a "single sensation". We can also perceive the spectral content of a sound. Just like our vision system, our hearing has some very sophisticated signal processing capabilities.
$endgroup$
– whatsisname
Mar 21 at 1:53
4
$begingroup$
@HotLicks- it is a common misconception that the 'hairs' vibrate at different frequencies -- they are all identical (and far too small for audible frequencies). They are positioned along the sides of a long (coiled) tube and detect frequencies as the locations where the reflection from the end of the tube matches the incoming wave.
$endgroup$
– amI
Mar 21 at 5:03
$begingroup$
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
Mar 20 at 22:23
$begingroup$
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
Mar 20 at 22:23
$begingroup$
@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
Mar 20 at 22:30
$begingroup$
@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
Mar 20 at 22:30
$begingroup$
You're assuming linearity.
$endgroup$
– Hot Licks
Mar 20 at 22:32
$begingroup$
You're assuming linearity.
$endgroup$
– Hot Licks
Mar 20 at 22:32
$begingroup$
@HotLicks: it can hardly boil down to a "single sensation". We can also perceive the spectral content of a sound. Just like our vision system, our hearing has some very sophisticated signal processing capabilities.
$endgroup$
– whatsisname
Mar 21 at 1:53
$begingroup$
@HotLicks: it can hardly boil down to a "single sensation". We can also perceive the spectral content of a sound. Just like our vision system, our hearing has some very sophisticated signal processing capabilities.
$endgroup$
– whatsisname
Mar 21 at 1:53
4
4
$begingroup$
@HotLicks- it is a common misconception that the 'hairs' vibrate at different frequencies -- they are all identical (and far too small for audible frequencies). They are positioned along the sides of a long (coiled) tube and detect frequencies as the locations where the reflection from the end of the tube matches the incoming wave.
$endgroup$
– amI
Mar 21 at 5:03
$begingroup$
@HotLicks- it is a common misconception that the 'hairs' vibrate at different frequencies -- they are all identical (and far too small for audible frequencies). They are positioned along the sides of a long (coiled) tube and detect frequencies as the locations where the reflection from the end of the tube matches the incoming wave.
$endgroup$
– amI
Mar 21 at 5:03
|
show 2 more comments
$begingroup$
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 (fundamental frequency $f_0$), and the overtones are integer multiples $nf_0$ 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.
However, one should not believe that this spectral line-up is a definitive explanation for the particularly pure perception of the octave by most people. Let me give the following reasons (citing from the answer of topo morto on Music SE) to a similar question:
- a higher note with a fundamental frequency that is the same as that of one of the lower note's higher (>2) harmonics will also have a subset of the lower note's harmonics
- a sound with only the first, third, and fifth harmonics (as produced, e.g., by some woodwind instruments) won't share any component pitches with the same timbre sounded an octave up
$endgroup$
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 (fundamental frequency $f_0$), and the overtones are integer multiples $nf_0$ 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.
However, one should not believe that this spectral line-up is a definitive explanation for the particularly pure perception of the octave by most people. Let me give the following reasons (citing from the answer of topo morto on Music SE) to a similar question:
- a higher note with a fundamental frequency that is the same as that of one of the lower note's higher (>2) harmonics will also have a subset of the lower note's harmonics
- a sound with only the first, third, and fifth harmonics (as produced, e.g., by some woodwind instruments) won't share any component pitches with the same timbre sounded an octave up
$endgroup$
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 (fundamental frequency $f_0$), and the overtones are integer multiples $nf_0$ 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.
However, one should not believe that this spectral line-up is a definitive explanation for the particularly pure perception of the octave by most people. Let me give the following reasons (citing from the answer of topo morto on Music SE) to a similar question:
- a higher note with a fundamental frequency that is the same as that of one of the lower note's higher (>2) harmonics will also have a subset of the lower note's harmonics
- a sound with only the first, third, and fifth harmonics (as produced, e.g., by some woodwind instruments) won't share any component pitches with the same timbre sounded an octave up
$endgroup$
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 (fundamental frequency $f_0$), and the overtones are integer multiples $nf_0$ 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.
However, one should not believe that this spectral line-up is a definitive explanation for the particularly pure perception of the octave by most people. Let me give the following reasons (citing from the answer of topo morto on Music SE) to a similar question:
- a higher note with a fundamental frequency that is the same as that of one of the lower note's higher (>2) harmonics will also have a subset of the lower note's harmonics
- a sound with only the first, third, and fifth harmonics (as produced, e.g., by some woodwind instruments) won't share any component pitches with the same timbre sounded an octave up
edited Mar 21 at 9:01
answered Mar 20 at 22:09
flaudemusflaudemus
1,983313
1,983313
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/
$endgroup$
$begingroup$
This doesn't answer the question, which is about octave identification.
$endgroup$
– Ben Crowell
Mar 20 at 18:49
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/
$endgroup$
$begingroup$
This doesn't answer the question, which is about octave identification.
$endgroup$
– Ben Crowell
Mar 20 at 18:49
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/
$endgroup$
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 Mar 20 at 22:24
flaudemus
1,983313
1,983313
answered Mar 20 at 18:38
PieterPieter
9,24731536
9,24731536
$begingroup$
This doesn't answer the question, which is about octave identification.
$endgroup$
– Ben Crowell
Mar 20 at 18:49
add a comment |
$begingroup$
This doesn't answer the question, which is about octave identification.
$endgroup$
– Ben Crowell
Mar 20 at 18:49
$begingroup$
This doesn't answer the question, which is about octave identification.
$endgroup$
– Ben Crowell
Mar 20 at 18:49
$begingroup$
This doesn't answer the question, which is about octave identification.
$endgroup$
– Ben Crowell
Mar 20 at 18:49
add a comment |
$begingroup$
Your ear recognizes different frequencies because hairs in the cochlea vibrate at certain frequencies, and they send a message to your brain telling you that you're hearing a particular frequency. Let's take the pitch A=440hz. That sets off the A440 receptor most strongly, but also sets off the A880 receptor less strongly. A880 is an octave higher than A440, and obviously the A880 receptor is expecting to be "pushed" 880 times per second, but A440 "pushes" the A880 receptor every other time it is expecting, so it sends a weaker signal to the brain, and our brain picks this multiples of frequencies up as an octave.
There's a vihart video on this topic that I think probably answers the question more clearly than I did, but this is the cliffnotes version.
$endgroup$
$begingroup$
Sorry, but Vi Hart is wrong there about how the cochlea works.
$endgroup$
– Pieter
Mar 21 at 8:44
add a comment |
$begingroup$
Your ear recognizes different frequencies because hairs in the cochlea vibrate at certain frequencies, and they send a message to your brain telling you that you're hearing a particular frequency. Let's take the pitch A=440hz. That sets off the A440 receptor most strongly, but also sets off the A880 receptor less strongly. A880 is an octave higher than A440, and obviously the A880 receptor is expecting to be "pushed" 880 times per second, but A440 "pushes" the A880 receptor every other time it is expecting, so it sends a weaker signal to the brain, and our brain picks this multiples of frequencies up as an octave.
There's a vihart video on this topic that I think probably answers the question more clearly than I did, but this is the cliffnotes version.
$endgroup$
$begingroup$
Sorry, but Vi Hart is wrong there about how the cochlea works.
$endgroup$
– Pieter
Mar 21 at 8:44
add a comment |
$begingroup$
Your ear recognizes different frequencies because hairs in the cochlea vibrate at certain frequencies, and they send a message to your brain telling you that you're hearing a particular frequency. Let's take the pitch A=440hz. That sets off the A440 receptor most strongly, but also sets off the A880 receptor less strongly. A880 is an octave higher than A440, and obviously the A880 receptor is expecting to be "pushed" 880 times per second, but A440 "pushes" the A880 receptor every other time it is expecting, so it sends a weaker signal to the brain, and our brain picks this multiples of frequencies up as an octave.
There's a vihart video on this topic that I think probably answers the question more clearly than I did, but this is the cliffnotes version.
$endgroup$
Your ear recognizes different frequencies because hairs in the cochlea vibrate at certain frequencies, and they send a message to your brain telling you that you're hearing a particular frequency. Let's take the pitch A=440hz. That sets off the A440 receptor most strongly, but also sets off the A880 receptor less strongly. A880 is an octave higher than A440, and obviously the A880 receptor is expecting to be "pushed" 880 times per second, but A440 "pushes" the A880 receptor every other time it is expecting, so it sends a weaker signal to the brain, and our brain picks this multiples of frequencies up as an octave.
There's a vihart video on this topic that I think probably answers the question more clearly than I did, but this is the cliffnotes version.
answered Mar 21 at 3:37
Kai ColemanKai Coleman
91
91
$begingroup$
Sorry, but Vi Hart is wrong there about how the cochlea works.
$endgroup$
– Pieter
Mar 21 at 8:44
add a comment |
$begingroup$
Sorry, but Vi Hart is wrong there about how the cochlea works.
$endgroup$
– Pieter
Mar 21 at 8:44
$begingroup$
Sorry, but Vi Hart is wrong there about how the cochlea works.
$endgroup$
– Pieter
Mar 21 at 8:44
$begingroup$
Sorry, but Vi Hart is wrong there about how the cochlea works.
$endgroup$
– Pieter
Mar 21 at 8:44
add a comment |
Thanks for contributing an answer to Physics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphysics.stackexchange.com%2fquestions%2f467666%2fsound-waves-in-different-octaves%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
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
Mar 20 at 17:44
1
$begingroup$
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
Mar 20 at 18:06
5
$begingroup$
@PhysicsDave Middle c is at 262 hertz (in current standard tuning where a' is att 440 hertz).
$endgroup$
– Pieter
Mar 20 at 19:11
1
$begingroup$
Heavily related is music.stackexchange.com/q/44783/45266, which I believe answers the question pretty well.
$endgroup$
– user45266
Mar 21 at 1:19
1
$begingroup$
And certainly music.stackexchange.com/q/43335/45266, specifically the answers. Check these out, guys!
$endgroup$
– user45266
Mar 21 at 1:25