# Acoustics of Dissonance



## Polednice (Sep 13, 2009)

This might sound like a ridiculous question, but I'm an incorrigible idiot.

Why does dissonance work? In other words, why does the human brain perceive certain intervals as clashing and other intervals as harmonious? I know (I think) that the more harmonious intervals have nicer mathematical ratios, but why would the brain find that pleasant?


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## pjang23 (Oct 8, 2009)

Try this:






An interval is represented by two pitches and thus two (fundamental) frequencies. When these frequencies are in ratios of small integers (2:1 for octave, 3:2 for perfect fifth, 4:3 for perfect fourth, etc) the sine waves fit together nicely. These cases are "harmonious intervals".


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## Polednice (Sep 13, 2009)

Thanks! Gotta love the brain!


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## Philip (Mar 22, 2011)

at a lower level i think it has to do with the physiology of the ear and the way harmonics are heard for every sound. when different sounds share many harmonics, their vibrations physically coincide and create harmony. when different sounds don't share harmonics, they clash, much like pushing a child on a swing at an irregular interval produces collisions.

edit: i was gonna post the exact same video!


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## ComposerOfAvantGarde (Dec 2, 2011)

> Dissonances are only the more remote consonances.


- Arnold Schoenberg.


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## Polednice (Sep 13, 2009)

Schoenberg clearly didn't know his acoustic science.


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## Philip (Mar 22, 2011)

ComposerOfAvantGarde said:


> Dissonances are only the more remote consonances.


this is only true if the frequencies in question are rational numbers, eg. 1Hz and pi-Hz will never meet in phase


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## ComposerOfAvantGarde (Dec 2, 2011)

Actually I think that something doesn't have to be any tonal triad thing/whatever to be consonant. Dissonance means "the need to resolve." I have heard plenty of non tonal (even entirely dodecaphonic) works where you get a clear sense of consonance and dissonance.


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## pjang23 (Oct 8, 2009)

ComposerOfAvantGarde said:


> Actually I think that something doesn't have to be any tonal triad thing/whatever to be consonant. *Dissonance means "the need to resolve."* I have heard plenty of non tonal (even entirely dodecaphonic) works where you get a clear sense of consonance and dissonance.


Dissonance is actually not a subjective matter, but a physical one. There is no actual line between "consonant" and "dissonant" (the decision of when to stop in the overtone series is arbitrary), but "more dissonant" and "less dissonant" are based on real physical relations.


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## ComposerOfAvantGarde (Dec 2, 2011)

pjang23 said:


> Dissonance is actually not a subjective matter, but a physical one. There is no actual line between "consonant" and "dissonant" (the decision of when to stop in the overtone series is arbitrary), but "more dissonant" and "less dissonant" are based on real physical relations.


Well, yes I suppose dissonance isn't subjective but I did have some understanding that it would be a physical matter.

From what I have learnt in music theory: in the key of C major, a G major chord would be considered dissonant and needs to lead onto something else because of how often we hear perfect (and imperfect for that matter) cadences. A G dominant seventh chord would be more dissonant because the addition of the F makes the listener expect that note to resolve onto an E, the third degree of a C major triad.


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## Guest (Jan 7, 2012)

As always, there are physical things, and there are reactions to those things.

The way you respond to those physical things differs from person to person and from group to group.

This story should be better known: Berlioz took a choir from the big city out into a rural area. The choir sang in standard four part harmony and, since this sometime between 1830 and 1850, the music was tonal.* The villagers' response? That the choir members seemed like nice people and all but they couldn't sing in tune.

In tune for those villagers was unisons and octaves only.

I can't think of anything that sounds abnormal to me. When I was in college, I used to have to play scales for my trumpet lessons. I liked to end them with pitches other than the expected one. I did that so much, that C to C# started to sound as "normal" as C to C. At first, for me, it was for shock effect. But once the shock wore off, I was left with simply another sequence. C, D, E, F, G, A, B, C#. C, D, E, F, G, A, B, D.

Perhaps that was one reason it was so easy for me to hear musics by Bartok and Stravinsky and then Carter and Stockhausen and then Mumma and Varese as completely fine and normal.

There is a thing called acoustics. There are frequencies. Different frequencies can sound simultaneously. But how we react to those things puts us right back to that subjective stuff that seems to exercise so many people. Heigh ho. 

And it's true that if you halve a vibrating string, you'll get a pitch that's an octave higher. And the unwary have always wanted to make a big deal out of that. But as Berlioz pointed out almost two hundred years ago now, making strings vibrate is not the only way to make sounds. It's not even the only way to make sychronous pitches. Hitting bits of wood or metal can make pitches, too, as can blowing through tubes of various lengths, thicknesses, and materials. And in those cases, there's no simple cutting in half strategem for making an octave.

As for all the wonderful world of the overtone series and such, the tempered scale that our ears have become so accustomed to is itself a strategem that means that everything is always just a little bit out of tune. So much so, that something in just intonation will sound out of tune to most people.


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## ComposerOfAvantGarde (Dec 2, 2011)

^I am with you, some guy.


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## Philip (Mar 22, 2011)

some guy said:


> And it's true that if you halve a vibrating string, you'll get a pitch that's an octave higher. And the unwary have always wanted to make a big deal out of that. But as Berlioz pointed out almost two hundred years ago now, making strings vibrate is not the only way to make sounds. It's not even the only way to make sychronous pitches. Hitting bits of wood or metal can make pitches, too, as can blowing through tubes of various lengths, thicknesses, and materials. And in those cases, there's no simple cutting in half strategem for making an octave.


it's a big deal because in frequency these ratios are absolute, whatever the geometry of the object.


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## Polednice (Sep 13, 2009)

some guy said:


> As always, there are physical things, and there are reactions to those things.
> 
> BLAAAAAAAAAAAAAAAH


Yes, thanks, I'm talking about physical things.


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## Couchie (Dec 9, 2010)

some guy said:


> And it's true that if you halve a vibrating string, you'll get a pitch that's an octave higher. And the unwary have always wanted to make a big deal out of that. But as Berlioz pointed out almost two hundred years ago now, making strings vibrate is not the only way to make sounds. It's not even the only way to make sychronous pitches. Hitting bits of wood or metal can make pitches, too, as can blowing through tubes of various lengths, thicknesses, and materials. And in those cases, there's no simple cutting in half strategem for making an octave.


All sound is waves, whether its generated by a vibrating string or a knock on wood is irrelevant. Knocking on a piece of wood that generates a wave twice as frequent as another piece will raise the sound an octave, same story as a string.


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## Guest (Jan 9, 2012)

Polednice said:


> Yes, thanks, I'm talking about physical things.


Dissonance is not a physical thing, though. Dissonance describes how we respond to certain combinations of sounds. And "we" are all different. What you call dissonant, I might merely call pleasant.

That is "the human brain" does not perceive certain intervals as clashing and other intervals as harmonious. *A* human's brain, may be. *The* human brain. Nah. That was the point of the Berlioz anecdote. The villager's brains perceived very ordinary harmonies as being out of tune. To their brains, only octaves and unisons were "harmonious."


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## Polednice (Sep 13, 2009)

There is some conditioning, there is some innateness. Let's not draw absolute lines in either direction.


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