# Why do music chords sound "good"? **URL:** \ **Category:** Factual Questions\ **Created:** [October 21, 2014, 12:00pm UTC](https://boards.straightdope.com/t/why-do-music-chords-sound-good/702016 "2014-10-21T12:00:53Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [October 21, 2014, 12:00pm UTC](https://boards.straightdope.com/t/why-do-music-chords-sound-good/702016/1 "2014-10-21T12:00:53Z")
I recogize that “good” or “pleasing to the ear” are subjective terms, but there seems to be near-universal agreement that certain acoustic frequencies, when overlaid, are pleasing to the ear. I’m at a loss to understand why. The relative frequencies involved in a pleasing chord don’t bear any mathematical relationship that appears especially significant to an analytical mind. Consider for example an A440, a 440-Hz tone. There are twelve chromatic steps in an octave, so each for each chromatic step up, the frequency increases by a multiple of 2[sup]1/12[/sup] (12 steps up = (2[sup]1/12[/sup])[sup]12[/sup], or double the frequency of the note at the bottom of the octave). So if the bottom of my chord is an A440, then the C# (for a major chord) is 544.4 Hz. So 440 Hz and 544.4 Hz sound “good” when played at the same time. Why is this? They aren’t any kind of integer multiple of each other. Their ratio, 1.2592…, doesn’t appear to be any more meaningful than the relationship between any two other notes. So what gives? ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [October 21, 2014, 12:10pm UTC](https://boards.straightdope.com/t/why-do-music-chords-sound-good/702016/2 "2014-10-21T12:10:51Z")
They sound good because they are close to an integer multiple. 1.2592 is close to 5/4. 2^5/12 = 1.3348 which is about 4/3 2^7/12 = 1.4983 whihc is about 3/2 They aren’t exact integer multiples when you have equal-temperament tuning, but there are other tunings where the notes _are_ exact integer multiples (at the cost of some pairs of notes in other keys being even farther off). ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [October 21, 2014, 12:20pm UTC](https://boards.straightdope.com/t/why-do-music-chords-sound-good/702016/3 "2014-10-21T12:20:20Z")
By “integer multiple” do you mean to refer to ratios of small integers? ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [October 21, 2014, 12:35pm UTC](https://boards.straightdope.com/t/why-do-music-chords-sound-good/702016/4 "2014-10-21T12:35:42Z")
> [@ZenBeam](#): > > They sound good because they are close to an integer multiple. 1.2592 is close to 5/4. > 2^5/12 = 1.3348 which is about 4/3 > 2^7/12 = 1.4983 whihc is about 3/2 > > They aren’t exact integer multiples when you have equal-temperament tuning, but there are other tunings where the notes _are_ exact integer multiples (at the cost of some pairs of notes in other keys being even farther off). So do chords sound even more pleasant if you deviate from conventional tuning and go with those exact integer ratios? ---
**Author:** ![bob\_2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bob_2/32/3341_2.png) [@bob\_2](https://boards.straightdope.com/u/bob_2)\ **Post date:** [October 21, 2014, 12:36pm UTC](https://boards.straightdope.com/t/why-do-music-chords-sound-good/702016/5 "2014-10-21T12:36:56Z")
Our brains work in mysterious ways. What sounds good to you, may not sound so great to an oriental and vice versa. ---
**Author:** ![Folacin](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/folacin/32/3195_2.png) [@Folacin](https://boards.straightdope.com/u/Folacin)\ **Post date:** [October 21, 2014, 12:43pm UTC](https://boards.straightdope.com/t/why-do-music-chords-sound-good/702016/6 "2014-10-21T12:43:07Z")
And Hertz is based on an arbitrary measurement. Possibly you could define a second to be slightly longer or shorter, and then pleasing chords might be an exact integer. ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [October 21, 2014, 12:50pm UTC](https://boards.straightdope.com/t/why-do-music-chords-sound-good/702016/7 "2014-10-21T12:50:41Z")
Why comes in two parts. As Zenbeam notes, close ratios of integers sound consonant, and the equal temperament scale gets us close to these ratios. This is done in a manner that allows for transposition of between keys - but suffers by spreading the grief of bad ratios around, so that almost every interval is slightly wrong. (The alternatives give you some more consonant intervals and some really badly out ones - which can be a good compromise as well.) The 12[sup]th[/sup] of 2 is only true for the equal tempered scale, all the others being some other set of ratios and notes. The diatonic scale is conventionally described as ratios built out of the integers 2, 3, and 5. So 4/3 is a fourth, 3/2 is a fifth. You can then get into variations for the other scale tones. A major third can be 5/4 (just intonation) or 81/64 (Pythagorean.) Equal temperament has varying errors from these. As to why we perceive these intervals as pleasing - well that is really hard. But it is worth noting that there is a clear element of learned response - with different cultures having different harmonic root to their music. Not only that, but the really strong intervals can start to sound boring. Western music has mined a deep and rich seam of tonality and atonality, in the last century, and just what defines a really pleasing harmony is a rubbery thing - something that seems to change as we learn and experience more musical complexity. Entire PhD theses can (and have) been written about nothing more than the questions of the various ratios and the harmonic structure inherent in them. The equal temperament scale is what everyone is taught, but it is to a large extent a bit (or a lot) of a lie. It only really matters for transposing instruments (piano, guitar etc) but even here the reality is that there is scope for tweaking which is commonly taken advantage of - both for musical reasons and for issues imposed by the physical realisation of the instrument. ---
**Author:** ![njtt](https://avatars.discourse-cdn.com/v4/letter/n/ecd19e/32.png) [@njtt](https://boards.straightdope.com/u/njtt)\ **Post date:** [October 21, 2014, 12:54pm UTC](https://boards.straightdope.com/t/why-do-music-chords-sound-good/702016/8 "2014-10-21T12:54:26Z")
It seems to me that even if (or when) you have found nice elegant mathematical relationships between the note frequencies, you still have not really explained much if anything about why notes with those sorts of relationships sound _ **good** _ together. _Pace_ **bob++** , I am pretty sure it is not entirely (or even mostly) a matter of culture and of what we are used to. There are human universals regarding harmony, so plainly there is some biological basis for the pleasure it evokes, but I do not think it is well understood. ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [October 21, 2014, 12:55pm UTC](https://boards.straightdope.com/t/why-do-music-chords-sound-good/702016/9 "2014-10-21T12:55:57Z")
> [@Folacin](#): > > And Hertz is based on an arbitrary measurement. Possibly you could define a second to be slightly longer or shorter, and then pleasing chords might be an exact integer. Not really. These are ratios, and are independent of the absolute frequencies. A signal of 100Hz and one of 150Hz will get you an interval of a fifth. So too will 123Hz and 184.5Hz. As noted above, the ratios are all integer ratios, but you can’t create the equal tempered scale with these ratios, and so we give up the perfect harmonies in return for the ability to transpose and modulate between keys. For the most part this is considered a fair trade (but not everyone agrees.) ---
**Author:** ![UncleFred](https://avatars.discourse-cdn.com/v4/letter/u/f0a364/32.png) [@UncleFred](https://boards.straightdope.com/u/UncleFred)\ **Post date:** [October 21, 2014, 12:56pm UTC](https://boards.straightdope.com/t/why-do-music-chords-sound-good/702016/10 "2014-10-21T12:56:32Z")
> [@Machine\_Elf](#): > > So 440 Hz and 544.4 Hz sound “good” when played at the same time. Why is this? They aren’t any kind of integer multiple of each other. Their ratio, 1.2592…, doesn’t appear to be any more meaningful than the relationship between any two other notes. There’s a bit more to it than just the fundamental tones. Any musical instrument will generate that base frequency as well as a number of integer (and maybe integer-ratio?) tones above the base frequency. A guitar string will generate the fundamental note as well as other ‘standing wave’ frequencies that propagate on the same length/tension string. Similar things happen with wind instruments. Electronic instruments try to mimic the harmonic content of their physical counterparts. I suppose you could program an electronic organ to only generate ‘pure’ tones but I suspect it wouldn’t sound very good. ---
**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\ **Post date:** [October 21, 2014, 12:58pm UTC](https://boards.straightdope.com/t/why-do-music-chords-sound-good/702016/11 "2014-10-21T12:58:01Z")
> [@Machine\_Elf](#): > > So do chords sound even more pleasant if you deviate from conventional tuning and go with those exact integer ratios? Yes. This is the difference between [just intonation](http://en.wikipedia.org/wiki/Just_intonation) and [equal temperament.](http://en.wikipedia.org/wiki/Equal_temperament) Early systems of tuning used something more like just intonation, where the intervals and chords were related by ratios of small integers. However, it was quickly discovered that if you tuned your organ (say) so that the chords sounded great for pieces in one key, they would then sound awful for pieces in any other key. People then proceeded to tweak the tunings of individual notes in the scale, coming up with all sorts of idiosyncratic frequency ratios to construct their scales according to their own preferences of “pure” intervals versus being able to play in all keys. In the end, “being able to play in all keys” won the day, and we ended up with equal temperament. Also: it’s important to remember that most musical instruments do not create a single, pure tone of (say) 440 Hz. Instead, they created a combination of the fundamental tone (440) and its overtones (880 Hz, 1320 Hz, 1760 Hz, etc.) This means that if you play a 440 Hz tone and a 660 Hz tone on the same instrument, a lot of their overtones will be common multiples of both fundamentals, and will line up with each other (1320, 2640, 3960, etc.) In general, notes whose fundamentals are related by a ratio of small integers will more of these overtones overlap with each other, and so will sound better. ETA: If you’re interested in learning more about the history of tuning systems (and who isn’t?), Stuart Isacoff’s _Temperament: How Music Became a Battleground for the Great Minds of Western Civilization_ is a pretty good read. ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [October 21, 2014, 1:25pm UTC](https://boards.straightdope.com/t/why-do-music-chords-sound-good/702016/12 "2014-10-21T13:25:36Z")
(I’m clearly on a favourite subject here) This is the mini story of the integers and the scales. You can create a simple instrument that has perfect harmonic relationships between the notes - but only for one key (aka the root of the scale of notes.) For instruments like wind instruments you have all sorts of other issues that control the precise frequencies of notes. So we could make a simple instrument that has the notes in the scale: 1 (fundamental), 9/8, 81/64, 4/3, 3/2, 27/16, 243/128, 2 (octave) and we can repeat this for another octave by doubling everything. So far so good. But say someone wants to play in a different key? Say our instrument is in C (1 = 256Hz) and someone wants to play in G. If you just start playing the scale starting at G, you discover that the notes don’t all fit properly. In fact they can fit pretty badly. The fourth above the G should be C, and we can see that 3/2 (the G) times 4/3 (the interval of a fourth) is right - we get the next C. But a tone above G is the second of the G scale (A) and would be 3/2 \* 9/8 = 27/16 - which is not the 5/3 (A in the C major scale) that we actually find in that spot. 27/16 is not all that far from 5/3 1.6875 versus 1.666667 - a 1.2% error. But it is audible. So harmonic development is not easy. One trick is to tweak the frequencies a bit so that the keys and intervals you most use are favoured, and those that are seldom used get the big miss-matches. The other way out is to define a scale that uses exactly the same ratio between every chromatic note, and thus no matter what key you are in, the scale intervals are always exactly the same. Since an octave is a doubling in frequency, and there are twelve notes in an octave, the interval is the 12[sup]th[/sup] root of two. It is as simple as that. Sadly, if you multiply out the scale tones and compare them with the nice integer ratios they should be, you can find some nasty errors. But in the West we have been brought up with the equal tempered scale, and for the most part we ignore the deficiencies. Or musicians ignore the scale. Both happen. ---
**Author:** ![friedo](https://avatars.discourse-cdn.com/v4/letter/f/8edcca/32.png) [@friedo](https://boards.straightdope.com/u/friedo)\ **Post date:** [October 21, 2014, 2:00pm UTC](https://boards.straightdope.com/t/why-do-music-chords-sound-good/702016/13 "2014-10-21T14:00:50Z")
If you’re interested in the development of equal temperament and the fascinating world of frequency ratios, read [this book](http://www.amazon.com/dp/0375703306/). A very quick read and it explains everything very clearly. ---
**Author:** ![babygoat666](https://avatars.discourse-cdn.com/v4/letter/b/2acd7d/32.png) [@babygoat666](https://boards.straightdope.com/u/babygoat666)\ **Post date:** [October 21, 2014, 2:02pm UTC](https://boards.straightdope.com/t/why-do-music-chords-sound-good/702016/14 "2014-10-21T14:02:00Z")
> [@bob\_2](#): > > Our brains work in mysterious ways. What sounds good to you, may not sound so great to an oriental and vice versa. WTF is “an oriental”? ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [October 21, 2014, 2:21pm UTC](https://boards.straightdope.com/t/why-do-music-chords-sound-good/702016/15 "2014-10-21T14:21:48Z")
> [@Frylock](#): > > By “integer multiple” do you mean to refer to ratios of small integers? Oops, yes. > [@Machine\_Elf](#): > > So do chords sound even more pleasant if you deviate from conventional tuning and go with those exact integer ratios? **MikeS** gave a good answer, but I wonder if it actually being more pleasant to _you_ will depend on your ear training. I suspect it wouldn’t matter much to me. I think my son would notice, though. It almost certainly depends on the type of music being played as well. ---
**Author:** ![Colibri](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/colibri/32/1841_2.png) [@Colibri](https://boards.straightdope.com/u/Colibri)\ **Post date:** [October 21, 2014, 3:51pm UTC](https://boards.straightdope.com/t/why-do-music-chords-sound-good/702016/16 "2014-10-21T15:51:22Z")
> [@bob\_2](#): > > Our brains work in mysterious ways. What sounds good to you, may not sound so great to an oriental and vice versa. > [@babygoat666](#): > > WTF is “an oriental”? **Moderating** To preempt further comment on this, it should be noted that the term “oriental” to refer to people from East Asia is considered by some to be derogatory, at least in the US. (“Oriental” as an adjective to refer to things, such as an oriental rug, is OK.) If you wish to discuss this term and whether or not it should be considered derogatory, please start another thread in GD or IMHO. Colibri General Questions Moderator ---
**Author:** ![Quercus](https://avatars.discourse-cdn.com/v4/letter/q/7ab992/32.png) [@Quercus](https://boards.straightdope.com/u/Quercus)\ **Post date:** [October 21, 2014, 4:11pm UTC](https://boards.straightdope.com/t/why-do-music-chords-sound-good/702016/17 "2014-10-21T16:11:27Z")
> [@Machine\_Elf](#): > > So do chords sound even more pleasant if you deviate from conventional tuning and go with those exact integer ratios? Yeah, but not so much better that most people notice. The general consensus since Bach’s time is that audiences don’t really notice the decline in pleasantness from convention well-tempered tuning, but they do notice how bad it sounds when you play a perfect-tuned instrument in the wrong key. And they notice how boring it gets when you play everything in the same key. ---
**Author:** ![chappachula](https://avatars.discourse-cdn.com/v4/letter/c/d2c977/32.png) [@chappachula](https://boards.straightdope.com/u/chappachula)\ **Post date:** [October 21, 2014, 7:32pm UTC](https://boards.straightdope.com/t/why-do-music-chords-sound-good/702016/18 "2014-10-21T19:32:37Z")
> [@bob\_2](#): > > Our brains work in mysterious ways. What sounds good to you, may not sound so great to an [Asian person] and vice versa. I admit that I don’t understand all the math in this thread.But I think that just as important as the frequency and herz, is our cultural experience. Here is a [1-minute clip](http://www.youtube.com/watch?v=mN9iXlfxpxI) of a Chinese opera. And, to me, it does _not_ sound good. Tinny, screeching sounds that my ears have no experience with. and do not find pleasant. ---
**Author:** ![Kimstu](https://avatars.discourse-cdn.com/v4/letter/k/ecd19e/32.png) [@Kimstu](https://boards.straightdope.com/u/Kimstu)\ **Post date:** [October 21, 2014, 7:51pm UTC](https://boards.straightdope.com/t/why-do-music-chords-sound-good/702016/19 "2014-10-21T19:51:59Z")
> [@chappachula](#): > > Here is a [1-minute clip](http://www.youtube.com/watch?v=mN9iXlfxpxI) of a Chinese opera. > And, to me, it does _not_ sound good. > Tinny, screeching sounds that my ears have no experience with. and do not find pleasant. But I think what you’re reacting to there is not the tonal structure of the actual melody/harmony, but rather the _timbre_ or tone color of the singer’s voice. Yes, many Asian musical traditions appreciate a strongly nasal timbre in vocal music (particularly in the female voice) that many Western listeners find unattractive. But that has nothing to do with whether you think the actual _pitches_ or _chords_ sound good. In that clip, for example, if the singer’s voice bothered you but the instrumental accompaniment sounded okay, then the cultural differences here have to do with vocal timbre, not the notes themselves. ---
**Author:** ![FXMastermind](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/fxmastermind/32/7289_2.png) [@FXMastermind](https://boards.straightdope.com/u/FXMastermind)\ **Post date:** [October 21, 2014, 8:14pm UTC](https://boards.straightdope.com/t/why-do-music-chords-sound-good/702016/20 "2014-10-21T20:14:04Z")
> [@Machine\_Elf](#): > > I recogize that “good” or “pleasing to the ear” are subjective terms, but there seems to be near-universal agreement that certain acoustic frequencies, when overlaid, are pleasing to the ear. Simple answer: Notes that sound “bad” create “beats” that are not regular, they interfere with each other to create tension, because the beats are not synchronized. It’s much like if you are driving and your engine starts running uneven, or starts missing and stuttering, it creates a definite feeling of something is wrong. Sounds that are pleasing do not create tension, they do not seem uneven. (see below) Of course in music chords and melodies are used that intentionally create discord, or tension, but most people expect this to resolve before the piece ends. More complicated answer: Tension also can sound “good”, but we expect the tension to be what we are used to, minor chords, and other additions to create some stress, some feeling, but not if it is an “out of tune” feeling. Tuning is actually physical, in that strings that are tuned will excite each other, causing complex overtones and pleasing sounds. Out of tune, or unexpected tunings sound “wrong”, and again this is due to destructive interference, where the energy in the sound is not creating complex regular beats, but out of sync beats. It’s like asking why drumbeats sound good. What sounds bad is somebody beating on something with no regular beat, or two different beats that are not in sync in any way. [Next page](https://boards.straightdope.com/t/why-do-music-chords-sound-good/702016.md?page=2)