You Know That Certain Musical Notes Sound Good Together

This was originally a response to a question on Quora.

Two notes sounding "adept" together sounds similar a very subjective statement.  The songs we like and the sounds we like are incredibly dependent on our civilisation, personality, mood, etc.

Just at that place is something that feels fundamentally dissimilar about certain pairs of notes that sound "practiced" together.  All over the earth humans have independently chosen to put the same intervals between notes in their music.  The feeling of harmony we get when nosotros hear the notes C and G together and the feeling of disharmony we get when we hear C and Yard apartment together turns out to be office of the universal human experience.

Instead of from subjective notions of "skilful" and "bad", scientists call the feeling of harmony "consonance" and the feeling of disharmony "racket".  Some cultures and genes of music use a lot more noise, but near humans perceive the same relative amounts of dissonance between pairs of notes.

The most consonant pairs of sounds are 2 sounds that are perceived as having the aforementioned "pitch" .  In other words, the K fundamental below middle C on my piano is so consonant with the G cord on my guitar that they are said to exist the same notation.

Here is a recording of one 2d of me playing the G-string on my guitar.  This graph shows the waveformof the audio, which is really just a rapid serial of changes in the air pressure.  Hidden within this waveform are patterns that our ears and brain perceive.

These waves then cause little hairs in our ears, called stereocillia, to vibrate, with different hairs vibrating at different frequencies. We perceive this sound through stereocillia in our ear that vibrate at different frequencies  You tin can think of sound as the sum of different frequencies of vibrations and the hairs on our ears excerpt the amount of each frequency contained in the sound.  Nosotros can also use math to extract the frequencies contained in the sound equally I did below with something called a Fourier Transform.

We unremarkably think of a pitch, like a 1000,  sometimes think of pitches equally having a single "frequency" but sounds the graph shows that it's are actually composed of diverse amounts of many different frequencies.  In this instance the lowest frequency of the cord is 196Hz or 196 vibrations per 2nd, but the string is also vibrating at double, triple, 4x times that.  The everyman frequency is called the fundamental frequency.  These higher frequencies are called overtones also known equally harmonics when they are at simple multiples of the fundamental frequency.  Instruments with vibrating strings similar my guitar tend to vibrate at multiple frequencies where each frequency is a multiple of the lowest frequency – this is related to the physics of a cord and it will exist actually important here.

Hither is a 1-second recording of me singing along to the Grand-string.

This audio waveform looks pretty different from the recording of my guitar, just when we await at the frequencies we tin see that the ii match up.

I added red dots to this frequency graph to highlight where the harmonic frequencies are and show the uniform spacing.  Each dot is exactly 196Hz apart but like in the graph of the guitar's frequencies.

The lowest or fundamental frequency of the recording of my voice matches the 196Hz of my guitar string shown on the previous graph.  It's astonishing that nosotros are able to make our voices harmonize and so exactly without even thinking about it.

When I sing the 1000 note along with my guitar my voice and my instrument are causing the same hairs in my ear to vibrate.

The fact that the frequency peaks or cherry dots are even spaced is a physical property of our song chords and comes from the fact that our vocal chords are essentially a long tube of air.  Other instruments that are similar longs tubes of air have the same property such every bit flutes, saxophones, horns and harmonicas.

When I play my guitar an octave college I can brand a harmony.  A one second recording looks like this – again totally unlike from the previous two.

Merely when I look at the frequencies in its composition, they are exactly double the the frequencies of the low G cord or me singing the low G.  The ruddy dots evidence the spikes from our earlier depression G graph, the yellow dots are the frequency spikes from the loftier Thousand sound.

So when you get an octave upwards, the same hairs will vibrate as with the lower octave, although not all of them. That's what gives us the senseof two "notes" existence the same even when they're an octave apart.

Almost every culture that has a notion of an octavealso has a notion of a "fifth" or note halfway between an octave.  Two notes that are a fifth apart are the most consonant of any two notes that are not the same.

The K note is the "5th" of a C note.  In western music, all of the virtually common chords with a C root take a G notation in them.   Why does a C and a G fit so well together?  Here are the frequencies of playinga C on my guitar.

Yous can see in red the harmonics (or frequency spikes) of my K notation and in yellow the harmonics of my C annotation.  They don't ever line up but because my C note's cardinal frequency (need to ascertain this)  is 3/2 of my Chiliad annotation they line upward every tertiary harmonic of the C and every 2d harmonic for the G.

The two notes that audio nigh consonant with a C are F and Thou, corresponding to the "perfect 4th" and "perfect 5th" intervalsfrom C.  Why do they line up so well?  We can look at how many of the harmonics line up.

Yous tin can meet that Chiliad and F harmonics line up quite often with C'southward harmonics at the bottom.  But notice that Thou and F's harmonics don't line up with each other very oft.  So K and C audio very consonant and F and C sound very consonant only G and F sound much more anomalous.  This is why information technology's very common to play G and C together or F and C together but information technology's unusual less mutual to play a C, 1000 and F all at once.

All of the notes that are consonant with C take intervals with many harmonics overlapping equally you lot can encounter on this bigger chart.

You can come across here that C and East take lots of overlapping harmonics – C, E and M would be a C major chord.  C and D# have almost as many overlapping harmonics and C, D# and G would be a C modest chord.

Some notes don't correspond to whatever simple fractional interval, and those notes sound very dissonant.  For example, playing C and F# together is extremely dissonant because there are no overlapping harmonics (the F# doesn't quite even line upward with 2/5 interval – for more on this encounter my respond to Why are there 12 notes?).

Some instruments don't produce these overtones at simple multiples of the fundamental frequency.  Drums commonly don't produce simple overtones because the vibrations travel across them in more i dimension, which creates more than complicated patterns.  This is why you can't typically hear drums harmonizing with each other even though they take a recognizable pitch.

We tin stop at that place if nosotros desire to, simply there are other psycho-acoustic effects that touch on consonance vs. racket.  One upshot worth mentioning is the racket we hither when ii frequencies are close but non overlapping.  .

When two notes are played close together the waveforms await roughly like this:

When we extend out the waveforms we tin can see that they motion in and out phase.

Our ear hears the sum of the bluish and the orange waveform which looks like this.

Or looking at a longer fourth dimension menstruation:

When the moving ridge forms are in sync at the beginning they amplify each other, but every bit they get out of phase they decrease from each other.  This creats theabeating sound that is very recognizabe if you've ever heard an out of tune piano or an out of tune guitar.

To western ears this sounds like an out of tune instrument.  Some cultures contain this sound into their music.  Information technology'south pretty clear that this is an issue associated with dissonance.  As other people have mentioned in their answers, two pure sounds with frequencies that are within a note or two are universally heard as dissonant.

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Source: https://lukasbiewald.com/2015/06/11/why-do-certain-musical-notes-sound-good-together/