Sounds are waves !

Click here for the general overview

In western music, we know that there are 7 notes : C – D – E – F – G – A – B.

But why are there only 7 ? And how do they relate to music ?

To understand this, we must look into the very fabric of Music. And that is sound. Music is made of sounds, I think we can agree on that.

But what is a sound ? Physically speaking, a sound is a vibration of air molecules. Those vibrations bounce onto your ear-drum, and by means of a very complicated, and yet not well understood mechanism (at least not by me !), it’s your brain that transforms them into music.

Those vibrations can be imagined as a wave. And like any other wave, a sound wave has a cycle : it goes up and it goes down, and then it goes up again and down, etc.

You can measure those cycles. That’s what a guy named Hertz did. He measured the frequency, i.e. the number of cycles a wave has per second. 1 cycle per second = 1 Hertz (Hz), 10 cycles per second = 10 Hz, etc.

For instance, the note that we call “A” is a sound (aka “pitch”) with 440 Hz. That’s the number you’ll see on your tuner !

But actually, the A-string on your guitar vibrates with a frequency of 110 Hz. We’ll see in a minute how’s that possible. For now, here are the frequencies of the various strings on your guitar (source : Wikipedia)

String	Note	Frequency
1	E	329.63 Hz
2	B	246.94 Hz
3	G	196.00 Hz
4	D	146.83 Hz
5	A	110.00 Hz
6	“Low” E	82.41 Hz

A very important conclusion that we can draw from this table is : the higher the frequency, the higher the pitch.

So, how many sounds or pitches are there ? In theory, you can have an near infinite number of cycles per second, but in reality that’s not the case (*). Studies show that the human ear can hear only between 15 Hz and 20 KHz. (1 KHz = 1000 Hz). Still, that makes a lot of frequencies. So, the question remains : why only 7 notes ?

Well, this is where “conventions” come into play !

The first convention is that frequencies that you multiply with or divide by 2, will all have the same note ! So, for instance, if you take the note “A”, which has 440 Hz, and you divide 440 Hz by 2 = 220 Hz, you'll have again "A". If you divide again by 2, you have 110 Hz, which is the frequency of the A-string on the guitar.  

So, when multiplying with or dividing a frequency by 2, the convention is that we talk about the same note, “A” for instance. But following our first conclusion above, the “A” of 110 Hz will sound lower or deeper than the “A” of 220 Hz, and the “A” of 440 Hz will sound higher.

Let’s do a little experiment to prove this. Take a guitar and measure - in inch or centimeter - the length of any string, from nut to bridge. Write this down and divide it by two.

Now play the open string. Then use your finger to press down the string on the fret board exactly halfway of the string, as you calculated. Now play the string again. You will hear the same note, but higher in pitch ! What you did is shortening the string by half, thus letting it vibrate twice as much, thus doubling its frequency, thus making the pitch twice as high !

Also notice that you positioned your finger on the 12th fret. That’s where the string’s half is. On most guitars (and banjos) this 12th fret will be marked in some particular way or another.

This is important, because from the 12th fret onwards, the notes repeat itself ! So, the note of the open string and the note on the 12th fret – although higher pitched – are the same. But also, the note of the 1st fret and the 13th fret are the same ! And the 2nd and the 14th are the same, and so on and so forth.

So, how many “A”’s can we hear ? If you keep dividing and multiplying 440 Hz by 2, you’ll have this list : 27.5 – 55 – 110 – 220 – 440 – 880 – 1760 – 3520 – 7040 – 14080, so that makes 10 “A”’s in our audio-range !

Okay, let’s move on to the second most important convention. And that is that there is a "auditive distance" between 2 adjacent notes. That distance can be a whole tone or a half- or semi-tone.

Now, READ THIS CAREFULLY, BECAUSE THIS IS REALLY REALLY IMPORTANT : on a guitar, a banjo or any “fretted” instrument (mandolin, ukulele, bouzouki, etc.) the difference between a tone and a semi-tone is childishly easy : a semi-tone is ONE fret, and a whole tone is TWO frets ! (repeat after me : semi-tone : 1 fret, whole tone : 2 frets)So if you put your finger on a string on a fret and play it, and then you move your finger up- or downwards 1 fret, and play the string again, you have played a semi-tone interval. If you move your finger 2 frets down- or upwards, you play a whole tone interval. (BTW between the open string and the 1st fret there is also a semi-tone interval).

Now that we are aware of the 2 most important conventions, we are ready to look for ways to organize all those whole tones and semi-tones. Indeed, there ARE systems for organizing them. They are called “scales”. I’ll discuss the 2 most important of them in the next blog. Also – finally ! – there you’ll find why there are but 7 notes.

For now, I think you have enough for one Pomodoro. If you have time over, re-read this blog, or try to experiment a bit on your guitar. For example : how many semi-tones are there between an open string and the 12th fret ?

See you at the next Pomodoro, whenever you’re ready !

-----------

(*) The higher the frequency of the wave, the more energy you have to put in it. Since Einstein and quantum mechanics, we know it’s not possible to put an infinite amount of energy into something, so you cannot have an infinite number of wave-cycle per second. But you certainly don’t have to know that to play music !