Organizing notes : scales and keys

Click here for the general overview

In the previous blog, we saw 2 important conventions :

1. A note with a frequency that you divide by or multiply with 2, remains the same note. For example, A = 440 Hz, but also 220 Hz, 110 Hz, 880 Hz, and so on.
2. Between 2 adjacent notes there is an “auditive” distance which can be a tone or a semi-tone (half-tone). On an instrument with frets, that interval is easy to find : a semi-tone is 1 fret, a whole tone 2 frets.

Now, let’s do the following experiment on your guitar : from any string, play the open string, then all the semi-tones until you have the same note as the open string again.

I’ll wait a minute here until you’ve finished.

If you did the experiment right, you played 13 different pitches : first the open string, then you put your finger on the 1st fret, then the 2nd, then the 3rd, and so on, until you arrive at the 12th fret. As we’ve seen in the previous blog, the 12th fret is half the string, so there’s the same note as the open string.

Congratulations ! You played your first scale ! The chromatic scale to be more precise. So, what is a scale ? Before I can answer that, I need to introduce yet 2 other terms. Don’t worry, they’re both very simple.

The first term is : the “root note” – or “root” in short. The root is the note with which you start a scale. It’s also called the “key”. So, if you started the scale with the 1st open string, your root or key was “E”. If it was the 2nd open string, the root was B, if it was the 3rd then the root was G, the 4th was G, the 5th was A and the 6th was again E.

Now, the second word I want to introduce is the “octave”. We’ll see more about that later, but for now, let’s say that an octave is the same note as the root note, but with twice (or half) its frequency. In other words : it’s the note you play on the 12th fret.

With those 2 terms, we have all the information to define what a scale is : a scale is a pattern of tones (whole tones and semi-tones) to go from a root note to its octave.

That’s it. Simple, isn’t it ?

In the chromatic scale, the pattern is really really really easy : it’s all semi-tones from the root to the octave. You demonstrated that when you played every fret from the open string to the 12th fret.

You can play a scale in ascending or descending order : from the root to it’s upper octave (from the open string to the 12th fret), or from the root to it’s lower octave (from the 12th fret to the open string). That’s why I like the Dutch word for scale : “toonladder” : it shows nicely that you can go up or down. I’m sure it doesn’t need an English translation. By the way, in English, in stead of talking of a whole tone and semi- or half tone, you can also say : a whole step or half a step. In a way, this also refers to a ladder.

But the chromatic scale is by no means the only scale, or pattern, to organize notes ! You have many of them, amongst which is for example the very important “minor pentatonic scale”, that is used abundantly in blues-music.

But there is one that is overly dominant in western music, and that is really “home” for music theory. It is the diatonic scale.

The pattern of the diatonic scale seems a bit complex at first sight, but we’ll see later how we can break it down into simpler fractions. Ok, here’s the pattern :

whole tone – whole tone – half-tone – whole tone – whole tone – whole tone – half-tone

(remember, in stead of “tone”, you can also use the word “step”)

If you like numbers, I guess you can write it down like this :

1 – 1 – 1/2 – 1 – 1 – 1 – 1/2

Or, if you – like me – prefer a more visual way :

Now, let’s apply this pattern on the guitar, and we choose the first fret of the 2nd string as our root note, which happens to be C.

Before we start playing the scale, let’s think a moment where we want to end up. If we start on the 1st fret of the string, which fret on that string will be the octave ? We know from the previous blog that from the 12th fret onwards, the notes repeat themselves. So, the note of the open string and the 12th fret are the same, and so are the notes on the 1st fret and the 13th fret. In other words, the 13th fret is the octave of the 1st fret, so that’s where we’re want to land on.

Here we go : we play the 1st fret, then leave a whole tone (we move 2 frets), that means the 3rd fret. Then leave again a whole tone (move 2 frets) and play the 5th fret. Then only a half step (move 1 fret), play the 6th fret, then a whole tone (2 frets), so play the 8th fret, again a whole tone, play the 10th fret, and again a whole step, play the 12th fret, and then finally a half step, which brings us indeed to the 13th fret, the octave.

Congratulations again ! You just played the diatonic scale in the key of C ! (C being the root).

You can do that again if you like, and you can also play it in ascending order : 13th – 12th – 10th – 8th – 6th – 5th – 3rd – 1st. I’ll just wait here until you’ve finished…

Now, let me ask you the following question : how many different pitches did you play ? And the next question : how many different notes ? Maybe, get back to your guitar and count the number of pitches and notes you play in the diatonic scale ! (Again, I’ll wait a bit….)

The answer is that you played 8 different pitches, but you only played 7 different notes ! The different notes were : 1st fret – 3rd fret – 5th fret – 6th fret – 8th fret – 10th fret – 12th fret, which are of course also different pitches. But then you played also the 13th fret, which is indeed a different pitch, but not a different note (I refer to the 1st convention : the octave is the same note as the root !).

So, now everything falls into place : in the specific pattern of tones that is called the diatonic scale, there are only 7 notes. In the key of C which we played, these notes are : C – D – E – F – G – A – B. The high C was the 8th pitch that you played, and that’s why it’s called the “octave” (the Latin word “octo” means 8, e.g. the “octopus” has 8 arms).

Wow ! We’ve come a long way ! From the thousands of frequencies that a human ear can hear, we organized them all in only 7 notes ! That’s quite a trick !

Some things to remember :

• from the E to the F, and from the B to the octave C, there’s a half step interval. Or in other words : from the 3rd note to the 4th, and from the 7th to the 8th, only half a step. Between all other notes, there’s a whole step difference.
• A scale is a pattern of whole and half tones, the root or the key is the note on which you start the scale !
  Having said that, because the diatonic scale is so overdominantly used in western music, and because the key of C is the “mother of all keys”, the terms “scale” and “key” (in particular the key of C) are often intermixed. So, if you read somewhere “the G-scale”, that means the diatonic scale in the key of G. (There’s no such thing as a “G-scale”).

I guess this is enough stuff to think about for this Pomodoro. At least (and at last) we know the notes in the key of C. But what about other keys ? We’ll see about them in another Pomodoro. But my next Pomodoro will first show how you can play the diatonic scale in the key of C on different strings on your guitar. And I’ll talk about a bit more too ! See you there !

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 !

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(*) 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 !

Pomodoro 1 : The General Picture

 

The Pomodoro Technique

I’ve been using the Pomodoro Technique for a couple of weeks now, and honestly, I wish I had known it earlier. As a matter of fact, a lot earlier, because I did my university studies more than 30 years ago ! Although I finished my studies successfully, I am convinced that if I knew this technique back then, I would have studied much more effectively and efficiently.

Some time ago, I started a blog about Basic Music Theory for banjo-players. Although it’s incomplete, I was quite happy about it. But then it struck me that it could be re-organized in little chunks of knowledge, that can be served as pomodoros. So, this is what’s this blog is about.

My aim is to give you an overview of Basic Music Theory in 11 Pomodoros. Given that a Pomodoro only lasts 25 minutes, this will take you less than 5 and a half hours to know the basic music theory !  Here a the topics :

1. The General Picture
2. Sound are waves !
3. Organizing notes : scales and keys
4. Things with strings
5. Building other keys in the diatonic scale
6. Building even more keys in the diatonic scale
7. Intermezzo : tempo and rhythm
8. Minor keys and scales
9. The hidden power of Modes 
10. 3-note chords
11. 4-note (seventh) chords beyond

Basic Music Theory : Melody, Harmony & Rhythm

When talking about music, most people will think of it as consisting of three components : melody, harmony and rhythm. And indeed, this is also what this blog will try to explain. When you go over the pomodoros above, you will see that 2 to 6, 8 and 9 will talk about melody. Pomodoros 10 and 11 have harmony as subject. And there’s only 1 pomodoro, nr 7, devoted to rhythm.

So, all in all, this is a quite traditional approach. You should realize however that this blog is NOT about MUSIC, but about music theory ! This difference can be compared to that between language and grammar. You don’t NEED to study the grammar of a language in order to speak it, but it can perhaps help you to learn it faster and more correctly.

If you want to know more about music itself, I strongly recommend to experience the double DVD “The Groove Workshop” by Victor L. Wooten, and its accompanying book “The Music Lesson”. If you are a skeptic, stick to the DVD’s, if you are more open to “fairy dust stuff”, you will be amazed by the book. Anyway, in both cases, Victor L. Wooten breaks music down in 10 elements. Some of these elements are covered in this blog. “Notes” (i.e. melody and harmony) is one of them, “tempo and rhythm” another. But  there are still 8 other elements of which Victor L. Wooten talks about and we don’t. Stuff like “phrasing”, “technique”, “feel” and all those other things that are equally important as notes in making music. I love this quote from the DVD : “What distinguishes an average trumpet player from someone like Miles Davis ? Not the notes : they both play the same notes. It’s the other elements that makes the difference !”.

So, music is more than just knowing the basic music theory. But at least, I hope it will help you to understand it, and more importantly, to listen to it more carefully.

Some disclaimers

1. I am not an accomplished musician or music teacher. I am an bluegrass banjo apprentice (with a very limited big-band jazz guitar background), who’s on a journey to be a better musician. I guess you are on a similar journey too, otherwise you wouldn’t read this blog. While I cannot give you guarantees, I’m quite sure that the theory you’ll find here is quite correct and solid.
2. This blog is about Basic Music Theory. In my mind that is stuff that any musician on an beginning or intermediate level should know. For more advanced subjects, like non-western scales and complex rhythms, I’m sure there are other sources to be found on the Internet.

So, without further ado, let’s get started. I realize this first chapter isn’t a full pomodoro, so what you can do to fill the remaining time of your 25 minutes, is get your guitar out, or sit behind your keyboard, and start playing “Do-Re-Mi” from the Sound Of Music !