The Ultimate Guide To Guitar. Chapter II: 1 Scales - Diatonic Scales In Theory

author: ZeGuitarist date: 12/01/2008 category: the guide to
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Part II - Chapter 1

"Scales - Diatonic Scales In Theory"

Hi all! Welcome to Part II of the Ultimate Guide to Guitar! You can now all call yourself novice players... And I promise you that this part is going to be a lot more exciting than the Beginners part! Why? Because, in the Beginners part, I taught you some basic theory and techniques so you can learn how to do stuff. The why, however, was always "for later"... I figured, all a beginning guitar player wants to do is learn how to play, without trying to understand the theory behind what you are doing! Well, I think it's time to move past that stage, so from now on I'm going to deliver you the full story on everything... Like in Part I, Part II will start with a couple of theory chapters, and after that some technique chapters. In Part I, the theory chapters consisted of a chapter on chords followed by a chapter on scales. This time, we will do it the other way around: the scales chapters first, then a chapter on chords... Why change the order, you might think? Well, actually it's more logical to learn scales first and then chords, because the chords theory is based on scales. For the Beginners part, I made an exception though: beginning players can learn chords first so that they are able to play songs straight away, and they don't have to know all the theory behind it to do this! But, as I said, we are past that now... So, scales! Where do we start? There's a lot of theory behind scales, and only when you understand all this, we can start implementing this knowledge in our guitar play in practice. That's why this chapter is the first of 2 scales chapters. In this one, we will look into scales theory only. In the next one we will look into practice: how to use scales for soloing! We will reach far beyond the basic knowledge you now have from the Beginner articles... So after these 2 articles, you will be able to play more advanced improvised solos! OK, what are we going to learn in this chapter? 1. Intervals: before learning scales, we need in-depth knowledge of the notes and the spaces in between, called "intervals"... 2. Definition of scales: the full definition this time! 2. Major scales: then, we will learn the intervals that define a major scale 3. Minor scales: next, the intervals that define a minor scale, and how major and minor scales relate OK! Let's get going...

Intervals

Do you remember the easy definitions I gave you in the Beginner scales chapter? If you do, you know that (diatonic) scales consist of 7 notes. You may also remember, that there are 12 existing notes to choose from:
C   C#   D   D#   E   F   F#   G   G#   A   A#   B
Db Eb Gb Ab Bb
Now, if you want to construct a scale with 7 out of these 12 notes, you pick one of these notes as a "root" note for your scale. For example, we are going to construct the scale of C Major, so we take C as the root note. Which other notes go with the root note to form the Major scale with that particular root? Well, this is pre-defined by the distances between the notes. For example, in a Major scale, the 2nd note is 2 semitones higher than the root note. The 3rd note is 2 semitones higher than the 2nd note, this is 4 semitones up from the root... So you see, that you construct scales by using notes with a certain distance from one another. These distances or "intervals" between the notes, are therefore so important in scales (and chords!) theory that they are given specific names. The given names are based on the distance between a note and a certain "root" note. I will now give you a complete list with the names of the intervals between notes, and then explain them to you.
Semitones    Interval
-----------------------
0 Unison
1 Flat 2nd
2 Natural 2nd
3 Minor 3rd
4 Major 3rd
5 Perfect 4th
6 Flat 5th (or: Diminished 5th, Augmented 4th)
7 Perfect 5th
8 Minor 6th (or: sharp 5th, Augmented 5th)
9 Major 6th
10 Minor 7th (or: Flat 7th)
11 Major 7th
12 Octave
Note: this table of intervals is from the lesson "Guide to Chord Formation" written by 0000409D. I didn't "steal" it, however, because intervals are uniformly named all over the world. I also slightly adapted the table. I did "borrow" his table layout though, because it was easy to read! Kudos to him... These are all the intervals you'll need when constructing scales. How are we going to use this table? Well, a minute ago we took C as a "root" note. Every other note will now have a relative distance in semitones from the root note! All you need to do is look at the scala of 12 possible notes, and count! For example:
  • D is 2 semitones up from C: C-C#-D
  • G is 7 semitones up from C: C-C#-D-D#-E-F-F#-G
  • See? Easy isn't it... Now, to give these intervals names, all you have to do is look at this table and give the interval the name that matches the distance in semitones! I'll take the same 2 examples:
  • D is a "natural 2nd" up from C (2 semitones)
  • G is a "perfect 5th" up from C (7 semitones) You may be wondering, why is a distance of 7 semitones called "perfect 5th" an not "perfect 7th" or something? That makes no sense... Well, it will start making sense when I show you how to use these intervals to construct a scale starting from any root! Therefore, we need to apply our knowledge of intervals to define scales... So, in the next paragraph, I give you the full and uncensored definition of a scale!

    Definition Of Scales

    Again, I'm going to ask you to recall an old definition. Remember what I used to say about scales? Scales are constructed of notes that "sound good together"... I told you then, that this definition was incomplete because I never said why they sound good together. Well, now we will find out! Finally, we're done with giving half definitions! Here is the full and correct definition of a scale: "A scale is a combination of notes based on a "root" note and a pre-defined series of intervals from that root note." So, according to this definition, intervals are the foundation to scales! A "pre-defined series of intervals" decides which notes fit into a scale with the root note... Which intervals are used depends entirely on which type of scale you are trying to construct. A Major scale doesn't use the same notes as a Minor scale with the same root, because a different scheme of intervals is used. However, every Major scale uses the same intervals, no matter what root you choose, and the same goes for Minor scales! I will now demonstrate this by explaining how to construct Major scales in the next paragraph, followed by the construction of Minor scales in the following paragraph.

    Major Scales

    Like I said, every Major scale is based on the same scheme of intervals. In this paragraph, I will first define Major scales using intervals, and then provide a couple of examples. A. Definition of Major scales In the following definition of a Major scale, you will learn what intervals are used in a Major scale: "Major scales are constructed of:
  • A root note
  • A natural 2nd
  • A major 3rd
  • A perfect 4th
  • A perfect 5th
  • A major 6th
  • A major 7th
  • An octave"
  • Using the table of intervals, you can easily find out the distance to the root note for each note in the scale, in semitones. Now you also know, why the interval names were numbered, for example "3rd", "4th", and "5th"... Because they are the 3rd, 4th, 5th note in a scale! So, the scale is defined by a scheme of 7 intervals. (Note that I included the octave in the definition, but because the octave is the same as the root note, there are only 7 "distinct" notes in the scale...) Now, using the above definition we can find every note in the scale by counting upwards from the root note. It may be easier and less laborious, though, if you count up from the previous note each time. Here is a scheme that shows the number of semitones ("st") between each note, based on the above definition:
    1     2     3     4     5     6     7     1
    \2st/ \2st/ \1st/ \2st/ \2st/ \2st/ \1st/
    This scheme is easier to remember: just remember that the notes in the Major scale are all separated by 2 semitones, except between notes 3-4 and 7-8, which are only 1 semitone apart. OK! We know now the distances between the notes in the Major scale... It's important to understand that this series of intervals defines the scale. You can take any root note, apply this scheme to find the 6 other notes in the scale, and that's the only solution. There's only one Major scale for every root note, and it's defined by the intervals given! I will give some examples. B. Examples of Major scales Because it's the first time we are going to construct a scale, I'm going to give you 3 examples! The first one is the easiest: the C Major scale. Then, I'll give you 2 examples that are slightly harder... You'll soon see why! C Major scale OK, so we want to construct the C Major scale. Where do we start? I'll give you a step-by-step guide so you can see how we find every note in the scale, counting up from the root note:
  • The first note is the root note, which is of course C. To find the other notes, we simply count up from C... Use the "scala of 12 notes" in the beginning of the lesson to count up, if you can't remember the notes.
  • The second note is the "natural 2nd" from C. A natural 2nd corresponds with 2 semitones, so we count 2 semitones up from C to find the 2nd note in the scale: D!
  • Similarly, we find the 3rd note in the scale by counting up a "major 3rd", or 4 semitones, from C: this brings us to E!
  • The next note is a "perfect 4th" or 5 semitones up from C, which is F.
  • The 5th note is a "perfect 5th" or 7 semitones up from C: this is G.
  • The 6th note is a "major 6th" or 9 semitones up from C, which is A.
  • And the 7th note is a "major 7th" or 11 semitones up, which is B.
  • To complete the circle, an octave or 12 semitones from C is, again, C! And voila, we have our C Major scale:
    C D E F G A B C
    Now, we found every note in the scale by counting upwards from the root note. We can find the notes in the Major scale faster, however, if we used the scheme that counts upwards from the previous note instead of the root note. For the scale of C Major, this would be:
    C     D     E     F     G     A     B     C
    \2st/ \2st/ \1st/ \2st/ \2st/ \2st/ \1st/
    You got that? That wasn't so hard, was it? Now, I specifically chose to construct the C Major scale first, because it uses only "natural" notes (no flats or sharps). If you choose another root, however, you will find that the use of flats and sharps is necessary! I'll give you an example of each: the G Major scale, which uses 1 sharp note, and the F Major scale, which uses 1 flat note. G Major scale We now know how to construct a Major scale based on any root... So, if we can do it for C, we can do it for G too! Below is the G Major scale:
    G     A     B     C     D     E     F#    G
    \2st/ \2st/ \1st/ \2st/ \2st/ \2st/ \1st/
    This is a correct Major scale, because we used the same scheme of semitones (counting up from the previous note) as the scheme of semitones of the C Major scale we just constructed. The intervals match, so it must be correct! Note, however, that in this scale there is an F#. Why is that? Well, if you used the "regular" F instead the scheme of intervals would be different:
    G     A     B     C     D     E     F     G
    \2st/ \2st/ \1st/ \2st/ \2st/ \1st/ \2st/
    The distances between the notes aren't the same anymore! In other words, it wouldn't be a Major scale anymore, but something different, something wrong! The sharp is used to "correct" this deviating scheme of intervals, so that you get the Major scheme again... Got that? Of course, if you know how to count, you don't even have to worry about this. Just use the "scala of 12 notes" I provided to count the distances and you get the correct notes automatically:
    C   C#   D   D#   E   F   F#   G   G#   A   A#   B
    Db Eb Gb Ab Bb
    4 5 6 7 1 2 3
    The underlined notes are the notes used in the scale! Simply start from the root, G, and count up 2 semitones to find A, another 2 semitones to find B, 1 semitone to find C, and so on... You can't go wrong if you construct scales this way! F Major scale The same goes for the F Major scale! This time, not a sharp but a flat is used to correct the intervals, but the purpose is the same: to return to the Major scale interval scheme we know!
    F     G     A     Bb    C     D     E     F
    \2st/ \2st/ \1st/ \2st/ \2st/ \2st/ \1st/
    The B flat (Bb) "corrects" the interval scheme so that we have a correct Major scale. If you didn't use the flat note, you would get this:
    F     G     A     B     C     D     E     F
    \2st/ \2st/ \2st/ \1st/ \2st/ \2st/ \1st/
    You see? This demonstrates how every Major scale uses the same scheme of intervals between the notes, no matter which root note you choose. Every Major scale uses different notes, a different number of flats or sharps, but in every Major scale the distances between the notes are the same! Got that? Then we can move on to Minor scales, which work exactly the same way! Note: You may be wondering after reading this: why does the G Major scale use a sharp and not a flat? And why doesn't the F Major scale use a sharp like the G Major scale, but a flat instead? Why is it that some scales use sharps to correct the intervals, and others use flats? And which scales use which? If you want to know this, I included an appendix explaining this (rather complicated) piece of music theory.

    Minor Scales

    OK! We know how to construct a Major scale! All you need to know, really, is the scheme of intervals that defines the notes in the scale. This is true for Minor scales too! In this paragraph, I will first give the definition of a Minor scale. Then, I'll give an example by constructing the A Minor scale... And last, I will explain to you how Major and Minor scales are somehow related! A. Definition of Minor scales "Minor scales are constructed of:
  • A root note
  • A natural 2nd
  • A minor 3rd
  • A perfect 4th
  • A perfect 5th
  • A minor 6th
  • A minor 7th
  • An octave"
  • You can see a couple of differences with the Major scale in this definition. The Minor scale uses a minor 3rd, 6th and 7th, where the Major scale uses the Major counterparts. The most important thing to remember is this:
  • A Major scale has a major 3rd, a Minor scale has a minor 3rd
  • Both a Major and Minor scale use a perfect 5th Why these 2 things are more important than the other differences/similarities, you will find out later... For now, just remember! Again, this scheme is easier to remember if we counted upwards from the previous note instead of from the root note. The distances in semitones ("st") between each note and the previous one can be seen on this scheme:
    1     2     3     4     5     6     7     1
    \2st/ \1st/ \2st/ \2st/ \1st/ \2st/ \2st/
    Minor scales consist of notes that are all 2 semitones apart, except for notes 2-3 and 5-6, which are only 1 semitone apart. Notice the difference with the Major scale? Like I said, a scale is defined by the intervals between the notes. This scheme is what makes a Minor scale "minor", the Major scheme is what makes the Major scale "major"! Good! Now I'm going to apply this scheme to the root note A to construct the A Minor scale as an example... B. Example of Minor scales This time, only one example should be enough to help you understand the construction of Minor scales. We are going to use the root note A, and construct the scale by counting up from the root note like this:
  • The first note is the root note, which is A. To find the other notes, we simply count up from A...
  • The second note is the "natural 2nd" from A. This is 2 semitones, so we count 2 semitones up to find B.
  • Similarly, we find the 3rd note in the scale by counting up a "minor 3rd", or 3 semitones, from A, which is C.
  • The next note is a "perfect 4th" or 5 semitones up from A, which is D.
  • The 5th note is a "perfect 5th" or 7 semitones up from A: this is E.
  • The 6th note is a "minor 6th" or 8 semitones up from A, which is F.
  • And the 7th note is a "minor 7th" or 10 semitones up, which is G.
  • And we're back to the beginning with an octave or 12 semitones from A which is, again, A... And there's our A Minor scale:
    A B C D E F G A
    We will find the same notes, if we use the other interval scheme, the one that counts upwards from the previous note:
    A     B     C     D     E     F     G     A
    \2st/ \1st/ \2st/ \2st/ \1st/ \2st/ \2st/
    And there! We now know how both Major and Minor scales are constructed! We're almost finished... But there's still something very important I haven't explained yet! C. Major and Minor relative scales Notice that the A Minor scale is constructed out of natural notes only, no flats and no sharps... Just like the C Major scale, isn't it? So we have 2 different scales, a Major and a Minor, both based on a different root, but constructed of the exact same 7 notes... These scales are called "relative scales". Just like C Major and A Minor, there is a relative Minor scale for every Major scale and vice versa. From the notes that compose a Major scale, you can always compose 1 (and only 1!) Minor scale, and the other way around... In short, scales come in pairs of a Major and a Minor! So, how do you know which Major scale relates to which Minor scale? The answer is very easy:
  • If you have a Major scale and want to know the relative Minor scale: the 6th note in the Major scale is the root of the relative Minor. For example, the 6th note in the G Major scale is E, so the relative Minor is E Minor.
  • If you have a Minor scale and want to know the relative Major scale: the 3rd note in the Minor scale is the root of the relative Major. Same example: the 3rd note in the E Minor scale is G, so the relative Major is G Major.
  • Now, why are these scales related? The answer is easy too. Just look at the intervals: you take the Major scale, take the 6th note and pretend it's the root. The intervals in the scale that starts on this new "root" are the intervals that define a Minor scale. Conversely, you can take the 3rd note of a Minor scale and pretend it's the root of a Major scale, and the intervals will fit perfectly!

    Conclusion

    OK! We can now construct Major and Minor scales, and we know how they are related! We are finished for this week... Although we haven't learned how to use this knowledge for your guitar playing yet! Don't worry, next week I will teach you the practical aspects of scales: the shapes of the Major and Minor scales' notes on the fretboard, and how to use both scales in solos! I hope you enjoyed this lesson as much as I did (it's a real joy digging into stuff I learned YEARS ago!), and I hope you are actually learning something... See you all next week! Cheers! ZeG

    Appendix

    This appendix goes a little deeper into the correct construction of scales using sharps and flats. In practice, this theory isn't as important as the rest of this lesson, but it's interesting to know and I do advise you to read it! In this section, we will learn which scales have sharps in them and which have flats, and how many. To understand this, I will first explain what enharmonics are. Then, I will explain how you know which key uses sharps/flats and how many, using the "Circle of Fifths"... And last, I will look into "enharmonic equivalents". Confused? Well, this appendix is here to clear it all up for you... A. Enharmonics First, I'll explain what enharmonics are. This is a very easy explanation... Why they are important, however, is not that easy to understand; it's the reason I have to write this appendix! Enharmonics are notes with a different name, but the same pitch. For example, F# and Gb are notes with the same pitch, but as you see there are 2 different names for that note. In music theory, they are even considered to be 2 entirely different notes, although they sound exactly the same. Other examples: C# and Db, E# and F, E and Fb, B# and C, B and Cb, ... Now, why are enharmonics important? Well, when constructing a Major or Minor scale, you need to make sure that they are "diatonically correct". This means, each note should be used once and only once. You have to make sure there is an A, B, C, D, E, F and G in each scale, possibly with flats or sharps, but never 2 notes with the same name in one scale. I will give a "wrong" example and a "right" example to clarify. The scale of F Major in a diatonically "incorrect" way:
    F     G     A     A#    C     D     E     F
    \2st/ \2st/ \1st/ \2st/ \2st/ \2st/ \1st/
    As you can see, the intervals are correct, so this is a "valid" F Major scale. However, there is something wrong with it. You can see that the A note is used twice ("natural" A and A#), and B isn't used at all. This is a diatonically incorrect F Major scale. How do we solve this problem? Just replace the diatonically incorrect note (in this case, the extra A) with an enharmonic: A# becomes Bb. And voila, you now have a diatonically correct scale with each note used once and only once!
    F     G     A     Bb    C     D     E     F
    \2st/ \2st/ \1st/ \2st/ \2st/ \2st/ \1st/
    In the case of F Major, it's an easy job figuring out where the flats and sharps are supposed to be, because it has only one. Other scales, however, use 3, 4, 5 or more sharps/flats, and putting them all in the right place by "trial and error" can be tough! Fortunately, there are rules for the placement of sharps and flats for each key. B. The Circle of Fifths There is a very easy way of remembering which scale uses which sharps/flats: it's called the "Circle of Fifths". In this paragraph, I will explain how the Circle of Fifths works. Below is an image of the Circle of Fifths (thanks to Wikipedia): That looks complicated doesn't it? Don't worry, here's the explanation. The Uppercase letters represent Major keys, the lowercase letters are the relative Minor keys. To understand how the Circle of Fifths works, we are going to start from the top (12 o'clock) position, and follow it both clockwise and counterclockwise.
  • In the clockwise direction, every key is a perfect 5th higher than the previous one, and uses 1 sharp note more than the previous one. So, we start at the key of C Major, which has no sharps or flats. If we move clockwise, we go up a perfect 5th to the key of G Major, which uses 1 sharp (F#). The next key is the key of D Major, which uses 2 sharps (F# and C#), and so on...
  • In the counterclockwise direction, every key is a perfect 5th lower (or perfect 4th higher) than the previous one, and uses 1 flat note more than the previous one. So, we start at the key of C Major, which has no sharps or flats. If we move counterclockwise, we go down a perfect 5th (or up a perfect 4th) to the key of F Major, which uses 1 flat (Bb). The next key is the key of Bb Major, which uses 2 flats (Bb and Eb), and so on...
  • Note: the same goes for Minor keys, of course, you just look at the lower case letters! So, it's kind of obvious where the name "Circle of Fifths" comes from: every next step in the Circle is a perfect 5th higher/lower than the previous one. Now you can use the Circle of Fifths to know how many sharps/flats a scale has... But wait, we don't know which notes are sharp/flat! How do we figure that out? That's relatively easy too:
  • Sharps are assigned in the following order: F#-C#-G#-D#-A#-E#-B#. This means, if you take A Major for example, which has 3 sharps, the 3 sharp notes will be F#, C# and G#. Note that this sequence of sharps is, again, a sequence of ascending perfect 5ths: if you start from F#, a perfect 5th up is C#, next is G#, and so on...
  • Flats are assigned in the following order: Bb-Eb-Ab-Db-Gb-Cb-Fb. This means, if you take Ab Major for example, which has 4 flats, the 4 flat notes will be Bb, Eb, Ab, and Db. Note that this sequence of flats is, again, a sequence of descending perfect 5ths (or ascending perfect 4ths): if you start from Bb, a perfect 5th down is Eb, next is Ab, and so on... Note also, that the sequence of flats resembles the sequence of sharps, but in reversed order!
  • There you go! From now on, when you construct a certain scale or use a scale to play in a certain key, you will know which sharps/flats are used in that scale. Conversely, you can derive which key a certain piece of music is played in when you know which sharps/flats are used. This concept is used in sheet music: at the beginning of the score, a series of sharps/flats indicate which notes are sharp/flat in this entire music piece. This indication is called the "key signature" of the music piece, because it defines the key of the piece. For example, if a music piece starts with the following key signature: ... the key will be A Major or F# Minor, because these are the scales that use 3 sharps! Got it? C. Enharmonic equivalents One more thing, before I conclude this appendix and this article. Most of the time, you will be able to construct only 1 "diatonically correct" scale for a certain root. For some root notes, however, there are 2 possibilities, called "enharmonic equivalents":
  • The B Major (or G# Minor) scale, which uses 5 sharps, and the Cb Major (or Ab Minor) scale, which uses 7 flats, are enharmonically equivalent. This means, they are constructed of notes with different names, but the same pitch! See for yourself:
    B Major:     B   c#  D#  E   F#  G#  A#  B
    Cb Major: Cb Db Eb Fb Gb Ab Bb Cb
    As you can see, all the notes in these 2 scales are each others enharmonics!
  • Same goes for the F# Major (D# Minor), with 6 sharps, and Gb Major (Eb Minor) scale, with 6 flats.
  • Also, the same goes for the C# Major (A# Minor), with 7 sharps, and Db Major (Bb Minor) scale, with 5 flats.
  • In the Circle of Fifths, these enharmonic equivalents are also included. If you follow the Circle clockwise, you will notice that the keys with 5, 6 and 7 sharps overlap with the keys with 5, 6 and 7 flats. These keys are the enharmonic equivalents: B and Cb, F# and Gb, and C# and Db. A last note: because B uses only 5 sharps as opposed to its enharmonic equivalent Cb with 7 flats, the key of Cb will be replaced by B most of the time. The same goes for Db (5 flats) replacing C# (7 sharps). For Gb and F#, it doesn't matter, because they both use 6 flats/sharps.
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