Beginner Intervals

author: DarthPew date: 11/07/2012 category: for beginners
rating: 8.9 / votes: 21 
Beginner Intervals
Hello all, just a heads up before you read on, I will state one more time this article is for Beginners. I got some e-mails concerning intervals, and so this is my response to those who need help building their foundation for those curious about my "How To Play Modes" and "How To Use Modes" articles. So this article is just strictly about finding your intervals based on a root note. I'll probably have made this article longer than I wanted to, but I would like to make sure the guitar players out there, especially the beginners are able to catch on to the number formulas circulating around my articles, whether it be chords, scales and your favorite, modes.

Let's get rolling then?

There are exactly 12 notes in music. They are as follows:
A  A#/Bb  B/Cb  B#/C  C#/Db  D  D#/Eb  E/Fb  E#/F  F#/Gb  G  G#/Ab
The "/" just means that these notes are enharmonically the same. Enharmonic means it's a different way of spelling/saying one note that sounds the same. Without enharmonics, there are two ways of looking at these notes in a semi-tone way: With flats:
A  Bb  B  C  Db  D  Eb  E   F  Gb  G  Ab
With sharps:
A  A# B  C  C#  D  D#  E  F  F#  G   G#
Hopefully, I explained it well enough for you to see that there are only 12 notes in music, and that these notes are placed in an ascending chromatic order all in semi-tone intervals. Some schools teach it differently, but hopefully you understood my method. If you haven't, just re-read the previous paragraph, until you are sure you understand the concept. When you see a numerical formula, you will notice for certain numbers there may be a # (sharp) or a b (flat) right in front of it. That is merely to identify the INTERVAL from the root note. For example, let's take A major. The numerical formula would be:
1 2 3 4 5 6 7
And so the scale would have these notes:
A B C# D E F# G# A

So, let's go through the numerical formula one number at a time

Key:
  • One whole tone = 2 frets away from the original note you press
  • One semi-tone = 1 fret away from the original note you press (1): This number represents THE ROOT. On a guitar, when starting your scale, it should be the first note that you play, and since we're in the key of A major, the first note would be A, on the 5th fret of the E string. (2): This number represents the MAJOR SECOND interval from the root. What this means is that this number (2) is two semi-tones/a whole tone away from the number (1). This is represented by climbing up the fretboard by two frets (one semi-tone = one fret). So in this case, a whole tone would be the 7th fret, two fret positions away from the 5th fret of the E string, so this would be a B note. (3): This number represents the MAJOR THIRD interval from the number (1). This is represented by climbing two whole tones/four semi-tones from the root note, or one whole tone/two semi-tones from the number (2) note. So, in this case, from the 5th fret, two whole tones would be four fret away from the 5th fret, which would be the 9th fret of the E string, or the 4th fret of the A string. These are both the exact same notes, just played on different locations on the fret board. Give it a try, and you will see that (when your guitar is in regular tuning and has good intonation they sound exactly the same). This note is your C#. (4): This number represents the PERFECT FOURTH interval from the root number (1). This is represented by climbing two whole tones and a half/5 semi-tones away from the number (1) note or a semi-tone away from the number (3) note. So, by climbing the fretboard by 5 semi-tones (which is equal to 5 frets) away from the 5th fret of the E string, you get to the 10th fret of the E string which would be your D note. Alternatively, the 10th fret is quite a stretch from the 5th fret of the E string, so you may alternatively play the same note on the 5th fret of the A string. (5): This number represents the PERFECT FIFTH interval from the root number (1). This is represented by climbing three whole tones and a half/seven semi-tones from the root number (1), or a whole tone/two semi-tones away from the number (4) note. So if we translate this to the fretboard, from the 5th note, this number would be exactly 7 frets away from the 5th fret, that being the 12th fret of the E string, being an E note. You can alternatively play this note on the 7th fret of the A string, as they would be the same note. (6): This number represents the MAJOR SIXTH interval from the root number (1). This is represented by climbing four whole tones and half/nine semi-tones away from the root number (1), or a whole tone/two semi-tones away from the number (5) note. So if you climb nine frets on the guitar from the 5th fret, you get to the 14th fret which would be your F# note, alternatively played on the 4th fret of the D string, or the 9th fret of the A string. (7): This number represents the MAJOR SEVENTH interval from the root number (1). This is represented by climbing five whole tones and a half/eleven semi-tones from the root number (1), or simply climbing a whole tone/two semi-tones from the number (6) note. This is then in turn represented on the fretboard by climbing 11 frets away from the 5th fret, being the 16th fret of your fret board. This note would then be your G#, alternatively found on the 6th fret of the D string. (8): This number represents the OCTAVE interval from the root number (1). This is represented by climbing six whole tones/twelve semi-tones away from the root number (1), or one semi-tone from the number (7) note. This is represented by climbing 12 frets away from the 5th fret on the E string, being the 17th fret of the E string, or the 12th fret on the A string, or the 7th fret of the D string. These three fret positions then represent an A note of the same octave, and a whole octave higher than the first note we started on, which was the A located on the 5th fret of the E string That's all the intervals for a major scale! It only covers one octave, as I hope you can build/find the exact same intervals from the octave using this explanation. It's a bit long, but I hope it's easy and comprehensible. If you got lost however, I encourage you to not give up, and just scroll up to re-read everything I just wrote. So as you see, just because the numerical formula 1 2 3 4 5 6 7 8 doesn't have any sharps or flats, the A major scale is written "A B C# D E F# G# A" because the numbers only represent the intervals, and not if the note has a sharp. That's why when you see certain numbers with #'s (sharps) or b's (flats), it doesn't necessarily mean that these notes are sharpened or flattened. We'll see why right now, as I shall explain now the numerical formula for the minor scale. We shall see the A minor scale just so then we can compare it to the A major scale later. Here is the numerical formula:
    1 2 b3 4 5 b6 b7 8
    Here are the notes for A minor:
    A B C D E F G A
    The intervals are the same, albeit three new ones. I'll list them and explain in detail how far they are from the root note A found on the fifth fret of the low E string: (b3): This number represents a MINOR THIRD interval from the root note number (1). This interval is found one whole tone and a half/three semi-tones away from the root number (1), or one semi-tone away from the number (2) note. On a fretboard, this is represented by moving three frets away from the original root note, being the 5th fret of the E string, so this new note is found on the 8th fret of the E string, or alternatively the 3rd fret of the A string. These frets represent the C note of the same octave found on two different fret positions. (b6): This number represents a MINOR THIRD interval from the root note number (1). This interval is represented by moving away four whole tones/eight semi-tones away from the root number (1), or a semi-tone away from the number (5). In turn, this means that you move 8 frets away from the original root number (1) on the 5th fret of the E string, being the 13th fret of the E string, identified as the F note. This note is also found on the 8th fret of the A string. (b7): This number represents a MINOR SEVENTH interval from the root note number (1). This is five whole tones/ten semi-tones away from the original root number, or one whole tone/two semi-tones away from the (b6) number, or even considered one whole tone below the octave number (8). This is then, in this case represented by moving ten frets from the 5th fret of the E string, being the 15th fret of the same string. This is then known as the G note, which can also be played on the 10th fret of the A string, or 5th fret of the D string.

    So shall we see the difference between the major scale and minor scale?

    Major:
    1 2 3  4 5 6  7  8
    A B C# D E F# G# A
    Minor:
    1 2 b3 4 5 b6 b7 8
    A B C  D E F  G A
    As we can see, just because a number is identified by a b3, that doesn't necessarily mean the note is a flat note, it just means that the interval is a minor interval. In most schools of music theory, and I would like to believe that ALL music theory schools would agree that a flat number just identifies a minor interval. For ease, and recap, this is all the intervals I know that exist, and the number of semi-tones they translate to:
    Interval      Semi Tones   Whole Tones
         1       =      0      =      0
         b2      =      1      =      0.5
         2       =      2      =      1
       #2/b3     =      3      =      1.5
        3/b4     =      4      =      2
       #3/4      =      5      =      2.5
       #4/b5     =      6      =      3
         5       =      7      =     3.5
       #5/b6     =      8      =      4
        6/bb7    =      9      =     4.5
       #6/b7     =      10     =      5
         7       =      11     =     5.5
         8       =      12     =      6
    And there you have it. To build upon this foundation, I recommend you read my article "How to Play Modes Re-Vamped" so that you may further see these numerical formulas and get used to them, as if you continue to read my articles, they will be featured many a time, if not, always. Enjoy your playing, and thank you for the read! Remember, if you got lost, don't feel discouraged, it's either because you misunderstood something and got lost, or I probably should have explained something in more detailed way. In either case, just scroll back up to see where you got lost!
  • More DarthPew lessons:
    + How To Use Modes. Part 3 Guitar Techniques 04/05/2013
    + How To Play Modes Re-Vamped Guitar Techniques 10/08/2012
    + How To Use Modes. Part 2 Guitar Techniques 10/01/2012
    + How To Use Modes. Part 1 Guitar Techniques 09/20/2012
    + How To Play Modes Guitar Techniques 09/13/2012
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