View source for 1st and 2nd Strings - Intervals


Playing on a single string is a complete pain.  You are constantly changing positions, restricted to simple melodies, and cannot create any harmony.  Let's add another string: the 2nd string or B string.

 fig. 1
 e--0--1--3--5--7--8--10--12--
 b--0--1--3--5--6--8--10--12--
    e  f  g  a  b  c  d   e
    b  c  d  e  f  g  a   b
   
If you look at the frets that fall in the C major scale, you'll notice this is identical to the 1st string frets, except here we use the 6th fret instead of 7th.  On the 1st string, that note is a B - the leading tone, which is a semitone below the tonic note.  Here, that note is an F, the 4th.

Remember that the 1st string is tuned a fourth above the 2nd string.  E is a fourth above B.  As we go up the fretboard, we see each note on the 2nd string has its relative 4th directly above it on the 1st string.  Starting with open we have:

 fig. 2 
{| class="wikitable"
|-
! Fret !! 2nd String !! 1st String
|-
|  0  || B || E
|-
| 1 || C || F
|-
| 3 || D || G
|-
| 5 || E || A
|-
| 6 || F || 
|-
| 7 ||   || B
|-
| 8 || G || C
|-
| 10 || A || D
|}

== Intervals ==
Two notes form an interval.  The distance between them determines what they are called and what they sound like.  Understanding intervals IS understanding harmony.  Let's look at all the possible intervals.

{| class="wikitable"
|-
! Root Note !! Other Note !! Semitones from Root to Other !! Interval Short Name !! Interval Full Name
|-
|  C  || C  || 0  || U  || Unison
|-
| C  || Db || 1  || m2 || Minor 2nd
|-
| C  || D  || 2  || M2 || (Major) 2nd
|-
| C  || Eb || 3  || m3 || Minor 3rd
|-
| C  || E  || 4  || M3 || Major 3rd
|-
| C  || F  || 5  || P4 || (Perfect) 4th
|-
| C  || F# || 6  || T  || Augmented 4th/Diminished 5th/Tritone
|-
| C  || G  || 7  || P5 || (Perfect) 5th
|-
| C  || Ab || 8  || m6 || Minor 6th
|-
| C  || A  || 9  || M6 || Major 6th
|-
| C  || Bb || 10 || 7  || (Dominant) 7th
|-
| C  || B  || 11 || M7 || Major 7th
|-
| C  || C  || 12 || U  || Unison or Octave
|}


Where the names have ()'s around a word in the description, that word is commonly optional.  Major 2nd, perfect 4th, perfect 5th, and dominant 7th are all implied by 2nd, 4th, 5th, and 7th.  Also, when we may occasionally omit the major/minor descriptor.  For instance, we may say that C - E is a 3rd without qualifying whether it is a major third or minor third.  Or we may say we're going to play a harmony line a 3rd above any given melody; this will likely include both major and minor thirds.  Let's look at the intervals from two different perspectives inside the key of C Major:

{| class="wikitable"
|-
! Root Note !! Other Note !! Semitones from Root to Other !! Interval Short Name !! Interval Full Name
|-
| C  || D  || 2  || M2 || (Major) 2nd
|-
| C  || E  || 4  || M3 || Major 3rd
|-
| C  || F  || 5  || P4 || (Perfect) 4th
|-
| C  || G  || 7  || P5 || (Perfect) 5th
|-
| C  || A  || 9  || M6 || Major 6th
|-
| C  || B  || 11 || M7 || Major 7th
|}

fig.5
{| class="wikitable"
|-
! Root Note !! Other Note !! Semitones from Root to Other !! Interval Short Name !! Interval Full Name
|-
| A || B || 2  || M2|| (Major) 2nd
|-
| A || C || 3  || m3 || Minor 3rd
|-
| A || D || 5  || P4 || (Perfect) 4th
|-
| A || E || 7  || P5 || (Perfect) 5th
|-
| A || F || 8  || m6 || Minor 6th
|-
| A || G || 10 || 7 || (Dominant) 7th
|}

Inside any particular major key, every note has a different set of intervals.  C and A share the major 2nd, perfect 4th, perfect 5th but have different 3rd, 6th, and 7th intervals.  Let's hear some of the different intervals:

 fig. 6
 e-0--0--0--0--0--0--0--0--0--0--0--0--0--
 b-5--6--7--8--9--10-11-12-13-14-15-16-17-
   u  m2 M2 m3 M3 P4 T  P5 m6 M6 7  M7 o

Figure 6 starts on E on both the 1st and 2nd strings.  The 2nd string moves up on fret each time: F, F#, G, G#, A, etc.  This allows us to hear all the intervals named in figure 3 above; however, unlike figure 3 we are hearing them all against E, not C.  That we are using E instead of C is immaterial.  The intervals have their own unique sound, and a major 3rd between E and G# will sound the same compared to a major 3rd between C and E.  Only the pitches are different; the relative distance and harmonic interaction between each pair of notes is the same.

The line below the tab indicates the interval.  Notice how nasty the m2 and T intervals are.  the M7 can also be a bit nasty, but because there's more space between the notes, it sounds less harsh.

Let's look at only the intervals listed in figures 4 and 5:

 fig. 7
 e-0--0--0--0--0--0--0--0--
 b-5--7--9--10-12-14-16-17-
   u  M2 M3 P4 P5 M6 M7 o

 fig. 8  
 e-0--0--0--0--0--0--0--0--
 b-5--7--8--10-12-13-15-17-
   u  M2 m3 P4 P5 m6 7  o
  
Notice the difference in the 3rds, 6ths, and 7ths.

Time for an exercise.  Let's play the C major scale with a constant interval above it.  First in 4ths:

 fig. 9
 Perfect 4th           Tritone
 |o|-|  |i|-|  |m|-|   |-|i|  |-|m|  |-|r|
 |o|-|  |i|-|  |i|-|   |o|-|  |i|-|  |m|-|
 open      other       open      other

 fig. 10
 e-1--3--5--7--8--10-12-13
 b-1--3--5--6--8--10-12-13-
   P  P  P  T  P  P  P  P
  
And 5ths:
 fig. 11
 Perfect 5th         
 |-|-|m|  |-|-|r|  |-|-|p| 
 |o|-|-|  |i|-|-|  |i|-|-| 
 open          other     

 fig. 12
 e-3--5--7--8--10-12-13-15
 b-1--3--5--6--8--10-12-13-
   P  P  P  P  P  P  T  P

Those Perfect 5ths are also called "power chords", which is a staple of rock and roll music.  They might sound a little weird on the 1st and 2nd strings, but try playing around with that shape on the 5th and 6th strings!

Playing the 4th or 5th intervals on a melody line isn't very interesting - you almost always have a perfect 4th or 5th.  Let's try thirds:

 fig. 13
     Major 3rd          Minor 3rd
 |o|-|-|  |i|-|-|   |o|-|-|  |i|-|-|
 |-|i|-|  |-|m|-|   |-|-|m|  |-|-|r|
  open     other     open     other

 fig. 14
 e-0--1--3--5--7--8--10-12-
 b-1--3--5--6--8--10-12-13-
   M  m  m  M  M  m  m  M
  
In some cases, we're using major 3rds, and in some cases minor 3rds.  Now that was a little more interesting!

One last thing about intervals - the name used is determined whether you are calculating the distance above or below a given pitch.  For example, G is 7 semitones above C, making it a Perfect 5th above C.  However, it is only 5 semitones below C, making it a perfect 4th below C.  Similarly, a G is a perfect 5th above C, but a C is only a perfect 4th above G.  Typically, we default to above and use the lowest of the 2 pitches in question as the base.  For example, if we are playing a C on the 2nd string in open position with the E on the 1st string above it, we would call that a Major 3rd, not a Minor 6th.

== C Major Scale on the 2nd String ==

 fig. 15
 b-0--1--3--5--6--8--10-12-13-
   b  c  d  e  f  g  a  b  c
  
Armed with this knowledge, let's play a song...

== Hot Cross Buns, Championship Editition ==

 fig. 16
   1   2   3   4  |1   2   3   4  |1 n 2 n 3 n 4 n|1   2   3   4  |
   q   q   h      |q   q   h      |e e e e e e e e|q   q   h      |
 e-0--------------|0--------------|---------------|0-------0------|
 b-----3---1------|----3---1------|1-1-1-1-3-3-3-3|----3---1------|

This is the same melody as before, but now we can play it in the key of C major.  It's a bit more difficult because you have to make sure you are playing the 2nd string most of the time, but occasionally play the 1st string.  And notice we end the song here with the C - E major 3rd interval to spice it up just a tad.

Let's add some more intervals:

 fig. 17
   1   2   3   4  |1   2   3   4  |1 n 2 n 3 n 4 n|1   2   3   4  |
   q   q   h      |q   q   h      |e e e e e e e e|q   q   h      |
 e-4---2---0------|4---2---0------|0-0-0-0-2-2-2-2|4---2---0------|
 b-4---4---0------|4---4---0------|0-0-0-0-0-0-0-0|4---4---5------|

We are back in the key of E major and have the same melody on the E string, but the B string is doing something a little different.  There's a little more depth to the piece now.  Is that a good or bad thing?  It's not necessarily either.  Some melodies are suitable for rich harmony, but simple ones like this are usually fundamentally changed if such were added.  For instance, try the following:

 fig. 18
   1   2   3   4  |1   2   3   4  |1 n 2 n 3 n 4 n|1   2   3   4  |
   q   q   h      |q   q   h      |e e e e e e e e|q   q   h      |
 e-4---2---0------|4---2---0------|0-0-0-0-2-2-2-2|4---2---0------|
 b-4---4---4------|2---2---2------|4-4-2-0-0-0-2-2|4---0---1------|

Ok, that's weird, right?  Sounds almost like a different song.  But again the melody is exactly the same.

== Homework ==
Practice the above figures.  Try to play in time, and play ascending and descending, but make sure to get comfortable with the fingerings before trying to play with a metronome.  Play figures 16 and 17 with a metronome, and try to improve timing and speed.  Figure 18 play slow and just try to hear the song - don't worry about playing it in-time just yet.