Difference between revisions of "1st and 2nd Strings - Intervals"

Revision as of 00:51, 22 February 2015

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.

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:

PreReqs

• Tuning and Harmonics
• 1st String

Intervals

Two notes form an interval. The distance between them determines what they are called and what they sound like when played together or in sequence. Understanding intervals IS understanding harmony. Let's look at all the possible intervals.

All Intervals

The intervals are numbered 2-7 corresponding to the common usage of Heptatonic (7-note) scales. A scale will typically use one of each of the numbers. For example, the common major scale uses M2, M3, P4, P5, M6, and M7.

Where the names have ()'s around a word in the description, that word is optional, and often omitted. Major 2nd, perfect 4th, and perfect 5th are all implied by 2nd, 4th, and 5th, as they are present in the common major as well as minor scales.

There are 5 different types of intervals:

• Augmented - One half-step larger than the corresponding major or perfect interval
• Major - The larger of the pair of 2nd 3rd, 6th, or 7th intervals
• Perfect - The harmonious 4th and 5th intervals near halfway between root and octave
• Minor - The smaller of the pair of 2nd 3rd, 6th, or 7th intervals
• Diminished - One half-step smaller than the corresponding major or perfect interval

The lower-pitched of the two notes is referred to as the root note. You'll notice the 4th and 5th intervals have the most harmonious ratios and reside near halfway between the root note and its octave. The tritone in the direct center is actually less harmonious than the neighboring 4th/5th. In the common major/minor scales, it appears in place of a 4th or 5th, so it is often regarded as a4/d5 rather than the tritone. The other numbered intervals come in pairs of major and minor, with the minor nearer the root and major further. Think minor = smaller and major = larger in terms of the distance between the component pitches.

Sometimes you may see interval names not listed above, like A6 (augmented 6th) or d7 (diminished 7th). Augmented simply means raised a half-step above a major or perfect interval and diminished means lowered a half-step below a minor or perfect interval. So an A6 is really the same interval as a m7, and a d7 is the same as a M6. The reason the alternate names are occasionally used is that the interval names are sometimes required to fulfill the practice of naming the intervals in a scale while using 2-7 once each, for more exotic scales. Also, interval names imply harmonic function - the alternate names suggest a different function from how such intervals usually act.

Let's play all of the different intervals:

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 tt P5 m6 M6 m7 M7 o

We start on E on both the 1st and 2nd strings. The 2nd string moves up one fret each time: F, F♯, G, G♯, A, etc. This allows us to hear all the intervals named in the tables above; however, we are hearing them all against the root note of E, not C.

That we are using E instead of C is immaterial. Remember: 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.

For now you should be mainly concerned with the sound and names of the intervals, not the pairs of notes involved in the example. The line below the tab indicates the interval. Notice how nasty the m2 and tt intervals are. the M7 can also be a bit nasty, but because there's more space between the notes, it sounds less harsh.

Eventually, you'll want to be able to know all the intervals in terms of every note. Like this:

Diatonic Intervals

When playing inside a certain scale or key, we may occasionally omit the major/minor descriptor and just say the interval number. For instance, I might to play the 6th above C without qualifying whether it is a major 6th or minor 6th. Or I might say we're going to play a harmony line a 3rd above any given melody, which will more than likely include both major and minor 3rds.

As mentioned above, common scales only contain 1 interval for each of the numbers 2-7. This applies not only to the root note of the scale, but to each additional note that is diatonic to (or part of) the scale. Each scale has its own set of diatonic intervals, just as it has diatonic notes.

Let's look at the intervals from two different perspectives inside the key of C Major:

Inside any particular major scale, every note has a different set of intervals for all the other notes in the same key. In C Major, C and A both have major 2nd, perfect 4th, perfect 5th intervals but have different 3rd, 6th, and 7ths. If we added a harmony line a 3rd above the melody, we'd have a major 3rd when the melody played C (C - E), but a minor third when the melody played A (A - C).

Let's look at only the intervals listed in the tables above:

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

E-0--0--0--0--0--0--0--0--
B-5--7--8--10-12-13-15-17-
  u  M2 m3 P4 P5 m6 m7 o
 

Notice the difference in the 3rds, 6ths, and 7ths.

Harmony in 4ths and 5ths

Time for an exercise. Let's play the C major scale with a constant interval above it. First we'll use 4ths. Chord charts for how to finger the 4th intervals in open and other positions are provided below.

o|-|
o|-|

|i|-|
|i|-| 

|m|-|
|i|-|

|r|-|
|m|-|

||i|
o|-|

|-|m|
|i|-|

|-|r|
|m|-|

|-|r|
|i|-|

These are pretty much the only ways to do it comfortably - you have a lot of options. Try them all and determine which one is the most comfortable for you. For the Perfect 4th that uses the index finger on both strings, you just flatten the finger, using your fingerprint to fret both strings. This breaks from the desired technique of using your finger tip, but it actually happens quite a lot and shouldn't be viewed with any kind of taboo.

  C4 D4 E4 F4 G4 A4 B4 C4
E-1--3--5--7--8--10-12-13
B-1--3--5--6--8--10-12-13-
  P  P  P  tt P  P  P  P

Notice the major scale only contains one tritone or augmented 4th. I find it's easiest to flatten the index finger and shift positions for each interval, but add the middle or ring finger for the tritone.

Let's try the same thing but using 5ths:

||-|m|
o|-|-|

|-|-|r|
|i|-|-|

|-|-|p|
|i|-|-|

  C5 D5 E5 F5 G5 A5 B5 C5
E-3--5--7--8--10-12-13-15
B-1--3--5--6--8--10-12-13-
  P  P  P  P  P  P  tt P

Very similar - only one tritone or diminished 5th (the fingering is the same as the example for 4ths). Again, it's easiest to use the index and ring fingers to make the perfect 5th shape and shift positions as you move up the fretboard, switching out the ring finger for the middle finger (or moving the ring finger back a fret) when you reach the tritone.

You may notice the 5ths sound rather similar to the 4ths. Remember that 4ths and 5ths are the most harmonious intervals, with ratios of 4:3 and 3:2, respectively.

Those Perfect 5ths are also called power chords, which are 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!

Harmony in 3rds

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 3rds:

o|-|
||i|

|i|-|
|-|m|

o|-|-|
||-|m|

|i|-|-|
|-|-|r|

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 is a little more interesting! Again, shift positions for each interval, leaving the index finger on the fretboard but shift between using the middle and ring fingers to make the major and minor shapes.

Intervals Above vs. Intervals Below and Inversions

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 refer to the interval above the root note and use the lowest of the 2 pitches (bass note) in question as the root. 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 is the root note and E is 4 half steps above C.

Calculating the interval the opposite way is called its inversion.

The 7ths/2nds, 3rds/6ths, and 4ths/5ths swap. This makes sense - the further a note is from some root note, the closer that note will be to the root note's octave. Yet notice the major intervals' inversions are minor intervals, the perfect intervals' inversions are also perfect intervals, and the tritone's inversion is also a tritone.

The major/minor swap may seem a little counter-intuitive at first. "Major" is often associated with harmonious and happy, while "minor" is associated with dissonant and dismal. That's more true of the major and minor keys than the intervals; however, I would even contest such a general statement. Songs in major keys can be sad and songs in minor keys happy given how they are written. Intervals are more basic, however. The major/minor label has less to do with their consonance and dissonance, then whether they are present in the major or minor scales. All the major/minor intervals in a major key against the root note are major, while 3/4 of the major/minor intervals are minor in a minor key.

Chords can be inverted without changing their harmonic function (although it does affect their percieved qualities), but intervals are a bit more sensitive. See the example below.

D----2--------2--
A-2--2-----3--3--
E-0--------0-----
  P5 P4    m6 M3

This demonstrates an E-B P5 interval and its inversion, a B-E P4 interval, then an E-C m6 interval and its inversion, a C-E M3 interval. Inverting the perfect intervals only create a slight difference in perception, while inverting 3rds or 6ths has a larger impact. The composer cannot simply swap them willy-nilly - they clearly have different qualities in terms of overall harmony although they do sound related.

C Major Scale on the 2nd String

B---0--1--3--5--6--8--10-12-13-
    B  C  D  E  F  G  A  B  C

Here's all the notes from the C Major scale on the 2nd string. Remember from the 1st String lesson that the notes can be grouped into sets of 3 for each position, with either a w/w, w/h, or h/w pattern.

h/w 0--1--3
w/w    1--3--5
w/h       3--5--6
h/w          5--6--8
w/w             6--8--10
w/w                8--10-12
w/h                   10-12-13

Armed with this knowledge, let's play a song...

Hot Cross Buns, Championship Editition

  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:

  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:

  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

Memorize all 11 intervals. Know that the intervals against the root in a major scale are M2, M3, P4, P5, M6, M7 - all major and perfect.

Play all the interval exercises above without a metronome - go slow and try to hear the sound of the intervals. Know how to finger the basic 3rd, 4th, and 5th intervals and play them ascending and descending the C Major scale.

Learn all the C Major notes on the B string. Play all the notes ascending 1 position at a time, like in the 1st String lesson, then try them descending.

Play Hot Cross Buns C.E. with a metronome, and try to improve timing and speed, except for the last example play slow and just try to hear the song - don't worry about playing it in-time just yet.

Q/A

Related Lessons

• Equal Temperament and Alternate Tunings
• Beginner Songs