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:
| 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 |
Contents
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
| Root Note | Other Note | Semitones from Root to Other |
Interval Short Name | Interval Full Name | Just Intonation Ratio |
|---|---|---|---|---|---|
| C | C | 0 | U | Unison | 1:1 |
| C | Db | 1 | m2 | Minor 2nd | 16:15 |
| C | D | 2 | M2 | (Major) 2nd | 9:8 |
| C | Eb | 3 | m3 | Minor 3rd | 6:5 |
| C | E | 4 | M3 | Major 3rd | 5:4 |
| C | F | 5 | P4 | (Perfect) | 4:3 |
| C | F# | 6 | a4, d5, tt | Augmented 4th/ Diminished 5th/ Tritone |
45:32 |
| C | G | 7 | P5 | (Perfect) | 3:2 |
| C | Ab | 8 | m6 | Minor 6th | 8:5 |
| C | A | 9 | M6 | Major 6th | 5:3 |
| C | Bb | 10 | m7 | (Minor) 7th | 9:5 |
| C | B | 11 | M7 | Major 7th | 15:8 |
| C | C | 12 | U | Unison or Octave | 2:1 |
Where the names have ()'s around a word in the description, that word is optional, and often omitted. Major 2nd, perfect 4th, perfect 5th, and minor 7th are all implied by 2nd, 4th, 5th, and 7th.
Let's hear some of the different intervals:
fig. 2 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
Figure 2 starts 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 common note of E, not C. That we are using E instead of C is immaterial. 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.
Diatonic Intervals
Also, 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 3rd or minor 3rd. Or we may 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 seen below.
Let's look at the intervals from two different perspectives inside the key of C Major:
| 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 |
| 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 | (Minor) 7th |
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 tables 2 and 3:
fig. 3 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. 4 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. Figure 5 shows chord charts for how to finger the 4th intervals in open and other positions.
fig. 5 Perfect 4th Tritone |o|-| |i|-| |m|-| |r|-| |-|i| |-|m| |-|r| |-|r| |o|-| |i|-| |i|-| |m|-| |o|-| |i|-| |m|-| |i|-| open ------ other ------ open ------ other ------
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.
fig. 6 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:
fig. 7 Perfect 5th |-|-|m| |-|-|r| |-|-|p| |o|-|-| |i|-|-| |i|-|-| open other
fig. 8 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:
fig. 9 Major 3rd Minor 3rd |o|-|-| |i|-|-| |o|-|-| |i|-|-| |-|i|-| |-|m|-| |-|-|m| |-|-|r| open other open other
fig. 10 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.
| Interval | m2 | M2 | m3 | M3 | P4 | tt | P5 | m6 | M6 | m7 | M7 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Inversion | M7 | m7 | M6 | m6 | P5 | tt | P4 | M3 | m3 | M2 | m2 |
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.
fig. 11 d----2--------2-- a-2--2-----3--3-- e-0--------0----- P5 P4 m6 M3
Figure 11 first 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
fig. 12
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
fig. 13 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. 14 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. 15 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.