Intervals III
Just three more intervals to learn before we look at our archetypal jazz chord types. Again, we'll begin by adding the definitions to those we've already encountered:
| Number of semitones | Abbreviation | Scale-degree / chord-tone | |
|---|---|---|---|
| Prime (unison) | 0 | P1 | 1 |
| Major Second | 2 | M2 | 2 |
| Minor third | 3 | m3 | ♭3 |
| Major third | 4 | M3 | 3 |
| Perfect fifth | 7 | P5 | 5 |
| Major Sixth | 9 | M6 | 6 |
| Minor Seventh | 10 | m7 | ♭7 |
| Octave | 12 | P8 or 8ve | 8 |
The Major Second
This interval is also known as the tone1 so it may come as no surprise to learn that it is equivalent to two semitones. The most obvious way to invoke this on the guitar is to play two notes on the same string 2 frets apart:
The alternative shape is to have the higher note on the next higher string:
I beseech, nay implore, ye to become as familiar with this shape as with the its one-string counterpart. Knowing this shape is, in my opinion, key to understanding and navigating musical structures on the guitar fretboard.
With this in mind, try the following exercises:
- Starting somewhere on the 6th string, play a sequence of notes, each one a M2 higher than its predecessor but confine yourself to a 4-fret section on the fretboard (e.g. frets 4 to 8). This will involve alternating the two M2 shapes shown above except that sometimes you will have to play the one-string form twice in succession. This is known as the whole-tone scale.
- The same as the previous exercise but start on the 1st string and work your way down to the 6th.
Incidentally, this is the first of our intervals that is traditionally considered to be a ‘discord’. It's all a bit subjective, but most people find that if you play the two notes of the 2-string M2 shape together the effect is mildly unpleasant.
The Major Sixth
This interval can be thought of as the ‘sum’ of a P5 and a M2. Although there's a version of this interval that spans only two strings, we'll ignore that for now and concentrate on the version that spans three. Given our previous shapes, we can achieve this by combining either the ‘2-string’ P5 shape and the ‘2-string’ M2 shape:
Or the ‘3-string’ P5 shape and the ‘1-string’ P2 shape
Either way, we end up with the following forms:
The Minor Seventh
This interval can be thought of as the ‘sum’ of a P5 and a m3 but you'll probably find it easier to think of it as an octave ‘minus’ a M2. Given our previous shapes, we can achieve this by combining either the ‘3-string’ P8 shape and the ‘1-string’ M2 shape:
Or the ‘4-string’ P8 shape and the ‘2-string’ P2 shape
Either way, we end up with the following forms:
Any two intervals that add up to an octave (like the m7 and the M2) are known as complementary intervals. Complementary intervals share certain characteristics so, for example, the m7 and the M2 are both mildly dissonant and considered to be discords. We could have defined the M6 as a P8 minus a m32 (which means they are complementary). These are both known as ‘imperfect concords’, that is, they have a full, rich sound when their component notes are played simultaneously. We'll talk a little more about these concepts when we have introduced all our intervals.