Intervals II
We're now going to add some more intervals to our collection. First we'll add their definitions to our collection so far:
| Number of semitones | Abbreviation | Scale-degree / chord-tone | |
|---|---|---|---|
| Prime (unison) | 0 | P1 | 1 |
| Minor third | 3 | m3 | ♭3 |
| Major third | 4 | M3 | 3 |
| Perfect fifth | 7 | P5 | 5 |
| Octave | 12 | P8 or 8ve | 8 |
The Prime
This is an interval that doesn't get talked about very much. It describes a pitch's relationship with itself so there's usually not much point in talking about it.1 Although the interval isn't the subject of much dinner-table conversation, its corresponding scale-degree / chord-tone (1) appears in just about every scale / chord formula. There's not much more to say, in fact we're not even going to include any diagrams for it because that would just be a waste of pixels.
The Octave
This is a very special interval both acoustically and musically. Acoustically, it represents the relationship between any two notes one of whose vibrating frequency is double the other's.
We'll consider two different octave shapes: one that covers three strings, with the higher note on the higher fret:
and one that covers four strings, with the higher note on the lower fret:
Musically, two notes an octave apart within a musical structure will convey very similar musical ‘meaning’ despite the obvious difference in pitch. They will also have the same name.
To illustrate this, consider the following open position shape.
If we decide to add a G♯, it doesn't really matter which one we choose, we'll end up with a ‘bright’ major sound:
Conversely, if we decide to add a G, we get a ‘darker’, minor sound, whichever G we use.
This brings us on to the idea of Pitch Classes. The following notes, are all ‘E’ (they are separated by one or more octaves). They belong to the pitch-class of E. When we say, for example that a chord of C major comprises the notes C, E and G, what we really mean is that any combination of notes that contains one or more members of each of the pitch classes of C, E and G and no notes from outside of these pitch-classes can be called a chord of C Major.2
We usually don't include 8 when describing scales and chords because it is implied by 1. However it's traditional to include both the top and bottom root note when practising scales and arpeggios, so you should be familiar with the following major shapes.
And minor shapes.
These are extensions of the subshapes we looked at in our first lesson. Eventually, you'll want to be as adept at identifying a chord-notes3 in relation to 8 as to 1, in fact, for some intervals this is actually more convenient.
It was mentioned in a footnote in the first lesson that there are several incomplete subshapes. These are shapes that are missing one or more notes due to them ending up on strings that don't exist on a standard guitar (either higher than string 1 or lower than string 6). Although you don't need to memorise these at this stage, you should at least understand how they fit in to their parent shapes and how they relate to the ‘complete’ subshapes. I coloured the non-root notes in the previous section to be the sama as the lowest root so that these can be more easily compared.
Here are the incomplete ‘red’ major subshapes. Try not to be disconcerted by the fact that the first of these doesn't actually contain any red notes!
... the incomplete ‘blue’ major subshapes:
... the incomplete ‘red’ minor subshapes:
... and, finally, the incomplete ‘blue’ minor subshapes:
Some of these might seem a little pointless at the moment, especially those comprising a single note.4 However, as we add more notes to our shapes, they will start to make more sense. It would be a good idea to try to identify at least some of these incomplete subshapes in the full major and minor arpeggio shapes.5