Determining intervals
I would now like to present two methods for determining intervals:
1. Determining using the accompanying major scale
Example – E - G sharp:
Count off the E major scale up to the note that starts with G. E - F sharp - G sharp. G sharp is the third note, so it is a third. As only major and pure intervals occur in the major scales (counted from the keynote), this is a major third.
Example – E - G:
Count off the E major scale again. E - F sharp - G sharp. G sharp is the third note, so it is a major third. G is a half tone below G sharp, so the E - G interval it is a minor third.
Example – A - G sharp:
Count off the A major scale up to the note that starts with G: A - B - C sharp - D - E - F sharp - G sharp. The A - G sharp interval is a major seventh (once again: intervals within the major scales are always pure or major).
Example – F sharp - C:
Count off the F sharp major scale. F sharp - G sharp - A sharp - B - C sharp. F sharp - C sharp is a pure fifth, C is a half tone below C sharp, so there is a diminished fifth (a tritone). The fifth is a pure interval, so it cannot be major or minor.
Example – G flat - A double flat:
Count off the G flat major scale up to the note that starts with A. G flat - A flat, therefore a second. A double flat is a half tone below A flat, so we have minor second.
It is important with this method that you know all major scales by heart.
2. Counting off the whole and half tone steps
This method is not quite so easy, but in some instances you won’t know the major scales by heart. Or do you, for example, know the G sharp major, or even worse, the E double flat major scales? (To be quite honest with you, nobody does ;-)
So then, what do we do with the G sharp - E interval?
First of all, an overview:
| Interval | Number of whole and half tones |
|---|---|
| Minor second | 1 half tone |
| Major second | 1 whole tone |
| Minor third | 1 whole tone + 1 half tone |
| Major third | 2 whole tones |
| Fourth | 2 whole tones + 1 half tone |
| Tritone | 3 whole tones |
| Fifth | 3 whole tones + 1 half tone |
| Minor sixth | 4 whole tones |
| Major sixth | 4 whole tones + 1 half tone |
| Minor seventh | 5 whole tones |
| Major seventh | 5 whole tones + 1 half tone |
| Octave | 6 whole tones |
Example – G sharp - E:
G sharp - A = 1 half tone, A - B = 1 whole tone, B - C = 1 half tone, C - D = 1 whole tone and D - E = 1 whole tone.
Counted together this produces 3 whole tones and 2 half tomes, so 4 whole tones altogether. According to the table this is a minor sixth.
A small tip: Make the counting off easier for yourself – you could also count G sharp - A sharp as a whole tone. But you are probably more familiar with the C major scale (as I am). So better count G sharp - A as a half tone, and then continue counting in the C major scale. Then add together at the end.
Example – C sharp - H:
Count backwards here. B - C sharp is a whole tone. You know immediately, C sharp - C sharp is an octave. An octave (6 whole tones) minus a whole tone is a minor seventh (5 whole tones).
Example – D sharp - F sharp:
D sharp - E = 1 half tone, E - F = 1 half tone, F - F sharp = 1 half tone. Produces 1 whole tone and 1 half tone, so a minor third.
Example – C sharp - G sharp:
I use a little trick here. The C - G interval (from C major) is a fifth. Both notes are a half tone higher, so C sharp - G sharp is also a fifth.
So you see, with a little practice, this is also possible. The longer you work at it, the more you can learn the intervals by heart, and therefore determine them easier. But be careful – the difficulty is in the details, as it so often is. You really have to be careful with augmented and diminished intervals in particular. You can easily enharmonically mix up the intervals when counting off the half and whole tone steps. But don’t worry – first of all it is important that you know all about the minor, pure and major intervals. You’ll absorb the rest bit by bit. Not just like that of course; you’ve got to practice as well!
