Intervals
Once you've finished this lesson, you'll be able to measure an interval in degrees and name it, whether it goes up or down.
An interval is the distance between two sounds (§ 76). You measure it by the number of degrees it contains, counting both the lower and the upper note, and that number gives the interval its name.
Ascending or descending
An interval is ascending when you measure it from low to high, so the first note named is the lower one. It is descending when you measure it from high to low, so the first note named is the higher one (§ 77). Unless stated otherwise, an interval is always taken as ascending (§ 78).
The unison
Before we name the intervals, one special case. A unison is the same sound produced by several voices or instruments. Danhauser points out that the unison is not an interval, since there is no distance from a sound to the same sound, just as in geometry there is no distance from a point to itself (§ 79).
The names of intervals
| Degrees included | Name | Example from C |
|---|---|---|
| 2 | second (2nd) | C-D |
| 3 | third (3rd) | C-E |
| 4 | fourth (4th) | C-F |
| 5 | fifth (5th) | C-G |
| 6 | sixth (6th) | C-A |
| 7 | seventh (7th) | C-B |
| 8 | octave (8ve) | C-C |
| 9 | ninth (9th) | C up to the next D |
| 10 | tenth (10th) | C up to the next E |
| ... | eleventh, twelfth, and so on |
Descending intervals
For a descending interval, you count the degrees starting from the upper note (§ 81). From E down to G, you count E, D, C, B, A and G. That makes six degrees, so it's a descending sixth.
- Steps
- 5 letter names, from C4 to G4
- Make-up
- 3 whole steps and 1 diatonic half step
- Half steps
- 7 half steps on a keyboard
- Inversion
- perfect fourth
- Type
- perfect consonance
Write out the table of interval names starting from D, then from A.
Name the interval between the two notes of each group (taken as ascending).
You can now name any interval by its number. Check your counting with the quiz, and then we'll go on to the quality of intervals.