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Intervals
A basic understanding of intervals is very important in understanding how music works and especially how Jazz theory works, as things in this genre of music do get particularly complicated. So here goes...
An interval is, in the most basic terms, the distance between two musical tones. It's that simple. Now it all comes down to understanding how to measure that distance and then learning everything so well that it becomes part of your own vocabulary. The smallest distance there can be between two notes (at least in western music) is a semitone or half-step. For example, every note on the guitar is a semitone apart the note next to it, a fret up or a fret down:
Now, if the distance of one fret is a semitone, two frets are a tone:
This is the second most basic interval and combined with the semitone they are also the building blocks of most scales, and the most basic one of all, the major scale. Now for the next section of this lesson, we are going to have a look at a major scale, and look at all the possible intervals that form in between the root and every other note in the scale. Look at the C Major scale below:
"W" represents a "whole-tone" distance between the two tones to its left and right and an "H" represents a "Half-tone", the two intervals we looked at before.
The diatonic intervals
Diatonic are the intervals which are formed between the root note of a scale and any of its tones, without altering (sharpening or flattening) any tones. Starting from the C (the root note), there are two semitones or half-steps to the next note which is D. These are C to C# and C# to D. We know this interval as a tone but it also has another name: Major 2nd. Now let's take the distance between the root note and the third note in the scale, the E. If we count the half-steps, there are four of them: C to C#, C# to D, D to D# and D# to E. This interval is called the Major 3rd. If we continue doing this process for all the notes in the scale, we come up with seven diatonic intervals and these are shown below with their names and distance in semitones from the root:
| Interval between notes... | Distance in semitones | Name of interval |
| C and D | 2 | Major 2nd |
| C and E | 4 | Major 3rd |
| C and F | 5 | Perfect 4th |
| C and G | 7 | Perfect 5th |
| C and A | 9 | Major 6th |
| C and B | 11 | Major 7th |
| C and C | 12 | Octave |
Of course you can do this for any scale, I was just using the C major scale as an example. You can also think of the diatonic intervals in a different way to make them easier to figure out. As an example, lets take two other notes, D and F#. Instead of counting all of the half-steps in between, just think of the D major scale and count which scale degree the F# is: D E F# G A B C# D (D major scale), so...the F# is the third degree, which makes the interval a Major 3rd. Now lets say you want the interval between F and Bb. First think of the F major scale: F G A Bb C D E F, then count to the Bb which is the fourth degree up the scale, which makes the interval a Perfect 4th.
Now let's try something different. Try to figure out what interval is formed between, lets say, a C and a Db. Here is the C major scale again: C D E F G A B C. Do you see the problem that arises? There is no Db in the C major scale. This is still an interval, just not a diatonic one...
Non-Diatonic intervals
A non-diatonic interval is the interval which is formed between two notes when the highest note of the two does not belong in the Major scale which has the first note as the root. Here is a table of all these intervals, taking C as the first note:
| Interval between notes... | Distance in semitones | Name of interval |
| C and C#/Db | 1 | Minor 2nd |
| C and D#/Eb | 3 | Minor 3rd |
| C and F#/Gb | 6 | Augmented 4th/Diminished 5th/Tritone |
| C and G#/Ab | 8 | Augmented 5th/Minor 6th |
| C and A#/Bb | 10 | Minor 7th |
Now, again, you don't have to think in terms of semitones to figure these out. Just think in terms of scale degrees. Let's say we want the interval between a D and an F. The D major scale is: D E F# G A B C# D, so there is no F natural, but there is an F# which is the third degree, i.e. it would form an interval of a Major 3rd with D; and what happens when we lower a Major 3rd by a semitone? It becomes a Minor 3rd. In the same way, lowering a Major 2nd makes it a Minor 2nd, raising a Perfect 4th makes it an Augmented 4th, lowering a Perfect 5th makes it a Diminished 5th or a Tritone (same thing), raising a Perfect 5th makes it an Augmented 5th, lowering a Major 6th makes it a Minor 6th and lowering a Major 7th makes it a Minor 7th...
So think of these in comparison to the diatonic intervals for some time, until you get used to them and they just come to you.
I hope everything got cleared up on the subject of intervals, if you have any questions please don't hesitate to use the Forum to ask, otherwise, just practice figuring out intervals for some time, perhaps on paper in the beginning but then in your head; it is only a matter of time before you know them all by heart