I’m back with the third installment of my Music Theory Concepts series. For this article I would like to talk about intervals. In common terms, an interval is the relative distance from one pitch to another. Intervals determine chord types, scales/modes, and provide the basis from which key signatures are determined.

There are two basic types of intervals – minor and major.

For the sake of simplicity were going to work with the note C as the starting note. The note C looks like this:

The first interval is the minor 2nd. To figure out what note this is we first want to figure out what a 2nd from C is. Basically, all you have to do is count up from the C note, using C as 1. So, if C is 1, then D must be 2 (the 2nd), right?

Well done. But we still have to determine the minor or major part of the interval. This is where key signatures come in. If you remember my key signatures article (shame on you if you don’t), the list of pitches in Western Music is:

C – C#/Db – D – D#/Eb – E – F – F#/Gb – G – G#/Ab – A – A#/Bb – B/Cb

For now, think of a minor interval as working with half steps, and think of major as working with whole steps. It’s not quite that simple in the grand scheme of things, but in dealing with intervals of a 2nd the concept will do.

If we are trying to determine a minor second, you want to go up one half step from the starting note (C in this case), which brings you to C#/Db. A minor second from C is C#/Db. (Remember that C# and Db are enharmonically the same.) They are notated this way:

Since we moved up one half step to get the minor second, to get the major second we want to move up another half step. You can also think of it as moving up one whole step from the original note. This gives us the note D:

Often you will hear someone say “D natural.” It’s the same note; saying “natural” after the note name implies that the tone is neither sharp nor flat, but just the plain old generic note.

If we continue to the minor third, we move up another half step from D which gives us D#/Eb:

The Major third would be E (natural).

Is it making sense to you so far? I’m going to assume the answer is yes, which is great. You should go through the rest of the intervals up to the octave yourself. When you think you have all of the intervals figured out in the key of C Major, try to do the rest with ALL of the major keys.

Here is something interesting to point out. Take the minor third example (C to Eb), reverse the order of notes (Eb to C), and move the C note up an octave. It looks like this:

If you had done your assignment and finished the rest of the intervals on your own you’ll notice that this interval is a major sixth. The point behind this exercise is to understand the relationship between intervals. When you reverse the order of notes and displace the octave, a minor interval automatically becomes a major interval. Also, the intervals are correlative. Meaning:

2nd correlates to 7th
3rd correlates to 6th
4th correlates to 5th
5th correlates to 4th
6th correlates to the 3rd
7th correlates to the 2nd

• A minor third when inverted properly becomes a major 6th (C to Eb is minor third; Eb to C is a major sixth).
• A major second (when inverted properly) becomes a minor 7th (C to D is a major second; D to C is a minor seventh).

Those Damn Wrenches!

There are three more small wrenches to throw into the mix. I figured I would save them for last, just in case you thought you were actually getting a handle on intervals and how they work. These wrenches are three other types of intervals in addition to major and minor. These new interval types are:

Perfect intervals
Augmented intervals
Diminished intervals

The perfect intervals are easy. Perfect intervals really only refer to 4ths and 5ths, when the notes are in accordance with the key signature. So in the key of C, the interval from C to F is known as a perfect 4th. The interval from C to G is known as a perfect 5th. In Ab, a perfect 4th would be Db, and in E a perfect 5th would be B.

If you were raise the F in the first example to F# this interval (C to F#) would be considered an augmented 4th. In the jazz world you could call it a sharp 4 or a raised 4th. It’s also commonly referred to as a tritone in all forms of music. (Tritone implies a flatted fifth interval, which is enharmonically the same as a raised fourth. The tritone interval cuts the major scale precisely in half).

A diminished fifth would technically be the same as the augmented fourth, so from C the diminished fifth would be Gb.

(I’m sorry that I don’t have a concrete way of explaining this better than I have.)

In my opinion, augmented and diminished is only used when describing intervals of the fourth and fifth.

Here’s a quick recap list of intervals in the key of C:

C to Db = minor second
C to D = major second
C to Eb = minor third
C to E = major third
C to F = perfect fourth
C to F# = augmented fourth (raised 4th, sharp 4)
C to Gb = diminished fifth (flat 5th – enharmonically the same as C to F#)
C to G = perfect fifth
C to Ab = minor sixth
C to A = major sixth
C to Bb = minor seventh
C to B = major seventh

Going Beyond the Octave

Sounds like a bad Dr. Who episode or something. Anyway, music obviously doesn’t stop at the octave; otherwise music would be very boring. If you go one whole step higher than the octave C, you have the note D again. This note is nine steps higher from the original (root) note, so we call this interval a 9th.

• The 9th is the interval of a second displaced an octave higher.
• An 11th is the interval of a fourth displaced an octave higher.
• A 13th is the interval of a sixth displaced an octave higher.

There really are no 15th, 17th, or 19th intervals to speak of. The reason for this is if you were to spell out all of the notes in a scale as a chord (playing every other note in order rather than every note in succession) all of the notes would be used up by the time you got to the 13th (the 6th of the scale). A 15th would be two octaves plus a third higher from the root, so we just say E, two octaves higher and leave the math to the guys at MIT and Intel.

9th, 11th, and 13th intervals become way more exciting – and useful – when the topic of chords comes up, and I’ll be hipping y’all to that very soon, so stay tuned!