Intervals


(entry for 8/23/2024)



A lot of musicians think that intervals— that is, distances between pitches— are defined by sound. If you’re studying ear training, that’s true. But in all other musical studies, it’s not true! Intervals are defined by how they’re ‘spelled.’ That is, they’re defined by the names of the notes involved.

For example, the distance from middle C to the F-sharp above has to be some kind of fourth, because there are four letter names involved: C, D, E, and F. ( Assuming treble clef.)




But the distance from middle C to G-flat is a fifth, because there are five names involved: C, D, E, F, and G.  (Again assuming treble clef.)


Yet the two intervals are identical in sound, because on a keyboard or other keyed or fretted instrument, the F sharp and the G flat are the same note.

There are many other examples of this phenomenon, but before we get to them, we need to cover some definitions.

‘Major,’ when it comes to intervals, simply means ‘larger.’ It has nothing to do with the idea of major sounding ‘happy’ and minor sounding ‘sad.’ In fact, it has nothing to do with sound at all! It simply means ‘larger than minor.’ 

‘Minor’ means ‘smaller.’ Again, this has nothing to do with sound. It simply means ‘smaller than major.’ (As in calling a child a ‘minor,’ because they’re smaller than they will be as an adult.) Since the two definitions create a circular logic, we need some examples. (Being sure to remember that intervals are named for the number of note names involved.)

Let’s say you go from middle C up to the next E. That’s obviously a third, because the names involved are C, D, and E. But going from middle C to E-flat is also a third, because the same three letters are involved. Of the two similarly spelled intervals, the one from C to E is called a ‘major’ third, because it is larger than the other one. (That is, the notes are farther apart on a keyboard.) Similarly, from C to E-flat is called a ‘minor’ third. (Because the notes are closer together.) 

The same principle applies to sixths. From middle C up to A is a major sixth. From middle C up to A-flat is a minor sixth. This has nothing to do with happy or sad. Most listeners say that both intervals sound equally ‘happy’ to them. The major and minor in this case have only to do with larger and smaller. Both are ‘assonances’ or ‘consonances,’ both of which are the opposite of ‘dissonances.’ (Dissonance in music means ‘discordant’ or ‘clashing.’ Try playing a ‘B’ and a ‘C’ together. You’ll cringe. It’s a ‘dissonant’ interval. Try playing a middle C together with C an octave higher. It sounds great. In fact it sounds so great that it’s hard to tell you’re playing two notes at once. It’s an ‘assonance’ or ‘consonance.’)

But a fourth is neither major or minor. If you play middle C with the F above, that’s obviously a fourth, because there are four names involved, as specified in the second paragraph. But if you play C and F-sharp, that’s a dissonance. It sounds ‘whine-y’ or ‘sour.’ It needs to be ‘resolved’ to a nicer sound. Our ears demand it. So the only fourth that is assonant or consonant is the one from C to F-natural. Therefore it is called ‘perfect.’ Neither major nor minor.

The same situation applies to the fifth. From C to G is a fifth. If the upper note is G-flat, that’s a dissonance. If you go C up to G-sharp, that sounds like a minor sixth (C to A-flat). So there is no major or minor fifth. Again, the name is ‘perfect.’

Any interval can be ‘stretched’ or ‘shrunk.’ A stretched interval is called ‘augmented.’ A shurnken interval is called ‘diminished.’ An example of a diminished interval would be from C-sharp up to E-flat. It has to be a third, because there are three note names involved. But it’s smaller than a minor third, so it’s diminished. (And it sounds like a major second, so in ear training, we’d call it that.) Likewise, from C up to A-sharp is an augmented sixth, because it’s larger than a major sixth. (If it’s spelled the more normal C up to B-flat, it’s a minor seventh.)

The two examples at the top of this post (below the second and third paragraphs) are therefore an augmented fourth and a diminished fifth. The very first example, before the title of the post, is (assuming treble clef again) a doubly-diminished fourth, because it’s even smaller than a diminished fourth! (It sounds like a minor third.)

Doubly-diminished and doubly-augmented intervals (such as D-flat up to A-sharp, which is a doubly-augmented fourth, sounding like a major sixth), are the practical limit. Theoretically there are such things as triply- and even quadruply- modified intervals, but in actual practice they will almost never be used.

To summarize, the intervals from a unison (both notes the same) to an octave (both notes the identical name but an octave apart) and in increasing order of size are: (lowest note first)

middle C and middle C (perfect unison)

middle C and C-sharp (augmented unison)

middle C and D-flat (minor second) – sounds the same as the augmented unison

middle C and D (major second)

middle C and D-sharp (augmented second) – sounds the same as the minor third

middle C and E-flat (minor third)

middle C and E (major third)

middle C and F (perfect fourth)

middle C and F-sharp (augmented fourth)

middle C and G-flat (diminished fifth) – sounds the same as augmented fourth

middle C and G (perfect fifth)

middle C and G-sharp (augmented fifth) – sounds the same as a minor sixth

middle C and A-flat (minor sixth)

middle C and A (major sixth)

middle C and A-sharp (augmented sixth) – sounds like a minor seventh

middle C and B-flat (minor seventh)

middle C and B (major seventh)

middle C up to C-flat (diminished octave) – sounds like a major seventh

middle C and the next C up (perfect octave)

When you leave the word ‘perfect’ off the name of the interval, that’s not a problem. People will know what you mean. But you can’t leave the word ‘major’ or ‘minor’ off, because with seconds, thirds, sixths, and sevenths, you need to know what kind. (‘Perfect’ is not an option for those.)

The intervals that are considered consonant or assonant are the perfect ones, plus major and minor 3rds and 6ths. (And their octave extensions, the 10ths and 13ths.) All the others are dissonant, though we’ve become so used to the minor seventh that it sounds almost assonant at times. (This will be covered much later in a post about types of chords.)

You don’t have to use middle C as the bottom note. You can start on any note of any pitch, whether natural, sharp, or flat, and go the proper distance up, and still have the same interval name. For example, from E up to F is a minor second. From G up to D is a fifth (perfect fifth). From D up to C-sharp is a major seventh. Etc.

One of my favorite sayings is ‘Music is not math, and math is not music.’ This business about interval names is a perfect example. In math, we don’t start counting with zero, we start with one. From three to five is only two numbers. We start on three, and count ‘one, two” as we move up to five. Five minus three is two. But in music we count the first note also, so from A to E is a fifth, even though E is only four letters up from A.  A fifth minus a third is another third!

That’s why we call B to B an octave, even though the second note is only seven notes higher than the first. Music is not math.  An octave plus another octave is a fifteenth, not a sixteenth. (Count the letters if you don't believe me.)

One more concept to be grasped before we move on to the next post, concerning transposition, is the matter of 'steps.' For example, from C to D is a 'whole step,' because there is another note in between. On a keyboard instrument, between the 'white' C and the 'white' D, there is a 'black' note called either C-sharp or D-flat. (I put the white and black in quotes, because many keyboards use other colors. There are even some with the colors totally reversed.) Fretted instruments don't use colors, but any guitarist knows there's another fret between the fret used for C and and the one used for D. On the other hand, there's no other note or fret between the one used for E and one used for F. We call that a half step. (There is also no note between B and C. Another half step.)

If you go up a major scale, the first two steps are whole steps. The next one is a half step. Then three more whole steps. Then a final half step. The sequence is different in minor scales, but the idea is similar.  The distance between C and E, therefore, or between F-sharp and A-sharp, is two whole steps, which we already know is also known as a major third. (Music is not math.)  Between E and G, however, or B and D, is a minor third, and comprises a whole step plus a half step or a half step plus a whole step. Take your pick! These concepts will become very important when we get eventually to chord construction. But before we get there, we need to talk about transposition, which puts this interval business to very good use

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