Which to Learn?

Question: I was about to memorize the number and types of intervals in the scales.

Then I noticed this distinction between keys and scales.

Any key (major or minor) comprises just 7 notes.

But a scale comprises 8 notes – we repeat the tonic note to make up an octave when playing our scales.

The consequence is that the number of the generic types of intervals varies according to whether you consider the key or the scale.

To illustrate I will use key and scale of C major – “ST” means “semitone”.

C major Key: C-(2xST)-D-(2xST)-E-(1xST)-F-(2xST)-G-(2xST)-A-(2xST)-B
C major Scale: C-(2xST)-D-(2xST)-E-(1xST)-F-(2xST)-G-(2xST)-A-(2xST)-B-(1xST)-C

It can be seen from the above that:

Type of Interval Number In Key Number In Scale

Seconds (1–2xST) 6 7
Thirds (3–4xST) 5 6
Perfect Fourth (5xST) 3 4
Tritone/Aug 4th/Dim 5th)(6xST) 1 (F-B) 1
Perfect Fifth (7xST) 3 4
Sixths (8–9xST) 2 3
Sevenths (10–11xST) 1 2

So, which should one concentrate upon: the key or scale intervals?

– Andrew Hart (Australia)

Albert’s reply: By semitones and 2x semitones, you’re referring to half steps and whole steps. (Half steps and whole steps are explained in detail in the lessons on how to play a piano scale and music modes.) I don’t entirely follow your table, but my explanation should resolve any confusion.

Let me simplify the task by way of example. I’ll also use C major since it’s so easy to visualize. The interval from the first note of a scale (called the tonic) to the second is a second – in this case, C to D. The interval from the tonic to the third note is a third – in this case, C to E. Similarly, the interval from the tonic to the fourth note of the scale is a fourth – C to F in this case – and so on.

To simplify even further, always count the starting note when determining the interval between two notes. Also, to determine the number of the interval (unison, second, third, fourth, etc.), strip the notes of any accidentals (sharps, flats and naturals) and only concentrate on the letters. So, to find the interval between C and F-sharp, discard the sharp for the time being and count C, D, E, F for a total of four notes – a fourth. (C to F-sharp happens to be an augmented fourth.) To find the interval between C and F, again simply count C, D, E, F: a fourth (in this case a perfect fourth).

For the interval between, say, E-flat and C, just count E, F, G, A, B, C for a total of six notes – a sixth (in this case a major sixth). For C down to E-flat, do the exact same: You can count up from E-flat to C – the interval is exactly the same. (Note that descending intervals are not the same as inverted intervals – these will be dealt with separately.)

It’s important to note that the type or quality of interval – diminished, minor, perfect, major, augmented – is different from the numeric value of the interval. It is the type of interval that depends on the exact number of half steps. There is a very technical way of determining exact intervals (involving both diatonic and chromatic intervals), but I’d prefer to spare my students complicated technicalities. It’s best to learn the intervals within the major scale:

Thus, the interval between the first note (tonic) and sixth note of a major scale is a major sixth; the interval between the tonic and fourth note of a major scale is a perfect fourth, and so on. I’ll provide more comprehensive details in an extensive lesson on intervals.