Figuring out the scale degrees in a secondary chord can be challenging because it requires relating two different scales. In Chapter 2, we constructed three secondary chords (V/V, V⁷/IV, and V/vi) on a piano to determine their scale degrees. In this appendix, we’ll show you an alternative way to figure out the scale degrees for any secondary chord that makes use of the Hooktheory staff.
First, consider the Hooktheory staff showing the seven scale degrees of the major scale.
An important thing to remember is that the scale degrees are not evenly spaced. (If we look at a piano, some of the notes have black keys in between them.) Here is the C major scale on the piano:
Notice how, for example, scale degrees 3 and 4 are right next to each other (E and F), but scale degrees 2 and 3 are not (there’s an E♭/D♯ in the middle). We can make these gaps explicit on the Hooktheory staff by adding space when there is a note in between two scale degrees that aren’t in the scale. When we do this, you get the following expanded staff:
When composing in Hookpad, you can switch to the expanded staff in the settings.
V/V chords are built off the major scale centered around the V chord (the 5th scale degree). If we line up another major scale starting from scale degree 5 of the original major scale, we can see how the notes in the two scales relate to one another:
The V chord of the new scale has scale degrees 5, 7, and 2, as shown below.
By looking at how these scale degrees from the second scale line up with the original scale, we can see that scale degree 5 lines up with scale degree 2 and that scale degree 2 lines up with scale degree 6. Scale degree 7 isn’t in the original scale at all; it’s between scale degrees 4 and 5 in the original scale, and we have indicated this by coloring the note with alternating green and blue.
The scale degree between 4 and 5 can be written in two ways. You can write it as a as a half-step higher than 4 and label it ♯4. Alternatively, you can write it as a half-step lower than 5 and label it ♭5. Which one should we use? A simple rule to determine which labeling is correct is that the scale degrees that make up a chord must always skip a numbered scale degree between each note. A chord built off scale degree 2 always has some kind of scale degree 4 and 6 in it (it skips scale degrees 3 and 5). This is how we know that V/V contains scale degrees 2, ♯4, and 6 (and not 2, ♭5, and 6). It’s the same reason we know that a D major chord contains an F♯ in it and not a G♭. All D chords (regardless of the quality), must contain some kind of D, F, and A in them (skipping E and G).
This technique can be used to determine the scale degrees of any secondary chord. We’ll do this one more time, this time figuring out the scale degrees of the V/iii chord:
