Applying Intervals to Chords
In: Music Theory
Someone recently asked me how musical intervals apply to chords. For example, if you have a chord formula that goes 1-3-5-♭7-9, and you want to build the chord on the root of A♭ how do you determine which notes are in that chord? Or maybe you discovered a chord that has the notes F-A♭-C-E♭, and you want know its intervals to determine the chord type. This article will address these problems.
If you are unfamiliar with the technicalities of musical intervals, I recommend you read this article before continuing.
Determining Note Letters from Intervals
There’s a lot of ways to do this, but the easiest way is probably just to determine the notes relative to the major scale.
Let’s say we have the following intervals:
1 – b3 – 5 – b7
Now, if we want to find the chord that follows that formula and has a root of F, what we need do is first determine the F major scale:
F – G – A – Bb – C – D – E
Now keeping in mind that the formula for the major scale is…
1 – 2 – 3 – 4 – 5 – 6 – 7
…we can simply pull notes with the same interval numbers as in the formula from the F major scale, and alter them based on the formula’s accidentals. If that sounds confusing it should make more sense with an example:
The first note should be obvious, F. The second note in the formula is a ♭3 or minor third, but the F major scale we’re using has a major third (in F Major this note is A). Since we need a minor third all we do is lower the A by one semitone to arrive at A♭. If the formula had called for a ♯3, then we would have used A♯, because an augmented third is one semitone above a major third.
Continuing this we arrive at the perfect fifth (5), which is a C. Finally, the minor seventh (♭7) is E♭.
So the final chord is:
F – Ab – C – Eb
Determining Intervals From Note Letters
Now let’s look at the opposite direction. Let’s say you came up with the following chord:
B – D# – F# – G#
…and needed to determine its intervals (most likely to determine what type of chord it is).
You could do this by doing the exact opposite of what I described in previous section, or I think there’s an easier way… Simply count the number of semitones between each note and the root, and then apply the information in the table to the right. Please note that this method will only work right if the chord is in its root inversion. If not you will end up with incorrect intervals.
So using our example, our root B would be 1. The next note, D♯ is 4 semitones above B, which means that it is a Major third. Next, F♯ is 7 semitones above B, which means that it is a Perfect 5th. Finally, G♯ is 9 semitones above B, which means that it is a Major 6th.
So we have the following intervals:
1 – 3 – 5 – 6
…and we can now determine the type of chord type, which in this case happens to be a Major 6th chord. If you’re looking for a reference of chord types and intervals, you might want to check this out.