A Simple Way of Calculating 7th Chords
A seventh chord in music theory is plainly a triad with the addition of the “7th interval” above the triad’s root. For example, the combination C, E, G, B is a seventh chord.
There are also different classifications of seventh chords. These are made by different combinations of Major, Minor, and Diminished sounds. Growing up, I had a hard time figuring these chords out, so I want to let you all know a simple system for calculating chord types.
Seventh Chord Types
There are 5 different types of seventh chords:
- Major Seventh
- Dominant Seventh
- Minor Seventh
- Half-Diminished Seventh
- Diminished Seventh
Each of these chords types are a combination of two parts: the triad + the seventh interval. This is particularly important to remember. I also highly suggest memorizing the order of sevenths I listed previously. This will make subsequent calculations easier.
The chord breakdowns can be generalized to the following:
- Major Seventh = Major Triad + Major Seventh
- Dominant Seventh = Major Triad + Minor Seventh
- Minor Seventh = Minor Triad + Minor Seventh
- Half-Diminished Seventh = Diminished Triad + Minor Seventh
- Diminished Seventh = Diminished Triad + Diminished Seventh
Going From Major to Diminished Seventh
I like to start all my calculations at the top. Let’s look at the easiest Major Chord: C. As we know from our key signature list, C has no sharps or flats. Therefore, the Major Seventh representation is: C, E, G, B.
From here, our job gets easier. First note that in order to move from a “more Major version” to a “more Minor version”, we can just flat specific notes. For instance, the major chord: C, E, G, becomes a minor chord when we flat E. Likewise, flatting the remaining top note, G, turns the chord into its diminished form.
i.e. C, E flat, G flat is c diminished
From this, we can see that we’re able to assign the location of flats as we move from Major to Minor.
Let C be equal to 1 and subsequent chord notes be a number higher than the previous. So for example, E is 2, G is 3, and B is 4. We can use these numbers to correspond to the steps we take in order to “minor” a chord.
In our original seventh chord – C, E, G, B – moving from Major Seventh to Dominant Seventh requires us to flat 4. To move from Dominant Seventh to Minor Seventh, we need to flat 2. To turn the Minor Seventh into a Half-Diminished Seventh, we need to flat 3. Finally, we flat 4 again to turn the seventh note into a diminished form.
If you look closely, I’m just “algorithmizing” the steps in the chord breakdown I listed above. In other words, when you start from a Major Chord (since it’s the easiest to remember), we can follow the “flatting” order: 4, 2, 3, 4 in order to move from a Major Seventh to a Diminished Seventh chord.
Let’s try a harder example.
From B Major to B Diminished Seventh
- We know that B Major has 5 sharps. This means we’re working with: B, D sharp, F sharp, A sharp
- To go from Major to Dominant, we just flat the 4: B, D sharp, F sharp, A
- Dominant -> Minor, flat the 2: B, D, F sharp, A
- Minor -> Half-Diminished, flat the 3: B, D, F, A
- Half-Diminished -> Diminished, flat the 4: B, D, F, A flat
And that’s it! You can use this method on any type of seventh chord. I usually like using this method because I remember the Major Key Signatures the best. It saves me a lot of time to start off with what I know and then work down the ladder to what I want.
Please make sure that when you’re doing this calculation, you’re working in Root form. You will get faulty results when applying this algorithm on inversions since this is assuming we’re in Root Position.
For example… when a problem asks for a diminished chord on: E, G, A, C (the second inversion on A), you must convert your chord to A, C, E, G before applying the algorithm. After your calculation, you can add the correct accidentals in inverted form.