I made a lot of mistakes on my homework. This is because there are actually several different ways to write chords:

Name	Notation
Major	Cmaj7, Cma7, C△7
Dominant	C7
Minor	Cmin7, Cmi7, C-7

I made the mistake that the major and dominant chords were the same, but they are not. For example, a Cmaj7 has the notes C E G B and a C7 has the notes C E G B♭.

This is because chord notation uses scale degrees and not the minor or major intervals. Scale degrees and intervals are correlated and are sometimes the same, but they can also be different. For example, Cmin9 would use the notes C E♭ G B♭ D and not C E♭ G B♭ D♭. Note the use of D, as it’s the 9th scale degree even though the minor 9th is technically D♭

Slash chords add another arbitrary note to the bottom of the chord. For example, Cmaj7/E is E C E G B.

You can also think of 251s as jumping 4ths between the root notes. For example, the 251 in Cmaj is D to G, then G to C.

Assignment: Find the 251s in the keys Gmaj and Amaj

• Gmaj: Amin7 (A, C, E, G) → D7 (D, F#, A, C) → Gmaj7 (G, B, D, F#)
• Amaj: Bmin7 (B, D, F#, A) → E7 (E, G#, B, D) → Amaj7 (A, C#, E, G#)