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A Slash Chord is a chord where the bass note - the lowest note heard in a chord - is different from the root note. In D Maj and D Maj7, usually the lowest note of the chord would be the note D:
However, with Slash Chords, there is a different note at the bottom, which is depicted by a slash after the main chord. The way you write a slash chord is: main chord / bass note.
This is read and spoken as “main chord over bass note”. So, for example, if you wrote the D Maj7 chord above (D-F#-A-C#) as DMaj7/A, it would look like this:
Slash chords are sometimes thought of as a simpler, more modern way to write chord inversions than the more complicated figured bass style.
Slash chords like D/F# also allow us to go all the way from D to G with a step in between, so it’s not as big of a leap in the bass note. Example: D – D/F# – G – A (Thinking out loud - Ed Sheeran).
A Suspended Chord is unique because it’s not made from 3rds. Chords made by stacking 3rds are called tertian chords, and Suspended chords are non-tertian.
Instead, a suspended chord has a note within it that is “suspended” either a 4th or a 2nd above the root note. For example, starting on the note G, a typical G Maj chord would be G – B – D.
Suspended Chords are chords where the middle note (the 3rd) is suspended in between the root and the 5th. There are two types of suspended chords: the sus2 and the sus 4.
A suspended chord keeps the two outer notes (the G and the D), but the B is changed for the note either a 4th above G or a 2nd above G. The note a 2nd above G is A, and the note a 4th above G is C, so the two suspended G chords are G – A – D and G – C – D:
Depending on whether the suspended note in the chord is a 4th or a 2nd above the root note of the chord we label it either sus4 or sus2.
Of the two, the sus4 version is much more popular – so much so that if you ever see the chord just written as Gsus (or Esus, Dsus, etc.) it will be the sus4 version.