Cmaj7/B = C/B Slash Chord on Guitar

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Slash chord, „[1] major seven over [maj7]”. On the left side of the slash you can see a chord, on the right side the lowest tone (bass).

The [1]maj7 chord consists of the tones [1] (1), [3] (3), [5] (5) and [maj7] (maj7). Thus, the bass [maj7] is part of the chord. Since the bass on the right of the slash does not necessarily be part of the chord symbol on the left, the [1]maj7/[maj7] can also be notated as [1]/[maj7] chord. Depending on the context (chord progression) you may prefer either notation. You'll find [1]/[maj7] and [1]maj7/[maj7] with about the same frequency.

Example progressions:
[maj7]  [maj7]m7 (=[2]/[maj7])  [b2]/[maj7]  [1]/[maj7]  [maj7]
You can find this chord progression for example in the jazz standard "On Green Dolphin Street". Several major chords are played over a static root („pedal bass”) here. In this case the notation [1]/[maj7] is favorable over [1]maj7/[maj7].

This chord is often used in ballads, where a descending bassline, but little harmonical movement is desired. For example, in the chord progression
[1]  [1]maj7/[maj7]  [6]m7  [6]m7/[5].
In this progression only the bass is moving. The [6]m7 can also be seen as [1]/[6] chord. And [6]m7/[5] in most cases is played as [1]/[5] chord here, because the root is continually descending and therefore is often not played anymore in the [6]m7/[5] chord. Consequently you can alternatively write this progression
[1]  [1]/[maj7]  [1]/[6]  [1]/[5]

[1]  [1]maj7/[maj7]  [1]7/[7] …
In this case the notation [1]maj7/[maj7] helps to quickly recognize the way the chord types are changing. When playing a guitar solo that for sure can accelerate the decision which scales, arpeggios or guide tones to play. For [1]maj7/[maj7] and [1]7/[7] you can even use chord shapes where the root [1] is not even played anymore and therefore all tones [1] of the first chord shape descend by a half-step ( C → B → Bb ).