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Just wondering, if the same chord is played for few bars. Is it common to invert this chord on every bar just to make it sound like the harmony is doing something?

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    If you want to make it sound like the harmony is doing something, maybe yes. Otherwise, maybe no. Eventually, you will learn that "there are no rules" except for "use your ears." - but not if you keep looking for rules that don't exist!
    – user19146
    May 14 '17 at 16:55
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When the same chord is repeated long enough, it tends to shift the focus to the rhythm. This is good if you want the rhythm to be the focus.

There are a few common things that are often done when the accompaniment keeps the same chord/harmony for a longer than usual time:

  • The chord is played with an interesting rhythm
  • The chord is arpeggiated and/or different notes of the chord are played in a certain sequence
  • The chord is replaced with a riff that implies the same tonality
  • A nearby or similar chord is played briefly between repeats of the actual harmony chord

The second bullet above is essentially playjng the chord in a repeating pattern of inversions, so the basic answer to your question is "yes". The inversion pattern is often repeated at least once a measure and if it's not repeated (i.e. If you just go through a long cycle of different inversions) then the effect will be to draw the focus back towards the harmony part, which you might not want.

Some examples to study and consider:

  • Any 12 bar blues song since the I is often repeated for four measures, especially delta blues
  • Bo Diddley, for example George Thorogood's cover of "Who Do You Love" is a whole song on basically one chord
  • Eric Clapton's cover of "Willie and the Hand Jive" shows a way to keep the same chord interesting for a whole verse
  • "Whole Lotta Love" by Led Zeppelin is basically an E minor chord all through the versus but instead of the chord there's an E minor riff that is repeated once a measure

Also note that a walking bassline under the same repeated chord is a tour of inversions.

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  • That's Bo Diddley with an 'e'. Perhaps it's worth noting that a series of inversions rising in pitch will tend to build drama. It can be effective to use this trick in the bar approaching a chord change. May 15 '17 at 1:17
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From a classical perspective - and referring to Walter Piston's textbook Harmony - changing the inversion of a chord gives you new voice leading possibilities. Although it's probably better to not think of only inversions - in the sense of the bass changing - but rather re-distributing the voices of the chord. In other words, you can also change the notes of the other voices above the bass.

Personally, I wouldn't call this 'making the harmony sound like it's doing something' as if it isn't important or meaningful. Sure, the chord root isn't changing, but the chords are changing. The effect can be more or less static depending on how it's handled. Arpeggiating the bass through root, third, fifth, octave could feel fairly static, whereas I to I6 has a more dynamic feel and can strongly imply moving to IV. Either way something is happening and should have some musical meaning.

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