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Chords can be thought of, in the most simplistic sense, as notes in a scale played simultaneously ( vertically ) as opposed to sequentially ( horizontally ). The notes in the chords are called voices and the combination of voices in a chord is called a voicing. For a given chord type ( e.g. Seventh, Ninth, ... ) there are numerous ways in which the chord can be voiced. In it's purest form, a seventh chord, for example, will contain the voices; 1, 3, 5, and 7. However, these voices can be combined in numorous permutations in any order with certain intervals being dropped or duplicated. When the 1 interval is the lowest note, the chord is in Root Position. When the 3 interval is the lowest note, the chord is in its First Inversion. Similarly, the 5th and 7th intervals in the bass are called Second and Third Inversions, respectively.
Chord voicings can be constructed simply by seeing what combinations of chord intervals can be played in a certain position. I prefer to take a mathematical approach and calculate what voicings exist and which ones are playable. Then, use these voicings to construct voicings for extended chords and chords with repeated and dropped intervals.
Calculating the permutations for the intervals 1, 3, & 5 that make up a Triad, we get:
  • 135
  • 153
  • 315
  • 351
  • 513
  • 531
When these voicings are applied to a fretboard, these voicings often must be played on not adjacent strings. To distinguish voicings in these situations, a '0' is inserted in the voicing to indicate that an unplayed string exists between the voices. This leads to the following voicings for the Guitar or Bass:
  • 135
  • 1503
  • 3015 and 3105
  • 351
  • 513
  • 5031
Additionally, some intervals can be played an octave higher. This results in a new set of voicings that have extra strings in between voices:
  • 13005 and 10035
  • 310005
  • 51003
  • 503001
  • etc ...
These voicings can also be combined to create voicings where certain intervals are repeated:
  • 1513
  • 151351
  • 1351
  • 10135
  • 30151
  • 301513
  • 3515
  • 5131
  • etc ...
Depending on the chord type, certain voicings will be playable and other won't. Some voicings will only be playable if open strings are used. Some voicings will only be playable in the upper frets where the frets are closer together.

There are certain voices which are playable against most chord types. For this reason, some voicings will be presented against multiple chord types to illustrate how chord types.
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