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Dizzying Dominant Sevenths
You may have noticed that the dominant 7th chord was extended in this way: 7th, ninth, 13th, and sharp 11.
The sharp 11 reflects the idea that a major triad type (any dominant or major type chord) should not include the natural 11th, as it clashes with the major third that is present. There occasional exceptions (the second measure of the head in "Now's the Time" by Charlie Parker, for example). For this reason, I most often include the #11 rather then the natural 11 when playing these chords.
The chords that I have showed so far are all considered extended rather then altered chords. I chose to add notes to the chord that are from the parent scale, rather then changing (altering) any of the notes. The #11 chord is considerd a part of both extended and altered chord catergories.
One can use extended chords (generally) whereever and whenever one woould use a dominant 7th chord.