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You are already acquainted with the nature of the perfect octave, from the perfect common chord.
The superfluous octave is a mere passing note, and it may be accompanied by the major third and perfect fifth.
![\new PianoStaff << \new Staff \relative { \time 4/4 \override Score.TimeSignature #'stencil = ##f << { c''2 cis <a d> <f b> } \\ { <e g>1 f2 d } >> <e c'!>1 \bar ".." } \new Staff { \clef bass c'1 ~ c' c } >>](http://upload.wikimedia.org/score/k/d/kd91wbcsog4hi5h9139mpkx2e6dynsh/kd91wbcs.png)
The minor and major ninth require the major third and perfect fifth by way of accompaniment, to which may also be added the minor seventh.
![\new PianoStaff << \new Staff \relative { \time 4/4 \override Score.TimeSignature #'stencil = ##f <g' c es>1 << { es'2^"×" d4 c } \\ <fis, a>1 >> <g b> \bar ".." <g c e!> << { e'2^"×" d4 c } \\ <fis, a>1 >> <g b> \bar ".." <g es'> << { es'2^"×" d } \\ <fis, a c>1 >> \bar ".." <g c e!> << { e'2^"×" d } \\ <fis, a c>1 >> \bar ".." } \new Staff { \clef bass c d g, c d g, c d c d } >>](http://upload.wikimedia.org/score/s/m/sml8wwjnudr56hnfdmmxo2p7b5xj5ql/sml8wwjn.png)
And from this you may perceive the difference between the ninth and the second.