Editing Interval (music) (section)

== Inversion ==
{{Main|Inversion (music)#Intervals}}
[[Image:Compound interval inversion.png|thumb|350px|Major 13th (compound major 6th) inverts to a minor 3rd by moving the bottom note up two octaves, the top note down two octaves, or both notes one octave.]]

A simple interval (i.e., an interval smaller than or equal to an octave) may be [[inversion (music)|inverted]] by raising the lower pitch an [[octave]] or lowering the upper pitch an octave. For example, the fourth from a lower C to a higher F may be inverted to make a fifth, from a lower F to a higher C.

: <score sound="1">
{
\override Score.TimeSignature
#'stencil = ##f
\override Score.SpacingSpanner.strict-note-spacing = ##t
\set Score.proportionalNotationDuration = #(ly:make-moment 1/4)
\new Staff <<
   \clef treble \time 4/4
   \new Voice \relative c' {
      \stemUp c2 c' c, c' c, c' c, c'
      } 
   \new Voice \relative c' {
      \stemDown c2 c d d e e f f
      }
   \addlyrics { "P1" -- "P8" "M2" -- "m7" "M3" -- "m6" "P4" -- "P5" }
>>
}
</score>

There are two rules to determine the number and quality of the inversion of any simple interval:<ref>[[Stefan Kostka|Kostka, Stefan]]; Payne, Dorothy (2008). ''Tonal Harmony'', p.&nbsp;21. First edition, 1984.</ref>
# The interval number and the number of its inversion always add up to nine (4 + 5 = 9, in the example just given).
# The inversion of a major interval is a minor interval, and vice versa; the inversion of a perfect interval is also perfect; the inversion of an augmented interval is a diminished interval, and vice versa; the inversion of a doubly augmented interval is a doubly diminished interval, and vice versa.
For example, the interval from C to the E{{Music|b}} above it is a minor third. By the two rules just given, the interval from E{{Music|b}} to the C above it must be a major sixth.

Since compound intervals are larger than an octave, "the inversion of any compound interval is always the same as the inversion of the simple interval from which it is compounded".<ref>[[Ebenezer Prout|Prout, Ebenezer]] (1903). ''Harmony: Its Theory and Practice'', 16th edition. London: Augener & Co. (facsimile reprint, St. Clair Shores, Michigan: Scholarly Press, 1970), p.&nbsp;10. {{ISBN|0-403-00326-1}}.</ref>

For intervals identified by their ratio, the inversion is determined by reversing the ratio and multiplying the ratio by 2 until it is greater than 1. For example, the inversion of a 5:4 ratio is an 8:5 ratio.

For intervals identified by an integer number of semitones, the inversion is obtained by subtracting that number from 12.

Since an [[interval class]] is the lower number selected among the interval integer and its inversion, interval classes cannot be inverted.