page_title: Interval (music)
section_title: Inversion
hierarchical_section_title: Interval (music) / Inversion
caption_attribution_description: English: Compound interval inversion: 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.
context_page_description: In music theory, an interval is the difference in pitch between two sounds.
  An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.
  In Western music, intervals are most commonly differences between notes of a diatonic scale. The smallest of these intervals is a semitone. Intervals smaller than a semitone are called microtones. They can be formed using the notes of various kinds of non-diatonic scales. Some of the very smallest ones are called commas, and describe small discrepancies, observed in some tuning systems, between enharmonically equivalent notes such as C♯ and D♭. Intervals can be arbitrarily small, and even imperceptible to the human ear.
  In physical terms, an interval is the ratio between two sonic frequencies. For example, any two notes an octave apart have a frequency ratio of 2:1. This means that successive increments of pitch by the same interval result in an exponential increase of frequency, even though the human ear perceives this as a linear increase in pitch.
context_section_description: A simple interval (i.e., an interval smaller than or equal to an octave) may be 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.
  There are two rules to determine the number and quality of the inversion of any simple interval:
  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♭ above it is a minor third. By the two rules just given, the interval from E♭ 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."
  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.
caption: 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
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