Get the interval between two pitches:

betweenPitches Pitch.c4 Pitch.g4 == perfectFifth

Check whether two intervals are equivalent:

isEqualTo augmentedFourth diminishedFifth == True

Check whether the distance of one interval is greater than another:

isGreaterThan perfectFifth perfectUnison == True

Check whether the distance of one interval is less than another:

isLessThan perfectFifth perfectUnison == False

Add two intervals together:

add majorSecond majorThird == augmentedFourth

Subtract two intervals:

subtract majorSecond minorThird == minorSecond

Convert any interval to its simple form. A simple interval is one that spans an octave or less.

simplify majorThirteenth == majorSixth

Add an octave to an interval:

addOctave majorSecond == majorNinth

Reverse the direction of an interval

Find out whether an interval is in the "up" direction:

isUp majorThird == True

Find out whether an interval is in the "down" direction:

isDown (reverse majorThird) == True

Get the number of semitones an interval spans:

semitones majorThird == 4

Get the short name of an interval:

toString perfectFifth == "P5"

Intervals in the "down" direction are shown with a negative sign:

toString (reverse perfectFifth) == "-P5"

Create a range of intervals:

range perfectUnison perfectFifth
    == { min = perfectUnison
       , max = perfectFifth
       }