The HD library contains structures and search functions based around James Tenney's notion of Harmonic Distance. It provides ways of measuring both the harmonic distance of a single interval and what Tenney called the "HD-sum", or the sum of the harmonic distances of all 2-combination intervals in a given aggregate.
The other theoretical sources, specific to the performance of music in just intonation, is the range of "tuneable intervals" developed by Marc Sabat and Wolfgang Von Schweinitz. This is a list of intervals that can be tuned by ear with relative accuracy, without the aid of an electronic tuner.
# You can create new Ratio objects
HD::Ratio[3,2] # => HD::Ratio.int(2): [ 3, 2 ]
HD::Ratio.from_s("3/2") == HD::Ratio[3, 2] # => true
HD.r(3,2) == HD::Ratio[3, 2] # => true
# You can get the distance from the Ratio to 1/1
HD.r(3,2).distance # => 2.58496
HD.r(9,8).distance # => 6.169925
# You can also get the distance from the Ratio to another Ratio
HD.r(3,2).distance HD.r(4,3) # => 6.169925
# You can also pass a HDConfig object to, for example, ignore octave displacement
HD.r(3,2).distance(HD.r(4,3), HD::HDConfig.new(:pc_only => true)) # => 3.169925
# ...or to double the effect of octave displacement
HD.r(3,2).distance(HD.r(4,3), HD::HDConfig.new(:prime_weights => [4, 3])) # => 9.169925 # You can also get useful info for annotating scores or making SuperCollider mockups
# Like the overall cents and the deviation of the interval from the nearest 12TET pitch (rounded)
HD.get_cents_from_vector([HD.r(4,3), HD.r(3,2)]) # => NArray.float(2,2): [ [ 498.045, -2.0 ], [ 701.955, 2.0 ] ]
# Despite the method name, you don't actually need a full vector
HD.get_cents_from_vector HD.r(4,3) # => NArray.float(2): [ 498.045, -2.0 ]
# You can also get frequencies
HD.get_frequencies_from_vector(HD::Ratio.from_s "3/2 4/3") # => NArray.float(2): [ 660.0, 586.667 ]
# These can be from any base frequency
HD.get_frequencies_from_vector(HD::Ratio.from_s("3/2 4/3"), 330) # => NArray.float(2): [ 495.0, 440.0 ] # Finally, HD::Ratio objects are Comparable and Enumerable
HD.r(3,2) > HD.r(4,3) # => true
HD.r(3,2) < HD.r(4,3) # => false
HD.r(3,2) <=> HD.r(4,3) # => 1
HD.r(3,2).each {|x| print "#{x}"} # => nil (prints "32")
HD.r(3,2).map {|x| x * 2.0} # => HD::Ratio.int(2): [ 6, 4 ]
# And they also respond to basic arithmetic
HD.r(3,2) - HD.r(4,3) # => HD::Ratio.int(2): [ 1, 6 ]
HD.r(3,2) * HD.r(4,3) # => HD::Ratio.int(2): [ 2, 1 ]Finally, there are some fun extra connections to the Morphological Metrics library elsewhere on Github. However, it is not 100% confirmed that all of these HD objects will work with the standard branch, so I maintain my own fork of Morphological Metrics that is adapted to work with the HD library. One of these days we will merge the two.