scale_arithmetic.rb

class Scale
  def initialize(steps)
    @steps = steps
  end
  
  # returns the number of half-steps from zero for any degree of a scale
  def [](degree)
    @steps[degree % @steps.length] + (12*(degree/@steps.length)) 
  end

  # finds the interval for any pitch in a scale
  # or nil if the pitch doesn't exist in a scale
  def index(pitch)
    i = base_index(pitch)
    return nil if i.nil?
    i + (@steps.length*(pitch/12)) # => 6, 6, 43, 43, 43
  end
  
  def base_index(pitch)  #probably needs a different name
    @steps.index(pitch % 12)
  end
  
  # for a scale begining on tonic return the pitch of the next interval 
  def next(tonic, pitch, interval=1)
    off = tonic % 12
    self[self.index(pitch - off) + interval] + off
  end
end

# Demonstration: (TextMate users hit cmd-ctrl-shift-e to play along)
# The steps of a major scale:
maj = Scale.new [0,2,4,5,7,9,11]

# The 6th degree is 11 half-steps from tonic
maj[6] # => 11
# and likewise, 11 half-notes is 6 degrees from tonic
maj.index(11) # => 6

# the Scale#[] is like an Array#[] except it extends the base pattern
(-6..6).collect {|x| maj[x] } # => [-10, -8, -7, -5, -3, -1, 0, 2, 4, 5, 7, 9, 11]
maj.index(11) # => 6

(0..12).map{|x|maj[44 + x]} # => [76, 77, 79, 81, 83, 84, 86, 88, 89, 91, 93, 95, 96]

# For a major scale with a tonic of 62(D4) find the next interval for pitch 76
# keep in mind 76 is assumed to be within the given scale
maj.next(62, 76) # => 78
maj.next(62, 76, 3) # => 81
maj.next(62, 76, -3) # => 71

# reference that sort of helps prove the maj.next statement
# borrowed from jvoorhis
C4  = 60    
CS4 = 61    
D4  = 62 # +0    
DS4 = 63       
E4  = 64 # +2    
F4  = 65        
FS4 = 66 # +4    
G4  = 67 # +5    
GS4 = 68        
A4  = 69 # +7    
AS4 = 70        
B4  = 71 # +9    
C5  = 72        
CS5 = 73 # +11   
D5  = 74 # +12   
DS5 = 75         
E5  = 76 #       
F5  = 77         
FS5 = 78 #       
G5  = 79 #       
GS5 = 80         
A5  = 81 #       
AS5 = 82         
B5  = 83 #       
C6  = 84         
CS6 = 85 #       
D6  = 86 #       
DS6 = 87         
E6  = 88         
F6  = 89         
FS6 = 90         
G6  = 91         
GS6 = 92         
A6  = 93         
AS6 = 94         
B6  = 95         
C7  = 96