Class: Tonal::Ratio::Approximation

Inherits:
Object
  • Object
show all
Extended by:
Forwardable
Defined in:
lib/tonal/approximation.rb

Defined Under Namespace

Classes: Set

Constant Summary collapse

DEFAULT_MIN_PRIME = 
2
DEFAULT_MAX_PRIME = 
Float::INFINITY
DEFAULT_MAX_GRID_SCALE = 
100
DEFAULT_MAX_GRID_BOUNDARY = 
5
DEFAULT_DEPTH = 
Float::INFINITY
DEFAULT_TREE_PATH_DEPTH = 
10
DEFAULT_SUPERPART_DEPTH = 
20
DEFAULT_NEIGHBORHOOD_DEPTH = 
10
DEFAULT_COMPLEXITY_AMOUNT = 
50.0
CONVERGENT_LIMIT = 
10

Instance Attribute Summary collapse

Class Method Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(ratio:) ⇒ Approximation

Returns a new instance of Approximation.

Raises:

  • (ArgumentError) 


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# File 'lib/tonal/approximation.rb', line 19

def initialize(ratio:)
  raise ArgumentError, "Tonal::Ratio required" unless ratio.kind_of?(Tonal::Ratio)
  @ratio = ratio
end

Instance Attribute Details

#ratio ⇒ Object (readonly)

Returns the value of attribute ratio.



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# File 'lib/tonal/approximation.rb', line 17

def ratio
  @ratio
end

Class Method Details

.neighbors(vacinity:, away: 1) ⇒ Array

Returns an array of Tonal::Ratio neighbors in the scaled ratio's grid neighborhood.

Examples:

Tonal::Ratio::Approximation.neighbors(vacinity: (3/2r).ratio(reduced:false).scale(256), away: 1)
  => [768/512, 769/512, 767/512, 768/513, 768/511, 769/513, 769/511, 767/513, 767/511]

Parameters:

  • away (Integer) (defaults to: 1) —

    the neighbors distance away from self's antecedent and consequent

Returns:

  • (Array) —

    an array of Tonal::Ratio neighbors in the scaled ratio's grid neighborhood



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# File 'lib/tonal/approximation.rb', line 167

def self.neighbors(vacinity:, away: 1)
  [vacinity,
   vacinity.class.new(vacinity.antecedent+away, vacinity.consequent),
   vacinity.class.new(vacinity.antecedent-away, vacinity.consequent),
   vacinity.class.new(vacinity.antecedent, vacinity.consequent+away),
   vacinity.class.new(vacinity.antecedent, vacinity.consequent-away),
   vacinity.class.new(vacinity.antecedent+away, vacinity.consequent+away),
   vacinity.class.new(vacinity.antecedent+away, vacinity.consequent-away),
   vacinity.class.new(vacinity.antecedent-away, vacinity.consequent+away),
   vacinity.class.new(vacinity.antecedent-away, vacinity.consequent-away)]
end

Instance Method Details

#by_continued_fraction(cents_tolerance: Tonal::Cents::TOLERANCE, depth: DEFAULT_DEPTH, max_prime: DEFAULT_MAX_PRIME, min_prime: DEFAULT_MIN_PRIME, conv_limit: CONVERGENT_LIMIT) ⇒ Tonal::Ratio::Approximation::Set

Returns of ratios within cent tolerance of self found using continued fraction approximation.

Examples:

Tonal::Ratio.ed(12,1).approximate.by_continued_fraction
=> 1.06: [17/16, 18/17, 89/84, 196/185, 1461/1379, 1657/1564, 3118/2943, 7893/7450, 18904/17843]

Parameters:

  • cents_tolerance (defaults to: Tonal::Cents::TOLERANCE) —

    the cents tolerance used to scope the collection

  • depth (defaults to: DEFAULT_DEPTH) —

    the maximum number of ratios in the collection

  • max_prime (defaults to: DEFAULT_MAX_PRIME) —

    the maximum prime number to allow in the collection

  • min_prime (defaults to: DEFAULT_MIN_PRIME) —

    the minimum prime number to allow in the collection

  • conv_limit (defaults to: CONVERGENT_LIMIT) —

    the number of convergents to limit the ContinuedFraction method

Returns:



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# File 'lib/tonal/approximation.rb', line 34

def by_continued_fraction(cents_tolerance: Tonal::Cents::TOLERANCE, depth: DEFAULT_DEPTH, max_prime: DEFAULT_MAX_PRIME, min_prime: DEFAULT_MIN_PRIME, conv_limit: CONVERGENT_LIMIT)
  return Set.new(ratio: ratio){|ratios| ratios << ratio} if (antecedent == 1) && (consequent == 1)
  self_in_cents = to_cents
  within = cents_tolerance.kind_of?(Tonal::Cents) ? cents_tolerance : Tonal::Cents.new(cents: cents_tolerance)
  Set.new(ratio: ratio) do |ratios|
    ContinuedFraction.new(antecedent.to_f/consequent, conv_limit).convergents.each do |convergent|
      ratio2 = ratio.class.new(convergent.numerator,convergent.denominator)
      ratios << ratio2 if ratio.class.within_cents?(self_in_cents, ratio2.to_cents, within) && max_prime_at_most?(ratio2, max_prime) && !prime_factor_at_most?(ratio2, min_prime - 1)
      break if ratios.length >= depth
    end
  end
end

#by_neighborhood(cents_tolerance: Tonal::Cents::TOLERANCE, depth: DEFAULT_NEIGHBORHOOD_DEPTH, max_prime: DEFAULT_MAX_PRIME, min_prime: DEFAULT_MIN_PRIME, max_boundary: DEFAULT_MAX_GRID_BOUNDARY, max_scale: DEFAULT_MAX_GRID_SCALE) ⇒ Array

Returns of ratios within cent tolerance of self found on the ratio grid.

Examples:

Tonal::Ratio.new(3,2).approximate.by_neighborhood
=> 3/2: [175/117, 178/119, 176/117, 181/121, 179/119, 184/123, 182/121, 187/125, 185/123, 190/127, 188/125]

Parameters:

  • cents_tolerance (defaults to: Tonal::Cents::TOLERANCE) —

    the cents tolerance used to scope the collection

  • depth (defaults to: DEFAULT_NEIGHBORHOOD_DEPTH) —

    the maximum number of ratios in the collection

  • max_prime (defaults to: DEFAULT_MAX_PRIME) —

    the maximum prime number to allow in the collection

  • min_prime (defaults to: DEFAULT_MIN_PRIME) —

    the minimum prime number to allow in the collection

  • max_boundary (defaults to: DEFAULT_MAX_GRID_BOUNDARY) —

    the maximum distance grid ratios will be from the scaled ratio

  • max_scale (defaults to: DEFAULT_MAX_GRID_SCALE) —

    the maximum self will be scaled

Returns:

  • (Array) —

    of ratios within cent tolerance of self found on the ratio grid



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# File 'lib/tonal/approximation.rb', line 107

def by_neighborhood(cents_tolerance: Tonal::Cents::TOLERANCE, depth: DEFAULT_NEIGHBORHOOD_DEPTH, max_prime: DEFAULT_MAX_PRIME, min_prime: DEFAULT_MIN_PRIME, max_boundary: DEFAULT_MAX_GRID_BOUNDARY, max_scale: DEFAULT_MAX_GRID_SCALE)
  self_in_cents = to_cents
  within = cents_tolerance.kind_of?(Tonal::Cents) ? cents_tolerance : Tonal::Cents.new(cents: cents_tolerance)
  Set.new(ratio: ratio) do |ratios|
    scale = 1
    boundary = 1

    while ratios.length <= depth && scale <= max_scale do
      while boundary <= max_boundary
        vacinity = ratio.respond_to?(:to_basic_ratio) ? to_basic_ratio.scale(scale) : ratio.scale(scale)
        self.class.neighbors(away: boundary, vacinity: vacinity).each do |neighbor|
          ratios << neighbor if (neighbor != ratio) && ratio.class.within_cents?(self_in_cents, neighbor.to_cents, within) && max_prime_at_most?(neighbor, max_prime) && !prime_factor_at_most?(neighbor, min_prime - 1)
        end
        boundary += 1
      end
      boundary = 1
      scale += 1
    end
  end
end

#by_superparticular(cents_tolerance: Tonal::Cents::TOLERANCE, depth: DEFAULT_SUPERPART_DEPTH, max_prime: DEFAULT_MAX_PRIME, min_prime: DEFAULT_MIN_PRIME, superpart: :upper) ⇒ Tonal::Ratio::Approximation::Set

Returns of superparticular approximations within cent tolerance of self.

Examples:

Tonal::Ratio.new(3/2r).approximate.by_superparticular
=> 3/2: [1041/692, 1044/694, 1047/696, 1050/698, 1053/700, 1056/702, 1059/704, 1062/706, 1065/708, 1068/710, 1071/712, 1074/714, 1077/716, 1080/718, 1083/720, 1086/722, 1089/724, 1092/726, 1095/728, 1098/730]

Parameters:

  • cents_tolerance (defaults to: Tonal::Cents::TOLERANCE) —

    the cents tolerance used to scope the collection

  • depth (defaults to: DEFAULT_SUPERPART_DEPTH) —

    the maximum number of ratios in the collection

  • max_prime (defaults to: DEFAULT_MAX_PRIME) —

    the maximum prime number to allow in the collection

  • min_prime (defaults to: DEFAULT_MIN_PRIME) —

    the minimum prime number to allow in the collection

  • superpart (defaults to: :upper) —

    if the superior part is the numerator or denominator

Returns:



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# File 'lib/tonal/approximation.rb', line 80

def by_superparticular(cents_tolerance: Tonal::Cents::TOLERANCE, depth: DEFAULT_SUPERPART_DEPTH, max_prime: DEFAULT_MAX_PRIME, min_prime: DEFAULT_MIN_PRIME, superpart: :upper)
  # One of n and n+1 is even, so every candidate has 2 as a factor and none can meet a higher min_prime
  return Set.new(ratio: ratio) if min_prime > 2
  self_in_cents = to_cents
  within = cents_tolerance.kind_of?(Tonal::Cents) ? cents_tolerance : Tonal::Cents.new(cents: cents_tolerance)
  Set.new(ratio: ratio) do |ratios|
    n = 1
    while true do
      ratio2 = ratio.class.superparticular(n, factor: ratio.to_r, superpart:)
      ratios << ratio2 if ratio.class.within_cents?(self_in_cents, ratio2.to_cents, within) && (ratio2 != ratio) && max_prime_at_most?(ratio2, max_prime) && !prime_factor_at_most?(ratio2, min_prime - 1)
      break if ratios.length >= depth
      n += 1
    end
  end
end

#by_tree_path(cents_tolerance: Tonal::Cents::TOLERANCE, depth: DEFAULT_TREE_PATH_DEPTH, max_prime: DEFAULT_MAX_PRIME, min_prime: DEFAULT_MIN_PRIME) ⇒ Tonal::Ratio::Approximation::Set

Returns of fraction tree ratios within cent tolerance of self.

Examples:

Tonal::Ratio.ed(12,1).approximate.by_tree_path
=> 1.06: [17/16, 18/17, 35/33, 53/50, 71/67, 89/84, 107/101, 196/185, 285/269, 481/454]

Parameters:

  • cents_tolerance (defaults to: Tonal::Cents::TOLERANCE) —

    the cents tolerance used to scope the collection

  • depth (defaults to: DEFAULT_TREE_PATH_DEPTH) —

    the maximum number of ratios in the collection

  • max_prime (defaults to: DEFAULT_MAX_PRIME) —

    the maximum prime number to allow in the collection

  • min_prime (defaults to: DEFAULT_MIN_PRIME) —

    the minimum prime number to allow in the collection

Returns:



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# File 'lib/tonal/approximation.rb', line 56

def by_tree_path(cents_tolerance: Tonal::Cents::TOLERANCE, depth: DEFAULT_TREE_PATH_DEPTH, max_prime: DEFAULT_MAX_PRIME, min_prime: DEFAULT_MIN_PRIME)
  return Set.new(ratio: ratio){|ratios| ratios << ratio} if (antecedent == 1) && (consequent == 1)
  self_in_cents = to_cents
  within = cents_tolerance.kind_of?(Tonal::Cents) ? cents_tolerance : Tonal::Cents.new(cents: cents_tolerance)
  Set.new(ratio: ratio) do |ratios|
    FractionTree.node(to_f).path.each do |node|
      next if node.number.infinite?
      ratio2 = ratio.class.new(node.number)
      ratios << ratio2 if ratio.class.within_cents?(self_in_cents, ratio2.to_cents, within) && max_prime_at_most?(ratio2, max_prime) && !prime_factor_at_most?(ratio2, min_prime - 1)
      break if ratios.length >= depth
    end
  end
end

#neighborhood(scale: 2**0, boundary: 1) ⇒ Array

Returns of bounding ratios in the ratio grid vacinity of antecedent/consequent scaled by scale.

Examples:

Tonal::ReducedRatio.new(3,2).neighborhood(scale: 256, boundary: 2)
  => [766/514, 768/514, 767/513, 766/512, 768/513, 767/512, 770/514, 769/513, 768/512, 767/511, 769/512, 766/510, 768/511, 770/512, 769/511, 768/510, 770/510]

Parameters:

  • scale (Integer) (defaults to: 2**0) —

    used to scale antecedent/consequent on coordinate system

  • boundary (Integer) (defaults to: 1) —

    limit within which to calculate neighboring ratios

Returns:

  • (Array) —

    of bounding ratios in the ratio grid vacinity of antecedent/consequent scaled by scale



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# File 'lib/tonal/approximation.rb', line 135

def neighborhood(scale: 2**0, boundary: 1)
  scale = scale.round
  vacinity = ratio.respond_to?(:to_basic_ratio) ? to_basic_ratio.scale(scale) : ratio.scale(scale)
  SortedSet.new([].tap do |ratio_list|
                     1.upto(boundary) do |away|
                       ratio_list << self.class.neighbors(away: away, vacinity: vacinity)
                     end
                   end.flatten).to_a
end