Class: Numeric

Inherits:
Object
  • Object
show all
Defined in:
lib/tonal/extensions.rb

Instance Method Summary collapse

Instance Method Details

#benedetti_height ⇒ Float Also known as: product_complexity

Returns the log product complexity of self.

Examples:

(3/2r).benedetti_height => 6

Returns:

  • (Float) —

    the log product complexity of self



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# File 'lib/tonal/extensions.rb', line 115

def benedetti_height = ratio.benedetti_height

#cents ⇒ Tonal::Cents

Returns of self interpreted as a cents quantity.

Examples:

700.0.cents => 700.0

Returns:

  • (Tonal::Cents) —

    of self interpreted as a cents quantity



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# File 'lib/tonal/extensions.rb', line 83

def cents = Tonal::Cents.new(cents: self)

#cents_difference_with(other_ratio) ⇒ Tonal::Cents

Returns difference between ratio (upper) and self (lower).

Examples:

(133).cents_difference_with(3/2r) => 635.62

Parameters:

  • other_ratio

Returns:

  • (Tonal::Cents) —

    difference between ratio (upper) and self (lower)



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# File 'lib/tonal/extensions.rb', line 177

def cents_difference_with(other_ratio) = interval_with(other_ratio).to_cents

#div_times(factor) ⇒ Array

Returns a tuple of self divided and multiplied by factor.

Examples:

Math::PI.div_times(3) => [1.0471975511965976, 9.42477796076938]

Parameters:

Returns:

  • (Array) —

    a tuple of self divided and multiplied by factor



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# File 'lib/tonal/extensions.rb', line 40

def div_times(factor) = [self / factor, self * factor]

#efficiency(modulo, reduced: false, is_step_efficiency: false) ⇒ Tonal::Cents

Returns the cents difference between self and its step in the given modulo.

Examples:

(3/2r).efficiency(12) => -1.96 ¢
(3/2r).efficiency(12, is_step_efficiency: true) => 1.96 ¢

Parameters:

  • modulo —

    against which the difference of self is compared

  • reduced (defaults to: false) —

    if true, self is reduced to the octave before calculating efficiency

  • is_step_efficiency (defaults to: false) —

    if true, calculates the efficiency of the step instead of the ratio (self). If the step efficiency is X cents, then the ratio efficiency is -X cents.

Returns:

  • (Tonal::Cents) —

    the cents difference between self and its step in the given modulo



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# File 'lib/tonal/extensions.rb', line 154

def efficiency(modulo, reduced: false, is_step_efficiency: false) = ratio(reduced:).efficiency(modulo, is_step_efficiency:)

#hz ⇒ Tonal::Hertz Also known as: to_hz

Returns of self.

Examples:

(440.0).hz => 440.0 Hz

Returns:



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# File 'lib/tonal/extensions.rb', line 101

def hz = Tonal::Hertz.new(self)

#interval_with(other_ratio, is_lower: true) ⇒ Tonal::Interval

Returns beween self (upper) and ratio (lower).

Examples:

(3/2r).interval_with(4/3r) => 9/8 (3/2 / 4/3)
(3/2r).interval_with(4/3r, is_lower: false) => 16/9 (4/3 / 3/2)

Parameters:

  • other_ratio —

    the other ratio to form the interval with

  • is_lower (Boolean) (defaults to: true) —

    if other_ratio is the lower (true) or upper (false) ratio

Returns:



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# File 'lib/tonal/extensions.rb', line 164

def interval_with(other_ratio, is_lower: true) = Tonal::Ratio.new(self).interval_with(other_ratio, is_lower:)

#log(base) ⇒ Tonal::Log Also known as: to_log

Returns the log of self to the given base.

Examples:

(3/2r).log(10) => 0.18

Returns:

  • (Tonal::Log) —

    the log of self to the given base



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# File 'lib/tonal/extensions.rb', line 68

def log(base) = Tonal::Log.new(logarithmand: self, base:)

#log2 ⇒ Tonal::Log2 Also known as: to_log2, span

Returns the log2 of self.

Examples:

(3/2r).log2 => 0.5849625007211562

Returns:



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# File 'lib/tonal/extensions.rb', line 75

def log2 = Tonal::Log2.new(logarithmand: self)

#log_floor(base = 10) ⇒ Integer

Returns the floor of the log (to the given base) of self.

Examples:

Math::PI.log_floor(2) => 1

Parameters:

  • base (defaults to: 10) —

    of the log

Returns:

  • (Integer) —

    the floor of the log (to the given base) of self



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# File 'lib/tonal/extensions.rb', line 235

def log_floor(base=10) = Math.log(self, base).floor

#log_weil_height ⇒ Tonal::Log2

Returns the log of Weil height.

Examples:

(3/2r).log_weil_height => 1.58

Returns:



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

def log_weil_height = ratio.log_weil_height

#max_prime(limit: Tonal::Ratio::PRIME_LIMIT) ⇒ Integer?

Returns the maximum prime factor of self, or nil if self has a prime factor above limit.

Examples:

(31/30r).max_prime => 31

Parameters:

  • limit (Integer) (defaults to: Tonal::Ratio::PRIME_LIMIT) —

    the largest prime to factor by, see Tonal::Ratio#prime_divisions

Returns:

  • (Integer, nil) —

    the maximum prime factor of self, or nil if self has a prime factor above limit



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# File 'lib/tonal/extensions.rb', line 201

def max_prime(limit: Tonal::Ratio::PRIME_LIMIT) = ratio.max_prime(limit:)

#min_prime(limit: Tonal::Ratio::PRIME_LIMIT) ⇒ Integer?

Returns the minimum prime factor of self, or nil if self has a prime factor above limit.

Examples:

(31/30r).min_prime => 2

Parameters:

  • limit (Integer) (defaults to: Tonal::Ratio::PRIME_LIMIT) —

    the largest prime to factor by, see Tonal::Ratio#prime_divisions

Returns:

  • (Integer, nil) —

    the minimum prime factor of self, or nil if self has a prime factor above limit



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# File 'lib/tonal/extensions.rb', line 208

def min_prime(limit: Tonal::Ratio::PRIME_LIMIT) = ratio.min_prime(limit:)

#mirror(axis = 1) ⇒ Tonal::Ratio

Returns , the ratio rotated on the given axis, default 1/1.

Examples:

(3/2r).mirror => (4/3)

Parameters:

  • axis (defaults to: 1) —

    around which self is mirrored

Returns:

  • (Tonal::Ratio) —

    , the ratio rotated on the given axis, default 1/1



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# File 'lib/tonal/extensions.rb', line 228

def mirror(axis=1/1r) = ratio.mirror(axis)

#modulo_translate(lower = 0, upper) ⇒ Numeric

Returns translated modularly.

Examples:

Math::PI.modulo_translate(-3, 3) => -2.858407346410207

Parameters:

  • lower (defaults to: 0) —

    the lower bound of the modulo range

  • upper —

    the upper bound of the modulo range

Returns:

  • (Numeric) —

    translated modularly



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# File 'lib/tonal/extensions.rb', line 21

def modulo_translate(lower=0, upper)
  range = (upper - lower) == 0 ? 1 : upper - lower
  (self - lower) % range + lower
end

#negative ⇒ Tonal::Ratio

Returns , the Ernst Levy negative of self.

Examples:

(7/4r).negative => (12/7)

Returns:



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# File 'lib/tonal/extensions.rb', line 221

def negative = ratio.negative

#period_degrees ⇒ Float

Returns , the degrees on a circle of self.

Examples:

(2**(6.0/12)).period_degrees => 180.0

Returns:

  • (Float) —

    , the degrees on a circle of self



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# File 'lib/tonal/extensions.rb', line 62

def period_degrees = ratio.period_degrees

#plus_minus(offset) ⇒ Array Also known as: min_plus

Returns a tuple of self offset positively/negatively.

Examples:

Math::PI.plus_minus(3)
  => [6.141592653589793, 0.14159265358979312]

Parameters:

  • offset —

    plus and minus distance from self

Returns:

  • (Array) —

    a tuple of self offset positively/negatively



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# File 'lib/tonal/extensions.rb', line 32

def plus_minus(offset) = [self + offset, self - offset]

#power(p, r = nil) ⇒ Numeric

Returns self raised to the given power/root.

Examples:

(3/2r).power(3,2) => 1.8371173070873832

Parameters:

  • p —

    the power

  • r (defaults to: nil) —

    the root

Returns:

  • (Numeric) —

    self raised to the given power/root



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# File 'lib/tonal/extensions.rb', line 249

def power(p, r=nil)
  if r
    (self.root(r))**p
  else
    self**p
  end
end

#prime_divisions(limit: Tonal::Ratio::PRIME_LIMIT) ⇒ Array?

Returns , self decomposed into its prime factors, or nil if self has a prime factor above limit.

Examples:

(31/30r).prime_divisions => [[[31, 1]], [[2, 1], [3, 1], [5, 1]]]

Parameters:

  • limit (Integer) (defaults to: Tonal::Ratio::PRIME_LIMIT) —

    the largest prime to factor by, see Tonal::Ratio#prime_divisions

Returns:

  • (Array, nil) —

    , self decomposed into its prime factors, or nil if self has a prime factor above limit



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# File 'lib/tonal/extensions.rb', line 194

def prime_divisions(limit: Tonal::Ratio::PRIME_LIMIT) = ratio.prime_divisions(limit:)

#prime_vector(reduced: false, limit: Tonal::Ratio::PRIME_LIMIT) ⇒ Vector Also known as: monzo, prime_exponent_vector

Returns , self represented as a prime vector.

Examples:

(3/2r).prime_vector => Vector[-1, 1]

Parameters:

  • reduced (defaults to: false)
  • limit (Integer) (defaults to: Tonal::Ratio::PRIME_LIMIT) —

    the largest prime to factor by, see Tonal::Ratio#prime_divisions

Returns:

  • (Vector) —

    , self represented as a prime vector



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# File 'lib/tonal/extensions.rb', line 185

def prime_vector(reduced: false, limit: Tonal::Ratio::PRIME_LIMIT) = ratio(reduced:).prime_vector(limit:)

#reciprocal ⇒ Rational

Returns the reciprocal of self.

Examples:

(3/2r).reciprocal => (2/3)

Returns:

  • (Rational) —

    the reciprocal of self



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# File 'lib/tonal/extensions.rb', line 241

def reciprocal = Rational(1, self)

#root(r) ⇒ Numeric

Returns self raised to the given root.

Examples:

(3/2r).root(2) => 1.224744871391589

Parameters:

  • r —

    the root

Returns:

  • (Numeric) —

    self raised to the given root



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# File 'lib/tonal/extensions.rb', line 262

def root(r)
  self**Rational(1, r)
end

#scale_step(modulo = 12) ⇒ Tonal::Scale::Step

Returns the step of self in the given modulo.

Examples:

(5/4r).scale_step(12) => 4\12

Parameters:

  • modulo (defaults to: 12)

Returns:



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# File 'lib/tonal/extensions.rb', line 109

def scale_step(modulo=12) = Tonal::Scale::Step.new(ratio: self, modulo:)

#tenney_height ⇒ Integer Also known as: log_product_complexity

Returns the product complexity of self.

Examples:

(3/2r).tenney_height => 2.58

Returns:

  • (Integer) —

    the product complexity of self



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# File 'lib/tonal/extensions.rb', line 122

def tenney_height = ratio.tenney_height

#to_cents ⇒ Tonal::Cents

Returns of self interpreted as a ratio.

Examples:

(3/2r).to_cents => 701.96

Returns:



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# File 'lib/tonal/extensions.rb', line 95

def to_cents = Tonal::Cents.new(ratio: self)

#to_interval ⇒ Tonal::Interval

Returns between 1/1 (lower) and self (upper).

Examples:

(3/2r).to_interval => 3/2 (3/2 / 1/1)

Returns:



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# File 'lib/tonal/extensions.rb', line 170

def to_interval = Tonal::Interval.new(self)

#to_ratio(reduced: false, equave: 2) ⇒ Tonal::Ratio Also known as: ratio

Returns the octave reduced ratio of self.

Examples:

(4/5r).to_ratio => 4/5

Parameters:

  • reduced (defaults to: false)
  • equave (defaults to: 2)

Returns:



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# File 'lib/tonal/extensions.rb', line 48

def to_ratio(reduced: false, equave: 2/1r) = reduced ? Tonal::ReducedRatio.new(self, equave:) : Tonal::Ratio.new(self, equave:)

#to_reduced_ratio(equave: 2) ⇒ Tonal::ReducedRatio

Examples:

(4/5r).to_reduced_ratio => 8/5

Parameters:

  • equave (defaults to: 2)

Returns:



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

def to_reduced_ratio(equave: 2/1r) = to_ratio(reduced: true, equave:)

#to_vector ⇒ Vector Also known as: vector

Returns , self expressed as a Vector.

Examples:

(3/2r).to_vector => Vector[3, 2]

Returns:

  • (Vector) —

    , self expressed as a Vector



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# File 'lib/tonal/extensions.rb', line 214

def to_vector = Vector[self.numerator, self.denominator]

#weil_height ⇒ Integer

Returns the Weil height.

Examples:

(3/2r).weil_height => 3

Returns:



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# File 'lib/tonal/extensions.rb', line 129

def weil_height = ratio.weil_height

#wilson_height(reduced: false, equave: 2, prime_rejects: [2]) ⇒ Integer

Returns the Wilson height.

Examples:

(14/9r).wilson_height => 13

Parameters:

  • reduced (defaults to: false)
  • equave (defaults to: 2)
  • prime_rejects (defaults to: [2])

Returns:



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# File 'lib/tonal/extensions.rb', line 143

def wilson_height(reduced: false, equave: 2/1r, prime_rejects: [2]) = ratio(reduced:, equave:).wilson_height(prime_rejects:)

#¢ ⇒ Tonal::Cents

Returns of self interpreted as a cents quantity.

Examples:

700.0.¢ => 700.0

Returns:

  • (Tonal::Cents) —

    of self interpreted as a cents quantity



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# File 'lib/tonal/extensions.rb', line 89

def ¢ = cents