Class: HeadMusic::Rudiment::Tuning::Meantone

Inherits:
HeadMusic::Rudiment::Tuning show all
Includes:
TonalCentered
Defined in:
lib/head_music/rudiment/tuning/meantone.rb

Overview

Quarter-comma meantone temperament Optimizes major thirds to be pure (5:4) at the expense of perfect fifths

Constant Summary collapse

INTERVAL_RATIOS =

Frequency ratios for intervals in quarter-comma meantone temperament The defining characteristic is that major thirds are pure (5:4) and the syntonic comma is distributed equally among the four fifths

{
  unison: Rational(1, 1),
  minor_second: 5.0**(1.0 / 4) / 2.0**(1.0 / 2),     # ~1.0697
  major_second: 5.0**(1.0 / 4),                       # ~1.1892 (fourth root of 5)
  minor_third: 5.0**(1.0 / 2) / 2.0**(1.0 / 2),      # ~1.5811
  major_third: Rational(5, 4),                        # Pure major third (1.25)
  perfect_fourth: 2.0**(1.0 / 2) / 5.0**(1.0 / 4),   # ~1.3375
  tritone: 5.0**(3.0 / 4) / 2.0**(1.0 / 2),          # ~1.6719
  perfect_fifth: Rational(3, 2),                      # ~1.4953 (slightly flat)
  minor_sixth: 2.0**(3.0 / 2) / 5.0**(1.0 / 4),      # ~1.6818
  major_sixth: 5.0**(3.0 / 4),                        # ~1.8877
  minor_seventh: 2.0**(3.0 / 2) / 5.0**(1.0 / 2),    # ~1.8877
  major_seventh: Rational(25, 16),                    # ~1.5625
  octave: Rational(2, 1)                              # Octave (2.0)
}.freeze

Instance Method Summary collapse

Instance Method Details

#initialize(reference_pitch: :a440, tonal_center: nil) ⇒ Object Originally defined in module TonalCentered