Class: Musa::Scales::EquallyTempered12ToneScaleSystem

Inherits:
TwelveSemitonesScaleSystem show all
Defined in:
lib/musa-dsl/music/equally-tempered-12-tone-scale-system.rb

Overview

Equal temperament 12-tone scale system.

EquallyTempered12ToneScaleSystem implements the standard equal temperament tuning where each semitone has exactly the same frequency ratio: 2^(1/12). This is the most common tuning system in modern Western music.

Frequency Calculation

Uses the equal temperament formula based on A440 concert pitch:

frequency = a_frequency × 2^((pitch - 69) / 12)

Where:

  • a_frequency: Reference A frequency (typically 440 Hz)
  • pitch: MIDI pitch number (69 = A4)

Historical Pitch Standards

Different A frequencies represent different historical standards:

  • 440 Hz: Modern concert pitch (ISO 16)
  • 442 Hz: Used by some orchestras (brighter sound)
  • 415 Hz: Baroque pitch (approximately A=415)
  • 432 Hz: Alternative tuning (some claim harmonic benefits)

Registration

This system is registered as the default scale system, accessible via:

Scales[:et12]                    # By ID
Scales.default_system            # As default

Usage

# Get system with standard A440 tuning
system = Scales[:et12][440.0]

# Get system with baroque tuning
baroque = Scales[:et12][415.0]

# Access scale kinds
c_major = system[:major][60]
a_minor = system[:minor][69]

See Also:

Class Method Summary collapse

Class Method Details

.frequency_of_pitch(pitch, _root_pitch, a_frequency) ⇒ Float

Calculates frequency for a pitch using equal temperament.

Implements the equal temperament tuning formula where each semitone has a frequency ratio of 2^(1/12) ≈ 1.059463.

Examples:

Standard A440 tuning

frequency_of_pitch(69, nil, 440.0)  # => 440.0 (A4)
frequency_of_pitch(60, nil, 440.0)  # => 261.63 (C4, middle C)

Baroque tuning

frequency_of_pitch(69, nil, 415.0)  # => 415.0 (A4)

Parameters:

  • pitch (Integer) —

    MIDI pitch number

  • _root_pitch (Integer) —

    unused (required by interface)

  • a_frequency (Numeric) —

    reference A4 frequency in Hz

Returns:

  • (Float) —

    frequency in Hz



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# File 'lib/musa-dsl/music/equally-tempered-12-tone-scale-system.rb', line 125

def frequency_of_pitch(pitch, _root_pitch, a_frequency)
  (a_frequency * Rational(2)**Rational(pitch - 69, 12)).to_f
end