Package eu.bandm.music.entities

Class Euler2

java.lang.Object
eu.bandm.music.entities.Euler2
public class Euler2 extends Object
Representation of pitch classes or interval classes in the Euler net. Each point has two coordinates, representing the application of the step of a pure fifth and of a major third. Historically, this was first used to represent physical tunings, and the intervals were interpreted as the exponents of pure tuning. Later it is used for "mental maps", for pyschological coordinate in the space of "functional music theory".

  • Field Details

    • _5

      protected final int _5
      The exponent of the applied fifth.

    • _3

      protected final int _3
      The exponent of the applied third.

    • class_c

      public static final FunctionalPitchModOctave class_c

  • Constructor Details

    • Euler2

      public Euler2(int _5, int _3)
      Only constructor, set both coordinates.

  • Method Details

    • get_5

      public int get_5()
      Return the exponent of the applied fifth.

    • get_3

      public int get_3()
      Return the exponent of the applied third.

    • equals

      public boolean equals(Object o)
      Overrides:
      equals in class Object

    • equals

      public boolean equals(Euler2 t)
      Evident

    • transpose_up

      public FunctionalPitchModOctave transpose_up(FunctionalPitchModOctave pitch)
      Interpret the coordinates as functional intervals (fifth and major third) and apply them to the given pitch.

    • pitchClassRepresentation

      public FunctionalPitchModOctave pitchClassRepresentation()
      Return a pitch class, when Euler2(0,0) is assigned to the pitch class "c"

    • pureTuningFactor

      public Rational pureTuningFactor()
      Return a tuning factor when the coordinates are interpreted as the application of the pure tuning intervals fifth = 3/2 and third = 5/4.

    • minimalDistance

      public Euler3 minimalDistance()
      Add a number of octaves to make the distance between the two notes minimal, i.e. shift the factor expressed by this interval into less than one octave distance, modulo octave.