Package eu.bandm.music.entities

Class Euler3

java.lang.Object
eu.bandm.music.entities.Euler3
public class Euler3 extends Object
Representation of pitch classes or interval classes in the Euler net, extended by octaves. Each point has three coordinates, representing the application of the step of a pure fifth, of a major third, and of an octave. Historically this is an extension to Euler2. Therfore the octave is the third coordinate of the constructor.

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    static final Rational
    _2_1
     
    protected final int
    _3
    The exponent of the applied third.
    static final Rational
    _3_2
     
    protected final int
    _5
    The exponent of the applied fifth.
    static final Rational
    _5_4
     
    protected final int
    _8
    The exponent of the applied octave.
    static final FunctionalPitch
    c_prime
    Auxiliary value for the pitch interpretation.

  • Constructor Summary

    Constructors
    Constructor
    Description
    Euler3(int _5, int _3, int _8)
    Constructor setting all coordinates explicitly.
    Euler3(Euler2 cls, int _8)
    Constructor enhancing a fifth/third oordinate pair by an octave exponent

  • Method Summary

    Modifier and Type
    Method
    Description
    Euler2
    asEuler2()
    Forget the octave coordinate.
    boolean
    equals(Euler3 t)
    Evident
    boolean
    equals(Object o)
     
    int
    get_3()
    Return the exponent of the applied third.
    int
    get_5()
    Return the exponent of the applied fifth.
    int
    get_8()
    Return the exponent of the applied octave.
    FunctionalPitch
    pitchRepresentation()
    Return a pitch class, when Euier3(0,0,0) is assigned to the pitch class "c'" (midi "c4")
    Rational
    pureTuningFactor()
    Return a tuning factor when the coordinates are interpreted as the application of the pure tuning intervals fifth = 3/2, third = 5/4 and oktabe = 2/1.
    FunctionalPitch
    transpose_up(FunctionalPitch pitch)
    Interpret the coordinates as functional intervals (fifth, major third and octave) and apply them to the given pitch.

    Methods inherited from class java.lang.Object

    clone, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Field Details

    • _5

      protected final int _5
      The exponent of the applied fifth.

    • _3

      protected final int _3
      The exponent of the applied third.

    • _8

      protected final int _8
      The exponent of the applied octave.

    • _2_1

      public static final Rational _2_1

    • _3_2

      public static final Rational _3_2

    • _5_4

      public static final Rational _5_4

    • c_prime

      public static final FunctionalPitch c_prime
      Auxiliary value for the pitch interpretation.

  • Constructor Details

    • Euler3

      public Euler3(int _5, int _3, int _8)
      Constructor setting all coordinates explicitly.

    • Euler3

      public Euler3(Euler2 cls, int _8)
      Constructor enhancing a fifth/third oordinate pair by an octave exponent

  • 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.

    • get_8

      public int get_8()
      Return the exponent of the applied octave.

    • equals

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

    • equals

      public boolean equals(Euler3 t)
      Evident

    • transpose_up

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

    • pitchRepresentation

      public FunctionalPitch pitchRepresentation()
      Return a pitch class, when Euier3(0,0,0) is assigned to the pitch class "c'" (midi "c4")

      (The other way is only possible from a pair of FunctionalPitch and syntonic comma, which is not yet modelled here.

    • pureTuningFactor

      public Rational pureTuningFactor()
      Return a tuning factor when the coordinates are interpreted as the application of the pure tuning intervals fifth = 3/2, third = 5/4 and oktabe = 2/1.

    • asEuler2

      public Euler2 asEuler2()
      Forget the octave coordinate. This is like going from pitch to pitch class.