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

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and 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 Detail

_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 Detail

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 Detail

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.