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 reprenset physical tunings, and the intervals were interepreted as the factors of pure tuning. Later it is used for "mental maps", for pschological coordinate in the space of "functional music theory".

Field Summary

Fields

Modifier and Type	Field and Description
protected int	_3 The exponent of the applied third.
protected int	_5 The exponent of the applied fifth.
static FunctionalPitchModOctave	class_c

Constructor Summary

Constructors

Constructor and Description
Euler2(int _5, int _3) Only constructor, set both coordinates.

Method Summary

Modifier and Type	Method and Description
boolean	equals(Euler2 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.
Euler3	minimalDistance() Add a number of octaves to make the distance between the two notes minimal, i.e.
FunctionalPitchModOctave	pitchClassRepresentation() Return a pitch class, when Euler2(0.0) is assigned to the pitch class "c"
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.
FunctionalPitchModOctave	transpose_up(FunctionalPitchModOctave pitch) Interpret the coordinates as functional intervals (fifth and major third) 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.

class_c

public static final FunctionalPitchModOctave class_c

Constructor Detail

Euler2

public Euler2(int _5,
              int _3)

Only constructor, set both coordinates.

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.

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.