com.dixshtix.audio.pitch
Class LinearTemperament

java.lang.Object
  |
  +--com.dixshtix.audio.pitch.AbstractTuning
        |
        +--com.dixshtix.audio.pitch.LinearTemperament

public class LinearTemperament

extends AbstractTuning

Linear Temperament is a system of altering fifths and thirds to make them "fit" into an octave.

There are two quite different kinds of temperament, the Linear and the Cyclic. The Linear contains an endless series of notes which never recur in pitch (because no combination of fifths and major thirds can be comeasurate with an octave). The cyclic contains also an endless series of notes which, however, do recur in pitch. Hence in Cyclic temperaments, all the intervals are made up of equal parts of an Octave. The advantage of the Cyclic over the Linear temperaments consists chiefly in a power of endless modulation, at the cost of harmoniousness.

Let us suppose that in any system of temperaments,

V

represents the adopted interval of a fifth.

T

represents the adopted interval of a major third.

K

represents the adopted interval corresponding to a Comma.

S

represents the adopted interval corresponding to a Skhisma.

O

represents the (perfect) interval of the octave.

Then the following relations must hold:

• 12 V - 7 O = K + S
• O - 3 T = 2 K - S

, which imply:

• V = 700 Cents + ( K + S ) / 12
• T = 300 Cents - ( 2 K - S ) / 3

. Thus there only two independent equations among the four adopted intervals. K and S can be derived from V and T by the following relations:

• K = 4 V - T - 2 O
• S = 8 V + T - 5 O

. Hence, on assuming values for any two of these intervals, we may find corresponding values for the other two. But no results are of any European interest unless V and T are very close to the values of AbstractTuning.justFifth and AbstractTuning.majorThird.

Version:

0.1

Author:

Richard C. Penner II

Field Summary

private java.lang.String	highNote
private double	K
private java.lang.String	lowNote
private java.lang.String	name
private java.lang.String	octaveBase
private double	S
private double	T
private java.lang.String	tuneBase
private double	tuneFrequency
private double	V

Fields inherited from class com.dixshtix.audio.pitch.AbstractTuning

A, Af, Aff, As, Ass, B, Bf, Bff, Bs, Bss, C, Cf, Cff, circleOfFifths, comma, Cs, Css, D, Df, Dff, didymusComma, doubleFlat, doubleSharp, Ds, Dss, E, Ef, Eff, equalTemperedFifth, equalTemperedThird, Es, Ess, F, Ff, Fff, flat, Fs, Fss, G, Gf, Gff, Gs, Gss, hemholtzFifth, justFifth, justOctave, majorThird, meantoneFifth, mercatorialComma, mercatorialFifth, pythagoreanComma, pythagoreanDiesis, sharp, skhisma, skhismicMajorThird

Constructor Summary

protected

LinearTemperament(java.lang.String name, double V, double T, double K, double S)

Method Summary

double	getComma()
static double	getCommaFromFifthAndThird(double V, double T) K = 4 V - T - 2 O
double	getFifth()
static double	getFifthFromCommaAndSkhisma(double K, double S) V = 700 Cents + ( K + S ) / 12
java.lang.String	getName()
java.lang.String	getOctaveBase()
double	getSkhisma()
static double	getSkhismaFromFifthAndComma(double V, double K) S = 12 V - 7 O - K
static double	getSkhismaFromFifthAndThird(double V, double T) S = 8 V + T - 5 O
double	getThird()
static double	getThirdFromCommaAndSkhisma(double K, double S) T = 400 Cents - ( 2 K - S ) / 3
static double	getThirdFromFifthAndComma(double V, double K) T = 4 V - 2 O - K
void	setNoteRange(java.lang.String lowNoteName, java.lang.String highNoteName)
void	setOctaveBase(java.lang.String noteName)
void	tune(java.lang.String noteName, double baseFrequency)

Methods inherited from class com.dixshtix.audio.pitch.AbstractTuning

centsToInterval, intervalToCents

Methods inherited from class java.lang.Object

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

Field Detail

name

private final java.lang.String name

V

private final double V

T

private final double T

K

private final double K

S

private final double S

octaveBase

private java.lang.String octaveBase

tuneBase

private java.lang.String tuneBase

tuneFrequency

private double tuneFrequency

lowNote

private java.lang.String lowNote

highNote

private java.lang.String highNote

Constructor Detail

LinearTemperament

protected LinearTemperament(java.lang.String name,
                            double V,
                            double T,
                            double K,
                            double S)

Method Detail

getName

public java.lang.String getName()

getFifth

public double getFifth()

getThird

public double getThird()

getComma

public double getComma()

getSkhisma

public double getSkhisma()

setOctaveBase

public void setOctaveBase(java.lang.String noteName)

getOctaveBase

public java.lang.String getOctaveBase()

tune

public void tune(java.lang.String noteName,
                 double baseFrequency)

setNoteRange

public void setNoteRange(java.lang.String lowNoteName,
                         java.lang.String highNoteName)

getFifthFromCommaAndSkhisma

public static double getFifthFromCommaAndSkhisma(double K,
                                                 double S)

V = 700 Cents + ( K + S ) / 12

getThirdFromCommaAndSkhisma

public static double getThirdFromCommaAndSkhisma(double K,
                                                 double S)

T = 400 Cents - ( 2 K - S ) / 3

getThirdFromFifthAndComma

public static double getThirdFromFifthAndComma(double V,
                                               double K)

T = 4 V - 2 O - K

getCommaFromFifthAndThird

public static double getCommaFromFifthAndThird(double V,
                                               double T)

K = 4 V - T - 2 O

getSkhismaFromFifthAndThird

public static double getSkhismaFromFifthAndThird(double V,
                                                 double T)

S = 8 V + T - 5 O

getSkhismaFromFifthAndComma

public static double getSkhismaFromFifthAndComma(double V,
                                                 double K)

S = 12 V - 7 O - K