Delta-rational chord: Difference between revisions

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== A remark on the definition ==

We will adopt the following mathematical definitions for convenience: A chord C = α1:...:αn is ''SDLR'' (from "some dyads linearly related") when the chord has two distinct dyads αk1:αk2 and αk3:αk4 such that (αk2 − αk1)/(αk4 − αk3) is rational. Chords that are audible as approximations of SDLR chords can be called delta-JI. When all dyads are linearly related, i.e. when the chord is of the form (α + k1):...:(α + kn), we call the chord ''ADLR'' for "all dyads linearly related".

Strictly speaking, delta-JI refers to an acoustic property, not a mathematical one. We will adopt the following mathematical definitions for convenience: A chord C = α1:...:αn is ''SDLR'' (from "some dyads linearly related") when the chord has two distinct dyads αk1:αk2 and αk3:αk4 such that (αk2 − αk1)/(αk4 − αk3) is rational. Chords that are audible as approximations of SDLR chords can be called delta-JI. When all dyads are linearly related, i.e. when the chord is of the form (α + k1):...:(α + kn), we call the chord ''ADLR'' for "all dyads linearly related".

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	== A remark on the definition ==		== A remark on the definition ==
	We will adopt the following mathematical definitions for convenience: A chord C = α<sub>1</sub>:...:α<sub>n</sub> is ''SDLR'' (from "some dyads linearly related") when the chord has two distinct dyads α<sub>k<sub>1</sub></sub>:α<sub>k<sub>2</sub></sub> and α<sub>k<sub>3</sub></sub>:α<sub>k<sub>4</sub></sub> such that (α<sub>k<sub>2</sub></sub> − α<sub>k<sub>1</sub></sub>)/(α<sub>k<sub>4</sub></sub> − α<sub>k<sub>3</sub></sub>) is rational. Chords that are audible as approximations of SDLR chords can be called delta-JI. When all dyads are linearly related, i.e. when the chord is of the form (α + k<sub>1</sub>):...:(α + k<sub>n</sub>), we call the chord ''ADLR'' for "all dyads linearly related".		Strictly speaking, delta-JI refers to an acoustic property, not a mathematical one. We will adopt the following mathematical definitions for convenience: A chord C = α<sub>1</sub>:...:α<sub>n</sub> is ''SDLR'' (from "some dyads linearly related") when the chord has two distinct dyads α<sub>k<sub>1</sub></sub>:α<sub>k<sub>2</sub></sub> and α<sub>k<sub>3</sub></sub>:α<sub>k<sub>4</sub></sub> such that (α<sub>k<sub>2</sub></sub> − α<sub>k<sub>1</sub></sub>)/(α<sub>k<sub>4</sub></sub> − α<sub>k<sub>3</sub></sub>) is rational. Chords that are audible as approximations of SDLR chords can be called delta-JI. When all dyads are linearly related, i.e. when the chord is of the form (α + k<sub>1</sub>):...:(α + k<sub>n</sub>), we call the chord ''ADLR'' for "all dyads linearly related".