Delta-rational chord: Difference between revisions
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JI chords and [[isodifferential chord]]s (chords of the form α : α + ''k''<sub>1</sub> : ... : α + ''k''<sub>n</sub> for any positive number α and integers k<sub>1</sub>, ..., k<sub>n</sub>) are a special case of pseudo-JI, but in these chords ''all'' dyads are rationally related in frequency space. | JI chords and [[isodifferential chord]]s (chords of the form α : α + ''k''<sub>1</sub> : ... : α + ''k''<sub>n</sub> for any positive number α and integers k<sub>1</sub>, ..., k<sub>n</sub>) are a special case of pseudo-JI, but in these chords ''all'' dyads are rationally related in frequency space. | ||
== | == A remark on the definition == | ||
Tom Price believes that a purely mathematical definition won't capture the set of chords that have the acoustic effect from interference. We will adopt the following mathematical definition for convenience: A chord C = α<sub>1</sub>:...:α<sub>n</sub> is ''mathematically pseudo-JI'' 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. Approximations of mathematically pseudo-JI chords can also be called pseudo-JI. | Tom Price believes that a purely mathematical definition won't capture the set of chords that have the acoustic effect from interference. We will adopt the following mathematical definition for convenience: A chord C = α<sub>1</sub>:...:α<sub>n</sub> is ''mathematically pseudo-JI'' 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. Approximations of mathematically pseudo-JI chords can also be called pseudo-JI. | ||