Delta-rational chord: Difference between revisions
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[[Category:Chords]] | [[Category:Chords]] | ||
== Higher-order differences of frequency == | == Higher-order differences of frequency == | ||
Generalizing, one could consider chords where differences between its frequency deltas (as Tom Price has called it, '''precession''') are commensurable, while the deltas themselves may not be. This corresponds to chords where differences between various interference beatings go in and out of sync in a periodic manner. One | Generalizing, one could consider chords where differences between its frequency deltas (as Tom Price has called it, '''precession''') are commensurable, while the deltas themselves may not be. This corresponds to chords where differences between various interference beatings go in and out of sync in a periodic manner. One precession-rational chord is 5:5.4142...:6.8284...:9.2426..., a +(sqrt(2) − 1) +sqrt(2) +(sqrt(2) + 1) chord. | ||
Precession being the second-order difference (Δ<sup>2</sup>) of frequency, we similarly have the theoretical notions of Δ<sup>3</sup>-rationality, Δ<sup>4</sup>-rationality, and so on. The practical consequences of higher-order differences are as of yet speculative, though a few people have reported finding precession psychoacoustically meaningful. | Precession being the second-order difference (Δ<sup>2</sup>) of frequency, we similarly have the theoretical notions of Δ<sup>3</sup>-rationality, Δ<sup>4</sup>-rationality, and so on. The practical consequences of higher-order differences are as of yet speculative, though a few people have reported finding precession psychoacoustically meaningful. | ||