Delta-rational chord: Difference between revisions

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[[Category:Chords]]

== Higher-order differences of frequency ==

To further generalize, one could consider chords where differences between frequency deltas ('''precession''') are commensurable, while deltas themselves may not be. This corresponds to chords where differences between various interference beatings go in and out of sync in a regular manner. One example would be a +(sqrt(2) − 1) +sqrt(2) +(sqrt(2) + 1) chord.

To further generalize, one could consider chords where differences between frequency deltas (as Tom Price has called it, '''precession''') are commensurable, while deltas themselves may not be. This corresponds to chords where differences between various interference beatings go in and out of sync in a regular manner. One example would be a +(sqrt(2) − 1) +sqrt(2) +(sqrt(2) + 1) chord.

Precession being the second-order difference (Δ2) of frequency, we similarly have the notions of Δ3-rationality, Δ4-rationality, and so on. The practical consequences of these higher-order differences are as of yet speculative, though a few people have reported finding precession psychoacoustically meaningful.

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 [[Category:Chords]]
 == Higher-order differences of frequency ==
-To further generalize, one could consider chords where differences between frequency deltas ('''precession''') are commensurable, while deltas themselves may not be. This corresponds to chords where differences between various interference beatings go in and out of sync in a regular manner. One example would be a +(sqrt(2) &minus; 1) +sqrt(2) +(sqrt(2) + 1) chord.
+To further generalize, one could consider chords where differences between frequency deltas (as Tom Price has called it, '''precession''') are commensurable, while deltas themselves may not be. This corresponds to chords where differences between various interference beatings go in and out of sync in a regular manner. One example would be a +(sqrt(2) &minus; 1) +sqrt(2) +(sqrt(2) + 1) chord.
 Precession being the second-order difference (Δ<sup>2</sup>) of frequency, we similarly have the notions of Δ<sup>3</sup>-rationality, Δ<sup>4</sup>-rationality, and so on. The practical consequences of these higher-order differences are as of yet speculative, though a few people have reported finding precession psychoacoustically meaningful.