Delta-rational chord: Difference between revisions

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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 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 higher-order differences are as of yet speculative, though a few people have reported finding precession psychoacoustically meaningful.

Precession being the second-order difference (Δ2) of frequency, we similarly have the theoretical notions of Δ3-rationality, Δ4-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.

== See also ==

* [[Linear chord]] - With linear chords, all the frequency differences between adjacent notes are simply related (i.e. equal or in a simple ratio like 1:2). With DR chords, some of them are, but not necessarily all of them.

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 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 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 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.
 == See also ==
 * [[Linear chord]] - With linear chords, all the frequency differences between adjacent notes are simply related (i.e. equal or in a simple ratio like 1:2). With DR chords, some of them are, but not necessarily all of them.