User:CompactStar/Super-pitch: Difference between revisions
m Marked as novelty (at least for as long as super-pitch doesn't have evidence of specific psychoacoustic effects) |
m Fredg999 moved page Super-pitch to User:CompactStar/Super-pitch over redirect: OR-3 (idiosyncratic framework and terminology) |
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'''Super-pitch''' is a quantity that is equal to the [https://en.wikipedia.org/wiki/Super-logarithm super-logarithm] (inverse [https://en.wikipedia.org/wiki/Tetration tetration]) of frequency, just as pitch is the logarithm of frequency. | '''Super-pitch'''{{idiosyncratic}} is a quantity that is equal to the [https://en.wikipedia.org/wiki/Super-logarithm super-logarithm] (inverse [https://en.wikipedia.org/wiki/Tetration tetration]) of frequency, just as pitch is the logarithm of frequency. | ||
The super-logarithm is traditionally defined the number of times a logarithm must be iterated to get to 1. For example, slog<sub>b</sub>(1) = 0, slog<sub>b</sub>(b) = 1, slog<sub>b</sub>(b<sup>b</sup>) = 2, slog<sub>b</sub>(b<sup>b<sup>b</sup></sup>) = 3, and so on. This definition only allows for inputs of the form 1, b, b<sup>b</sup>, b<sup>b<sup>b</sup></sup>, etc., although there are various continuous extensions of it for other outputs (most commonly the linear and quadratic approximations, as mentioned on the Wikipedia article) which have differing definitions. | The super-logarithm is traditionally defined the number of times a logarithm must be iterated to get to 1. For example, slog<sub>b</sub>(1) = 0, slog<sub>b</sub>(b) = 1, slog<sub>b</sub>(b<sup>b</sup>) = 2, slog<sub>b</sub>(b<sup>b<sup>b</sup></sup>) = 3, and so on. This definition only allows for inputs of the form 1, b, b<sup>b</sup>, b<sup>b<sup>b</sup></sup>, etc., although there are various continuous extensions of it for other outputs (most commonly the linear and quadratic approximations, as mentioned on the Wikipedia article) which have differing definitions. | ||
There is, notably, one extension for complex numbers developed by Kneser, which so far seems the best when implemented to the reals. | There is, notably, one extension for complex numbers developed by Kneser, which so far seems the best when implemented to the reals. | ||
The term "super-pitch" was proposed by [[User:CompactStar|CompactStar]]. | |||
== "Super-pitch equivalents" of different concepts == | == "Super-pitch equivalents" of different concepts == | ||