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== Super-pitch equivalents of different concepts == | == Super-pitch equivalents of different concepts == | ||
If super-pitch is used instead of pitch, equivalence works differently. For example, in a pitch-based system, the frequency x would be octave-equivalent to 2*x, 2*2*x, etc. and x/2, x/2/2, etc. But in a super-pitch based system, it would be octave-equivalent to 2<sup>2<sup>x</sup></sup>, etc. and log<sub>2</sub>(x), log<sub>2</sub>(log<sub>2</sub>(x)), etc. An "equal super-pitch divisions of the octave" is identical to an [[EDO]] within the range [[1/1]]-[[2/1]] if | If super-pitch is used instead of pitch, equivalence works differently. For example, in a pitch-based system, the frequency x would be octave-equivalent to 2*x, 2*2*x, etc. and x/2, x/2/2, etc. But in a super-pitch based system, it would be octave-equivalent to 2<sup>2<sup>x</sup></sup>, etc. and log<sub>2</sub>(x), log<sub>2</sub>(log<sub>2</sub>(x)), etc. An "equal super-pitch divisions of the octave" is identical to an [[EDO]] within the range [[1/1]]-[[2/1]] if using the linear approximation of super-logarithm, but it is distinct if using the quadratic approximation of super-logarithm. | ||
Revision as of 02:55, 20 June 2023
Super-pitch is a quantity that is equal to the super-logarithm (inverse tetration) of frequency, just as pitch is the logarithm of frequency. It should be noted that super-logarithms are traditionally only defined for integer outputs, and there are various extensions of it for non-integer outputs (most commonly the linear and quadratic approximations, as mentioned on the Wikipedia article) which have differing definitions.
Super-pitch equivalents of different concepts
If super-pitch is used instead of pitch, equivalence works differently. For example, in a pitch-based system, the frequency x would be octave-equivalent to 2*x, 2*2*x, etc. and x/2, x/2/2, etc. But in a super-pitch based system, it would be octave-equivalent to 22x, etc. and log2(x), log2(log2(x)), etc. An "equal super-pitch divisions of the octave" is identical to an EDO within the range 1/1-2/1 if using the linear approximation of super-logarithm, but it is distinct if using the quadratic approximation of super-logarithm.