User:CompactStar/Super-pitch: Difference between revisions

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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. 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''' is a quantity that is equal to the [https://en.wikipedia.org/wiki/Super-logarithm super-logarithm] or iterated logarithm (inverse [https://en.wikipedia.org/wiki/Tetration 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.

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.

Revision as of 02:53, 20 June 2023 view source CompactStar (talk \| contribs) autopatrolled 5,152 edits No edit summary ← Older edit		Revision as of 02:53, 20 June 2023 view source CompactStar (talk \| contribs) autopatrolled 5,152 edits No edit summary Newer edit →
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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. 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''' is a quantity that is equal to the [https://en.wikipedia.org/wiki/Super-logarithm super-logarithm] or iterated logarithm (inverse [https://en.wikipedia.org/wiki/Tetration 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.

	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 2x, 22*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.		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 2x, 22*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.