User:CompactStar/Super-pitch: Difference between revisions

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The super-pitch equivalent of [[just intonation]] is intervals of the form logb(x) for positive integers b and x. This includes all of just intonation, since all just intervals can be described as logarithms (e.g. [[3/2]] = log4(8)), in addition to some irrational numbers such as log2(3).

It is possible to construct super-pitch equivalents of most concepts in [[regular temperament theory]]. There exists a super-pitch analogue of prime factorization–every integer greater than 2 can be uniquely expressed as a power tower of numbers in the sequence OEIS [https://oeis.org/A007916] (non-perfect powers): 2 = 2, 3 = 3, 4 = 22, 5 = 5, 6 = 6, 7 = 7, 8 = 23, 9 = 32, etc.

It is possible to construct super-pitch equivalents of most concepts in [[regular temperament theory]]. There exists a super-pitch analogue of prime factorization–every integer greater than 2 can be uniquely expressed as a power tower of numbers in the sequence OEIS [https://oeis.org/A007916 A007916] (non-perfect powers): 2 = 2, 3 = 3, 4 = 22, 5 = 5, 6 = 6, 7 = 7, 8 = 23, 9 = 32, etc.

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	The super-pitch equivalent of [[just intonation]] is intervals of the form log<sub>b</sub>(x) for positive integers b and x. This includes all of just intonation, since all just intervals can be described as logarithms (e.g. [[3/2]] = log<sub>4</sub>(8)), in addition to some irrational numbers such as log<sub>2</sub>(3).		The super-pitch equivalent of [[just intonation]] is intervals of the form log<sub>b</sub>(x) for positive integers b and x. This includes all of just intonation, since all just intervals can be described as logarithms (e.g. [[3/2]] = log<sub>4</sub>(8)), in addition to some irrational numbers such as log<sub>2</sub>(3).

	It is possible to construct super-pitch equivalents of most concepts in [[regular temperament theory]]. There exists a super-pitch analogue of prime factorization–every integer greater than 2 can be uniquely expressed as a power tower of numbers in the sequence OEIS [https://oeis.org/A007916] (non-perfect powers): 2 = 2, 3 = 3, 4 = 2<sup>2</sup>, 5 = 5, 6 = 6, 7 = 7, 8 = 2<sup>3</sup>, 9 = 3<sup>2</sup>, etc.		It is possible to construct super-pitch equivalents of most concepts in [[regular temperament theory]]. There exists a super-pitch analogue of prime factorization–every integer greater than 2 can be uniquely expressed as a power tower of numbers in the sequence OEIS [https://oeis.org/A007916 A007916] (non-perfect powers): 2 = 2, 3 = 3, 4 = 2<sup>2</sup>, 5 = 5, 6 = 6, 7 = 7, 8 = 2<sup>3</sup>, 9 = 3<sup>2</sup>, etc.