User:CompactStar/Super-pitch: Difference between revisions
→"Super-pitch equivalents" of different concepts: call it superoctave |
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This is arguably the way to make super-pitch divisions of a given interval. For example, the following table shows 10 super-pitch divisions of the octave <ref name=":0" />: | This is arguably the way to make super-pitch divisions of a given interval. For example, the following table shows 10 super-pitch divisions of the octave <ref name=":0" />: | ||
{| class="wikitable" | {| class="wikitable" | ||
! colspan="2" |10 | ! colspan="2" |10 equal divisions of the superoctave | ||
<small>per Kneser's solution</small> | <small>per Kneser's solution</small> | ||
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|} | |} | ||
Since exponentiation is not commutative and has two inverses - root and logarithm which breed two distinct numbers, likewise tetration has similar inverses which are too sets of disjoint numbers - solution to x^x = 2 is not the same number as solution to slog2(x) = 0.5. A pure interpolative function does not cancel out, for example the interval step 5, 1.458782..., when raised to the power of itself does not yield 2. Likewise, the first step, 1.089118, power-tower-ated 10 times does not yield 2 either. | Since exponentiation is not commutative and has two inverses - root and logarithm which breed two distinct numbers, likewise tetration has similar inverses which are too sets of disjoint numbers - solution to x^x = 2 is not the same number as solution to slog2(x) = 0.5. A pure interpolative function does not cancel out, for example the interval step 5, 1.458782..., when raised to the power of itself does not yield 2. Likewise, the first step, 1.089118, power-tower-ated 10 times does not yield 2 either. | ||
=== Individual pages for EDSO === | |||
* [[8edso]] | |||
== References == | == References == | ||
<references /> | <references /> | ||