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12 tone equal temperament chromatic scale on C, one full octave ascending, notated only with sharps. Play ascending and descending ⓘ. An equal temperament is a musical temperament or tuning system that approximates just intervals by dividing an octave (or other interval) into steps such that the ratio of the frequencies of any adjacent pair of notes is the same.
By definition, in Pythagorean tuning 11 perfect fifths (P5 in the table) have a size of approximately 701.955 cents (700+ε cents, where ε ≈ 1.955 cents). Since the average size of the 12 fifths must equal exactly 700 cents (as in equal temperament), the other one must have a size of 700 − 11 ε cents, which is about 678.495 cents (the ...
The definition of "tempered representation" makes sense for arbitrary unimodular locally compact groups, but on groups with infinite centers such as infinite central extensions of semisimple Lie groups it does not behave well and is usually replaced by a slightly different definition.
For example, if s=2, then 𝜁(s) is the well-known series 1 + 1/4 + 1/9 + 1/16 + …, which strangely adds up to exactly 𝜋²/6. When s is a complex number—one that looks like a+b𝑖, using ...
No matter what dual topology is placed on ′ (), [note 13] a sequence of distributions converges in this topology if and only if it converges pointwise (although this need not be true of a net). No matter which topology is chosen, D ′ ( U ) {\displaystyle {\mathcal {D}}^{\prime }(U)} will be a non- metrizable , locally convex topological ...
For 12 tone equally-tempered tuning, the fifths have to be tempered by considerably less than a 1 / 4 comma (very close to a 1 / 11 syntonic comma, or a 1 / 12 Pythagorean comma), since they must form a perfect cycle, with no gap at the end, whereas 1 / 4 comma meantone tuning, as mentioned above, has a residual ...
In meantone temperament, this effect is even more pronounced (the fifth over the break in the circle is known as the Wolf interval, as its intense beating was likened to a "howling"). 53 equal temperament provides an extension of Pythagorean tuning, and 31 equal temperament is used nowadays to extend quarter-comma meantone.
12-tone equal temperament chromatic scale on C, one full octave ascending, notated only with sharps. Play ascending and descending ⓘ. 12 equal temperament (12-ET) [a] is the musical system that divides the octave into 12 parts, all of which are equally tempered (equally spaced) on a logarithmic scale, with a ratio equal to the 12th root of 2 (≈ 1.05946).