Search results
Results from the WOW.Com Content Network
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 ...
Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
Any irreducible tempered representation is a basic representation, and conversely any basic representation is the sum of a finite number of irreducible tempered representations. More precisely, it is a direct sum of 2 r irreducible tempered representations indexed by the characters of an elementary abelian group R of order 2 r (called the R ...
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 ...
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.
These identities also hold much more broadly in the sense of tempered distributions if one of f or g is a rapidly decreasing tempered distribution, a compactly supported tempered distribution or a Schwartz function and the other is a tempered distribution. On the other hand, two positive integrable and infinitely differentiable functions may ...
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
The set of all points of discontinuity of a function may be a discrete set, a dense set, or even the entire domain of the function. dot product In mathematics, the dot product or scalar product [note 1] is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single