Equave limit: Difference between revisions

Line 1:

The '''equave limit'''{{idiosyncratic}} generalizes the concept of [[odd limit]], extending for any [[equave]] what the odd-limit represents specifically for the equave 2/1.

==Definition==

== Definition ==

The '''q-equave-n-limit''' is defined as the set of all positive rationals <math>\displaystyle

The '''''q''-equave-''n''-limit''' is defined as the set of all positive rationals <math>\displaystyle

{q^z}\cdot\frac{u}{v}

</math>, where:

Line 10:

* <math>n \in \mathbb{Z}^{+}</math> (i.e., <math>n</math> is a positive integer), called the '''limit'''.

The parameter <math>n</math> places an upper bound on the values of the integers <math>u</math> and <math>v</math>, meaning that both <math>u</math> and <math>v</math> are less than or equal to <math>n</math>. Thus, the '''q-equave-n-limit~~'''~~ consists of ratios generated by multiplying a power of <math>q</math> by ratios <math>\displaystyle

The parameter <math>n</math> places an upper bound on the values of the integers <math>u</math> and <math>v</math>, meaning that both <math>u</math> and <math>v</math> are less than or equal to <math>n</math>. Thus, the ''q''-equave-''n''-limit consists of ratios generated by multiplying a power of <math>q</math> by ratios <math>\displaystyle

\frac{u}{v}

</math>, where the numerator and denominator are constrained by the limit <math>n</math>.

@@ Line 1: / Line 1: @@
 The '''equave limit'''{{idiosyncratic}} generalizes the concept of [[odd limit]], extending for any [[equave]] what the odd-limit represents specifically for the equave 2/1.
-==Definition==
+== Definition ==
-The '''q-equave-n-limit''' is defined as the set of all positive rationals <math>\displaystyle
+The '''''q''-equave-''n''-limit''' is defined as the set of all positive rationals <math>\displaystyle
 {q^z}\cdot\frac{u}{v}
 </math>, where:
@@ Line 10: / Line 10: @@
 * <math>n \in \mathbb{Z}^{+}</math> (i.e., <math>n</math> is a positive integer), called the '''limit'''.
-The parameter <math>n</math> places an upper bound on the values of the integers <math>u</math> and <math>v</math>, meaning that both <math>u</math> and <math>v</math> are less than or equal to <math>n</math>. Thus, the '''q-equave-n-limit''' consists of ratios generated by multiplying a power of <math>q</math> by ratios <math>\displaystyle
+The parameter <math>n</math> places an upper bound on the values of the integers <math>u</math> and <math>v</math>, meaning that both <math>u</math> and <math>v</math> are less than or equal to <math>n</math>. Thus, the ''q''-equave-''n''-limit consists of ratios generated by multiplying a power of <math>q</math> by ratios <math>\displaystyle
 \frac{u}{v}
 </math>, where the numerator and denominator are constrained by the limit <math>n</math>.