Equave limit - Revision history

ArrowHead294 at 15:39, 9 September 2024

2024-09-09T15:39:29Z

← Older revision		Revision as of 15:39, 9 September 2024
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	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.		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}		{q^z}\cdot\frac{u}{v}
	</math>, where:		</math>, where:
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	* <math>n \in \mathbb{Z}^{+}</math> (i.e., <math>n</math> is a positive integer), called the '''limit'''.		* <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}		\frac{u}{v}
	</math>, where the numerator and denominator are constrained by the limit <math>n</math>.		</math>, where the numerator and denominator are constrained by the limit <math>n</math>.

ArrowHead294 at 15:39, 9 September 2024

2024-09-09T15:39:06Z

← Older revision		Revision as of 15:39, 9 September 2024
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	==Definition==		==Definition==
	The '''q-equave-n-limit''' is defined as the set of all positive rationals ~~<big><big>~~<math>\displaystyle		The '''q-equave-n-limit''' is defined as the set of all positive rationals <math>\displaystyle
	{q^z}\cdot\frac{u}{v}		{q^z}\cdot\frac{u}{v}
	</math~~></big></big~~>, where:		</math>, where:
	* <math>~~q∈Q~~+</math> (i.e., <math>q</math> is a positive rational number), called the '''equave''',		* <math>q \in \mathbb{Q}^{+}</math> (i.e., <math>q</math> is a positive rational number), called the '''equave''',
	* <math>~~z∈Z~~</math> (i.e., <math>z</math> is an integer, positive or negative),		* <math>z \in \mathbb{Z}</math> (i.e., <math>z</math> is an integer, positive or negative),
	* <math>u,~~v∈Z~~+</math> (i.e., <math>u</math> and <math>v</math> are positive integers) such that <math>~~u≤n~~</math> and <math>~~v≤n~~</math>,		* <math>u,v \in \mathbb{Z}^{+}</math> (i.e., <math>u</math> and <math>v</math> are positive integers) such that <math>u \leqslant n</math> and <math>v \leqslant n</math>,
	* <math>~~n∈Z~~+</math> (i.e., <math>n</math> is a positive integer), called the '''limit'''.		* <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

Fredg999: Move "purpose" section to lead section, mark term as idiosyncratic, categories

2024-09-08T00:10:12Z

Move "purpose" section to lead section, mark term as idiosyncratic, categories

← Older revision		Revision as of 00:10, 8 September 2024
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	~~==Purpose==~~		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.
	The '''equave limit''' generalizes the concept of [[odd limit]], extending for any [[equave]] what the odd-limit represents specifically for the equave 2/1.

	==Definition==		==Definition==
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	\frac{u}{v}		\frac{u}{v}
	</math> by restricting them to a specific [[just intonation subgroup]].		</math> by restricting them to a specific [[just intonation subgroup]].

			[[Category:Limit]]

Contribution at 22:23, 7 September 2024

2024-09-07T22:23:38Z

← Older revision		Revision as of 22:23, 7 September 2024
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	==Definition==		==Definition==
	The '''q-equave-n-limit''' is defined as the set of all positive rationals <big><big><math>\displaystyle		The '''q-equave-n-limit''' is defined as the set of all positive rationals <big><big><math>\displaystyle
	{q^z}\frac{u}{v}		{q^z}\cdot\frac{u}{v}
	</math></big></big>, where:		</math></big></big>, where:
	* <math>q∈Q+</math> (i.e., <math>q</math> is a positive rational number), called the '''equave''',		* <math>q∈Q+</math> (i.e., <math>q</math> is a positive rational number), called the '''equave''',

Contribution at 22:18, 7 September 2024

2024-09-07T22:18:03Z

← Older revision		Revision as of 22:18, 7 September 2024
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	==Purpose==		==Purpose==
	The '''equave-limit''' generalizes the concept of [[odd limit]], extending for any [[equave]] what the odd-limit represents specifically for the equave 2/1.		The '''equave limit''' generalizes the concept of [[odd limit]], extending for any [[equave]] what the odd-limit represents specifically for the equave 2/1.

	==Definition==		==Definition==

Contribution at 22:09, 7 September 2024

2024-09-07T22:09:58Z

← Older revision		Revision as of 22:09, 7 September 2024
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	\frac{u}{v}		\frac{u}{v}
	</math>, where the numerator and denominator are constrained by the limit <math>n</math>.		</math>, where the numerator and denominator are constrained by the limit <math>n</math>.

			Additional constraints can be applied to the ratios <math>\displaystyle
			\frac{u}{v}
			</math> by restricting them to a specific [[just intonation subgroup]].

Contribution: Created page with "==Purpose== The '''equave-limit''' generalizes the concept of odd limit, extending for any equave what the odd-limit represents specifically for the equave 2/1. ==Def..."

2024-09-07T20:33:49Z

Created page with "==Purpose== The '''equave-limit''' generalizes the concept of odd limit, extending for any equave what the odd-limit represents specifically for the equave 2/1. ==Def..."

New page

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

==Definition==
The '''q-equave-n-limit''' is defined as the set of all positive rationals <big><big><math>\displaystyle
{q^z}\frac{u}{v}
</math></big></big>, where:
* <math>q∈Q+</math> (i.e., <math>q</math> is a positive rational number), called the '''equave''',
* <math>z∈Z</math> (i.e., <math>z</math> is an integer, positive or negative),
* <math>u,v∈Z+</math> (i.e., <math>u</math> and <math>v</math> are positive integers) such that <math>u≤n</math> and <math>v≤n</math>,
* <math>n∈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
\frac{u}{v}
</math>, where the numerator and denominator are constrained by the limit <math>n</math>.