Mina - Revision history

ArrowHead294 at 13:12, 10 April 2025

2025-04-10T13:12:07Z

← Older revision		Revision as of 13:12, 10 April 2025
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! ~~interval~~		! Interval
	! ~~size~~ in <br> cents		! Size in<br />cents
	! ~~size~~ in <br> minas		! Size in<br />minas
	! ~~size~~ as degrees <br> and minutes		! Size as degrees<br />and minutes
	\|-		\|-
	\| 1\2460		\| 1\2460
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	\|}		\|}

	Another notable feature of the mina is the accuracy and breadth of its approximations to just intervals. Accordingly it is hardly necessary to express intervals in non-integer values of mina, something that arguably cannot be said of cents. [[2460edo]] is uniquely [[consistent]] through to the [[27-odd-limit\|27-limit]], which is not very remarkable in itself ([[388edo]] is the first such system), but what is remarkable is the degree of accuracy to which it represents the 27-limit intervals. It is also a [[~~The~~ Riemann ~~Zeta Function~~ and ~~Tuning~~#Zeta EDO lists\|zeta peak edo]] and has a lower 19-limit [[~~Tenney-Euclidean~~ temperament measures#TE simple badness\|relative error]] than any edo until [[3395edo\|3395]], and a lower [[23-limit]] relative error than any until [[8269edo\|8269]]. Also it has a lower 23-limit [[~~Tenney-Euclidean~~ metrics#Logflat TE badness\|TE logflat badness]] than any smaller edo and less than any until [[16808edo\|16808]].		Another notable feature of the mina is the accuracy and breadth of its approximations to just intervals. Accordingly it is hardly necessary to express intervals in non-integer values of mina, something that arguably cannot be said of cents. [[2460edo]] is uniquely [[consistent]] through to the [[27-odd-limit\|27-limit]], which is not very remarkable in itself ([[388edo]] is the first such system), but what is remarkable is the degree of accuracy to which it represents the 27-limit intervals. It is also a [[the Riemann zeta function and tuning#Zeta EDO lists\|zeta peak edo]] and has a lower 19-limit [[Tenney–Euclidean temperament measures#TE simple badness\|relative error]] than any edo until [[3395edo\|3395]], and a lower [[23-limit]] relative error than any until [[8269edo\|8269]]. Also it has a lower 23-limit [[Tenney–Euclidean metrics#Logflat TE badness\|TE logflat badness]] than any smaller edo and less than any until [[16808edo\|16808]].

	Below the intervals of the [[27-odd-limit\|27-limit]] [[tonality diamond]] are tabulated, with the sizes listed in both [[cent]]s and minas and expressed as degrees and minutes (rounded to the nearest minute). The value in minas, rounded to the nearest integer, can be found by applying the 23-limit [[patent val]] {{val\| 2460 3899 5712 6906 8510 9103 10055 10450 11128 }} for 2460edo; this will not work for [[1200edo]] and cents.		Below the intervals of the [[27-odd-limit\|27-limit]] [[tonality diamond]] are tabulated, with the sizes listed in both [[cent]]s and minas and expressed as degrees and minutes (rounded to the nearest minute). The value in minas, rounded to the nearest integer, can be found by applying the 23-limit [[patent val]] {{val\| 2460 3899 5712 6906 8510 9103 10055 10450 11128 }} for 2460edo; this will not work for [[1200edo]] and cents.
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! interval <br>ratio		! interval<br />ratio
	! size <br> in cent		! size<br />in cent
	! size <br> in mina		! size<br />in mina
	! size as degrees <br> and minutes		! size as degrees<br />and minutes
	\|-		\|-
	\| 1		\| 1

AraMax: Added a redirect to 27-odd-limit

2024-10-16T09:55:18Z

Added a redirect to 27-odd-limit

← Older revision		Revision as of 09:55, 16 October 2024
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	\|}		\|}

	Another notable feature of the mina is the accuracy and breadth of its approximations to just intervals. Accordingly it is hardly necessary to express intervals in non-integer values of mina, something that arguably cannot be said of cents. [[2460edo]] is uniquely [[consistent]] through to the [[27-limit]], which is not very remarkable in itself ([[388edo]] is the first such system), but what is remarkable is the degree of accuracy to which it represents the 27-limit intervals. It is also a [[The Riemann Zeta Function and Tuning#Zeta EDO lists\|zeta peak edo]] and has a lower 19-limit [[Tenney-Euclidean temperament measures#TE simple badness\|relative error]] than any edo until [[3395edo\|3395]], and a lower [[23-limit]] relative error than any until [[8269edo\|8269]]. Also it has a lower 23-limit [[Tenney-Euclidean metrics#Logflat TE badness\|TE logflat badness]] than any smaller edo and less than any until [[16808edo\|16808]].		Another notable feature of the mina is the accuracy and breadth of its approximations to just intervals. Accordingly it is hardly necessary to express intervals in non-integer values of mina, something that arguably cannot be said of cents. [[2460edo]] is uniquely [[consistent]] through to the [[27-odd-limit\|27-limit]], which is not very remarkable in itself ([[388edo]] is the first such system), but what is remarkable is the degree of accuracy to which it represents the 27-limit intervals. It is also a [[The Riemann Zeta Function and Tuning#Zeta EDO lists\|zeta peak edo]] and has a lower 19-limit [[Tenney-Euclidean temperament measures#TE simple badness\|relative error]] than any edo until [[3395edo\|3395]], and a lower [[23-limit]] relative error than any until [[8269edo\|8269]]. Also it has a lower 23-limit [[Tenney-Euclidean metrics#Logflat TE badness\|TE logflat badness]] than any smaller edo and less than any until [[16808edo\|16808]].

	Below the intervals of the [[27-limit]] [[tonality diamond]] are tabulated, with the sizes listed in both [[cent]]s and minas and expressed as degrees and minutes (rounded to the nearest minute). The value in minas, rounded to the nearest integer, can be found by applying the 23-limit [[patent val]] {{val\| 2460 3899 5712 6906 8510 9103 10055 10450 11128 }} for 2460edo; this will not work for [[1200edo]] and cents.		Below the intervals of the [[27-odd-limit\|27-limit]] [[tonality diamond]] are tabulated, with the sizes listed in both [[cent]]s and minas and expressed as degrees and minutes (rounded to the nearest minute). The value in minas, rounded to the nearest integer, can be found by applying the 23-limit [[patent val]] {{val\| 2460 3899 5712 6906 8510 9103 10055 10450 11128 }} for 2460edo; this will not work for [[1200edo]] and cents.

	{\| class="wikitable"		{\| class="wikitable"

Fredg999: Categories

2024-07-05T04:54:13Z

Fredg999: External link

2024-07-05T04:37:18Z

External link

← Older revision		Revision as of 04:37, 5 July 2024
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	\| 41°		\| 41°
	\|}		\|}

			== External links ==
			* [http://tonalsoft.com/enc/m/mina.aspx mina] on [[Tonalsoft Encyclopedia]]

	[[Category:Mina\| ]] <!-- main article -->		[[Category:Mina\| ]] <!-- main article -->

FloraC: Recategorize

2023-11-26T11:21:20Z

Recategorize

← Older revision		Revision as of 11:21, 26 November 2023
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	[[Category:Mina\| ]] <!-- main article -->		[[Category:Mina\| ]] <!-- main article -->
	[[Category:2460edo]]		[[Category:2460edo]]
	[[Category:Interval size ~~measure~~]]		[[Category:Interval size measures]]
	[[Category:Logarithmic ~~measure~~]]		[[Category:Logarithmic measures]]

FloraC: +category

2023-08-29T08:36:56Z

+category

← Older revision		Revision as of 08:36, 29 August 2023
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	\|}		\|}

			[[Category:Mina\| ]] <!-- main article -->
			[[Category:2460edo]]
	[[Category:Interval size measure]]		[[Category:Interval size measure]]
	[[Category:Logarithmic measure]]		[[Category:Logarithmic measure]]
	~~[[Category:Mina]]~~

Fredg999: Internal link

2023-08-22T04:21:12Z

Internal link

← Older revision		Revision as of 04:21, 22 August 2023
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	The '''mina''' is a unit of interval size which has been proposed by [[George Secor]] and [[Dave Keenan]], and which is defined as 1/2460 of an [[octave]], the step size of [[2460edo]]. 2460 is divisible by both 12 and 41, two important systems, and it's been suggested that degrees and minutes can be used to express values in it, so that for instance 3/2, which is 1439 minas, could be denoted by 23°59', meaning very slightly flat of the 24\41 [[41edo]] fifths. This works out since 41 * 60 = 2460; an octave is therefore expressed as if it were an angle of 41 degrees.		The '''mina''' is a [[unit of interval size]] which has been proposed by [[George Secor]] and [[Dave Keenan]], and which is defined as 1/2460 of an [[octave]], the step size of [[2460edo]]. 2460 is divisible by both 12 and 41, two important systems, and it's been suggested that degrees and minutes can be used to express values in it, so that for instance 3/2, which is 1439 minas, could be denoted by 23°59', meaning very slightly flat of the 24\41 [[41edo]] fifths. This works out since 41 * 60 = 2460; an octave is therefore expressed as if it were an angle of 41 degrees.

	Other popular systems that can be represented exactly in whole numbers of minas include [[10edo]] and [[15edo]]. Moreover a cent is exactly 2.05 minas, and a ''[[mem]]'', 1\205 octaves, is exactly 12 minas.		Other popular systems that can be represented exactly in whole numbers of minas include [[10edo]] and [[15edo]]. Moreover a cent is exactly 2.05 minas, and a ''[[mem]]'', 1\205 octaves, is exactly 12 minas.

Fredg999 category edits: Removing from Category:Unit using Cat-a-lot

2023-04-26T02:22:08Z

Removing from Category:Unit using Cat-a-lot

← Older revision		Revision as of 02:22, 26 April 2023
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	[[Category:Logarithmic measure]]		[[Category:Logarithmic measure]]
	[[Category:Mina]]		[[Category:Mina]]
	~~[[Category:Unit]]~~

Fredg999 category edits: Removing from Category:Definition using Cat-a-lot

2023-03-06T21:52:07Z

Removing from Category:Definition using Cat-a-lot

← Older revision		Revision as of 21:52, 6 March 2023
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	\|}		\|}

	~~[[Category:Definition]]~~
	[[Category:Interval size measure]]		[[Category:Interval size measure]]
	[[Category:Logarithmic measure]]		[[Category:Logarithmic measure]]
	[[Category:Mina]]		[[Category:Mina]]
	[[Category:Unit]]		[[Category:Unit]]

Fredg999 category edits: Removing from Category:Measure using Cat-a-lot

2023-02-26T06:34:33Z

Removing from Category:Measure using Cat-a-lot

← Older revision		Revision as of 06:34, 26 February 2023
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	[[Category:Interval size measure]]		[[Category:Interval size measure]]
	[[Category:Logarithmic measure]]		[[Category:Logarithmic measure]]
	~~[[Category:Measure]]~~
	[[Category:Mina]]		[[Category:Mina]]
	[[Category:Unit]]		[[Category:Unit]]

← Older revision		Revision as of 04:54, 5 July 2024
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	[[Category:2460edo]]		[[Category:2460edo]]
	[[Category:Interval size measures]]		[[Category:Interval size measures]]
	~~[[Category:Logarithmic measures]]~~