Meter: Difference between revisions

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The '''meter''', also known as the '''metric comma''' ({{monzo|legend=1| -11 2 7 -3 }}, [[ratio]]: 703125/702464), is an [[unnoticeable comma|unnoticeable]] [[7-limit]] [[comma]] with a value of approximately 1.6 [[cent]]s. It is the difference between a stack of three [[225/224|septimal kleismas]] and a [[81/80|syntonic comma]].

The '''meter''', also known as the '''metric comma''' ({{monzo|legend=1| -11 2 7 -3 }}, [[ratio]]: 703125/702464), is an [[unnoticeable comma|unnoticeable]] [[7-limit]] [[comma]] with a value of approximately 1.6 [[cent]]s. It is the difference between [[45/32]] and a stack of three instances of [[28/25]], as well as the difference between three [[225/224|septimal kleismas]] and a [[81/80|syntonic comma]].

== Temperaments ==

Tempering it out leads to the ~~'''~~metric temperament~~'''~~, which splits the syntonic comma into three equal parts, one for the septimal kleisma, and two for the [[126/125|septimal semicomma]]. It is also tempered out in [[septimal meantone]], but this is a trivial case since 81/80 and 225/224 are both tempered out.

[[Tempering out]] this comma leads to the [[metric]] temperament, which splits the syntonic comma into three equal parts, one for the septimal kleisma, and two for the [[126/125|septimal semicomma]]. It is also tempered out in [[septimal meantone]], but this is a trivial case since 81/80 and 225/224 are both tempered out.

See [[~~metric~~ microtemperaments]] for a collection of rank-2 temperaments where it is tempered out.

See [[Metric microtemperaments]] for a collection of rank-2 temperaments where it is tempered out.

~~=== Metric (31 & 171 & 323) ===~~

~~[[Subgroup]]: 2.3.5.7~~

~~[[Comma list]]: 703125/702464~~

~~{{Mapping|legend=1| 1 0 2 1 | 0 1 1 3 | 0 0 -3 -7 }}~~

~~[[Optimal tuning]] ([[POTE]]): ~3/2 = 701.8766, ~75/56 = 505.2613~~

~~{{Optimal ET sequence|legend=1| 12, 19, 31, 81, 90, 102d, 109, 121, 140, 152, 171, 665, 836, 1007, 2185, 3192c }}~~

~~[[Badness]]: 0.1498 × 10<sup>-3</sup>~~

== Etymology ==

This comma was first named as ''tertiaendec'' by [[Gene Ward Smith]] in 2005 as a contraction of ''[[tertiaseptal]]'' and ''[[enneadecal]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group | ''Seven limit comma names from pairs of temperament names'']</ref>. It is not clear how it later became ''meter''.

This comma was first named as ''tertiaendec'' by [[Gene Ward Smith]] in 2005 as a contraction of ''[[tertiaseptal]]'' and ''[[enneadecal]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group | ''Seven limit comma names from pairs of temperament names'']</ref>. It is not clear how it later became ''meter'' in 2010<ref>See [https://en.xen.wiki/index.php?title=Small_comma&oldid=13579 Revision as of 18:42, 1 June 2010 by Wikispaces>genewardsmith].</ref>.

== ~~Notes~~ ==

== References ==

[[Category:Metric (temperament)]]

[[Category:Commas with unknown etymology]]

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 | Comma = yes
 }}
-The '''meter''', also known as the '''metric comma''' ({{monzo|legend=1| -11 2 7 -3 }}, [[ratio]]: 703125/702464), is an [[unnoticeable comma|unnoticeable]] [[7-limit]] [[comma]] with a value of approximately 1.6 [[cent]]s. It is the difference between a stack of three [[225/224|septimal kleismas]] and a [[81/80|syntonic comma]].
+The '''meter''', also known as the '''metric comma''' ({{monzo|legend=1| -11 2 7 -3 }}, [[ratio]]: 703125/702464), is an [[unnoticeable comma|unnoticeable]] [[7-limit]] [[comma]] with a value of approximately 1.6 [[cent]]s. It is the difference between [[45/32]] and a stack of three instances of [[28/25]], as well as the difference between three [[225/224|septimal kleismas]] and a [[81/80|syntonic comma]].
 == Temperaments ==
-Tempering it out leads to the '''metric temperament''', which splits the syntonic comma into three equal parts, one for the septimal kleisma, and two for the [[126/125|septimal semicomma]]. It is also tempered out in [[septimal meantone]], but this is a trivial case since 81/80 and 225/224 are both tempered out.
+[[Tempering out]] this comma leads to the [[metric]] temperament, which splits the syntonic comma into three equal parts, one for the septimal kleisma, and two for the [[126/125|septimal semicomma]]. It is also tempered out in [[septimal meantone]], but this is a trivial case since 81/80 and 225/224 are both tempered out.
-See [[metric microtemperaments]] for a collection of rank-2 temperaments where it is tempered out.
+See [[Metric microtemperaments]] for a collection of rank-2 temperaments where it is tempered out.
-=== Metric (31 & 171 & 323) ===
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 703125/702464
-{{Mapping|legend=1| 1 0 2 1 | 0 1 1 3 | 0 0 -3 -7 }}
-[[Optimal tuning]] ([[POTE]]): ~3/2 = 701.8766, ~75/56 = 505.2613
-{{Optimal ET sequence|legend=1| 12, 19, 31, 81, 90, 102d, 109, 121, 140, 152, 171, 665, 836, 1007, 2185, 3192c }}
-[[Badness]]: 0.1498 × 10<sup>-3</sup>
 == Etymology ==
-This comma was first named as ''tertiaendec'' by [[Gene Ward Smith]] in 2005 as a contraction of ''[[tertiaseptal]]'' and ''[[enneadecal]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group | ''Seven limit comma names from pairs of temperament names'']</ref>. It is not clear how it later became ''meter''.
+This comma was first named as ''tertiaendec'' by [[Gene Ward Smith]] in 2005 as a contraction of ''[[tertiaseptal]]'' and ''[[enneadecal]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group | ''Seven limit comma names from pairs of temperament names'']</ref>. It is not clear how it later became ''meter'' in 2010<ref>See [https://en.xen.wiki/index.php?title=Small_comma&oldid=13579 Revision as of 18:42, 1 June 2010 by Wikispaces>genewardsmith].</ref>.
-== Notes ==
+== References ==
 [[Category:Metric (temperament)]]
+[[Category:Commas with unknown etymology]]