Meter: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Ratio = 703125/702464

~~| Monzo = -11 2 7 -3~~

| Name = meter, metric comma

~~| Cents = 1.62828~~

| Color name = Lr3y7-4, latriru-asepyo negative 4th

| Name = meter comma~~, meter~~

| Comma = yes

| Color name =

| ~~FJS name =~~

~~| Sound~~ =

}}

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 comma~~''', ~~or more simply~~, the ~~'''meter'''~~, ~~is a~~ [[~~7-limit]] [[unnoticeable comma~~]] ~~with a ratio of '''703125/702464''' and a value of approximately 1.6 cents~~. It is ~~the difference between a stack of 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.

~~== Temperaments ==~~

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

~~Tempering it out splits the syntonic comma into three equal parts, one for the septimal kleisma, and two for the~~ [[~~126/125|septimal semicomma~~]].

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

Subgroup: 2.3.5.7

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 703125/702464

~~[[Mapping]]: [~~{{~~val~~| 1 0 2 1 ~~}}, {{val~~| 0 1 1 3 ~~}}, {{val~~| 0 0 -3 -7 }}]

[[POTE ~~generator~~]]s: ~3/2 = 701.8766, ~75/56 = 505.2613

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

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

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

[[Badness]]: 0.1498 × 10-3

== ~~See also~~ ==

== Etymology ==

* [[~~Metric microtemperaments~~]]~~, where it is tempered out~~

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>.

* [[~~Unnoticeable~~ comma]]

== Notes ==

~~[[Category:7-limit]]~~

~~[[Category:Unnoticeable comma]]~~

[[Category:Metric (temperament)]]

[[Category:Commas with unknown etymology]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
 | Ratio = 703125/702464
-| Monzo = -11 2 7 -3
+| Name = meter, metric comma
-| Cents = 1.62828
+| Color name = Lr<sup>3</sup>y<sup>7</sup>-4, latriru-asepyo negative 4th
-| Name = meter comma, <br> meter
+| Comma = yes
-| Color name =
-| FJS name =
-| Sound =
 }}
+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 comma''', or more simply, the '''meter''', is a [[7-limit]] [[unnoticeable comma]] with a ratio of '''703125/702464''' and a value of approximately 1.6 cents. It is the difference between a stack of 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.
-== Temperaments ==
+See [[metric microtemperaments]] for a collection of rank-2 temperaments where it is tempered out.
-Tempering it out splits the syntonic comma into three equal parts, one for the septimal kleisma, and two for the [[126/125|septimal semicomma]].
 === Metric (31 & 171 & 323) ===
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 703125/702464
-[[Mapping]]: [{{val| 1 0 2 1 }}, {{val| 0 1 1 3 }}, {{val| 0 0 -3 -7 }}]
+{{Mapping|legend=1| 1 0 2 1 | 0 1 1 3 | 0 0 -3 -7 }}
-[[POTE generator]]s: ~3/2 = 701.8766, ~75/56 = 505.2613
+[[Optimal tuning]] ([[POTE]]): ~3/2 = 701.8766, ~75/56 = 505.2613
-{{Val list|legend=1| 12, 19, 31, 81, 90, 102d, 109, 121, 140, 152, 171, 665, 836, 1007, 2185, 3192c }}
+{{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>
-== See also ==
+== Etymology ==
-* [[Metric microtemperaments]], where it is tempered out
+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>.
-* [[Unnoticeable comma]]
+== Notes ==
-[[Category:7-limit]]
-[[Category:Unnoticeable comma]]
 [[Category:Metric (temperament)]]
+[[Category:Commas with unknown etymology]]