Meter: Difference between revisions

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The '''meter ~~comma~~''' ~~is a 7-limit comma with a ratio of~~ '''~~703125/702464~~''' ~~and a [[monzo]] of~~ {{monzo|-11 2 7 -3}}~~. It~~ is an [[unnoticeable comma]] ~~of the~~ [[7-limit]] with a value of approximately 1.~~62828 cents, and~~ is ~~significant as~~ the difference between a stack of three [[225/224|septimal kleismas]] and ~~and the~~ [[81/80|syntonic comma]]. Tempering it out leads to a ~~form~~ of '''~~metric~~ temperament'''.

{{Infobox Interval

| Ratio = 703125/702464

| Name = meter, metric comma

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

| 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]].

== 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.

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

[[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 × 10-3

== 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'' 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 ==

[[Category:Metric (temperament)]]

[[Category:Commas with unknown etymology]]

@@ Line 1: / Line 1: @@
-The '''meter comma''' is a 7-limit comma with a ratio of '''703125/702464''' and a [[monzo]] of {{monzo|-11 2 7 -3}}.  It is an [[unnoticeable comma]] of the [[7-limit]] with a value of approximately 1.62828 cents, and is significant as the difference between a stack of three [[225/224|septimal kleismas]] and and the [[81/80|syntonic comma]].  Tempering it out leads to a form of '''metric temperament'''.
+{{Infobox Interval
+| Ratio = 703125/702464
+| Name = meter, metric comma
+| Color name = Lr<sup>3</sup>y<sup>7</sup>-4, latriru-asepyo negative 4th
+| 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]].
+== 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.
+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'' 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 ==
+[[Category:Metric (temperament)]]
+[[Category:Commas with unknown etymology]]