Meter: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 703125/702464 | | Ratio = 703125/702464 | ||
| Name = meter, metric comma | |||
| Color name = Lr<sup>3</sup>y<sup>7</sup>-4, latriru-asepyo negative 4th | |||
| Name = meter comma | | Comma = yes | ||
| Color name = | |||
| | |||
}} | }} | ||
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:Metric (temperament)]] | ||
[[Category:Commas with unknown etymology]] | |||
Latest revision as of 23:20, 3 November 2024
| Interval information |
metric comma
The meter, also known as the metric comma (monzo: [-11 2 7 -3⟩, ratio: 703125/702464), is an unnoticeable 7-limit comma with a value of approximately 1.6 cents. It is the difference between a stack of three septimal kleismas and a 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 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: [⟨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: 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[1]. It is not clear how it later became meter in 2010[2].