Meter: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 703125/702464 | | Ratio = 703125/702464 | ||
| Name = meter, metric | | Name = meter, metric comma | ||
| Color name = Lr<sup>3</sup>y<sup>7</sup>-4, latriru-asepyo negative 4th | | Color name = Lr<sup>3</sup>y<sup>7</sup>-4, latriru-asepyo negative 4th | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
The '''meter''', also known as the '''metric 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 a stack of three [[225/224|septimal kleismas]] and a [[81/80|syntonic comma]]. | ||
== Temperaments == | == Temperaments == | ||
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[[Comma list]]: 703125/702464 | [[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 tuning]] ([[POTE]]): ~3/2 = 701.8766, ~75/56 = 505.2613 | ||
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[[Badness]]: 0.1498 × 10<sup>-3</sup> | [[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''. | |||
== Notes == | |||
[[Category:Metric (temperament)]] | [[Category:Metric (temperament)]] | ||
Revision as of 12:16, 2 January 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.
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.