Enneadeca: Difference between revisions
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I haven't seen anyone use the term "19-tone-comma". It's not very clear anyway |
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The '''enneadeca''' ({{monzo|legend=1| -14 -19 19 }}) is an [[unnoticeable comma|unnoticeable]] [[5-limit]] [[comma]] of 2.816 [[cent]]s. It is the amount by which nineteen [[6/5|classical minor thirds]] fall short of five [[2/1|octaves]], that is, 2<sup>5</sup>/(6/5)<sup>19</sup>. | The '''enneadeca''' ({{monzo|legend=1| -14 -19 19 }}) is an [[unnoticeable comma|unnoticeable]] [[5-limit]] [[comma]] of 2.816 [[cent]]s. It is the amount by which nineteen [[6/5|classical minor thirds]] fall short of five [[2/1|octaves]], that is, 2<sup>5</sup>/(6/5)<sup>19</sup>. In terms of commas, it is the product of the [[ennealimma]] and the [[schisma]]. | ||
== Temperament == | == Temperament == | ||
[[Tempering out]] the enneadeca leads to the 5-limit [[enneadecal]] temperament, [[support]]ed by equal divisions divisible by 19 such as | [[Tempering out]] the enneadeca leads to the 5-limit [[enneadecal]] temperament, [[support]]ed by equal divisions divisible by 19 such as [[152edo]], [[171edo]], and [[190edo]]. | ||
== Etymology == | == Etymology == | ||
Latest revision as of 19:21, 19 July 2026
| Interval information |
The enneadeca (monzo: [-14 -19 19⟩) is an unnoticeable 5-limit comma of 2.816 cents. It is the amount by which nineteen classical minor thirds fall short of five octaves, that is, 25/(6/5)19. In terms of commas, it is the product of the ennealimma and the schisma.
Temperament
Tempering out the enneadeca leads to the 5-limit enneadecal temperament, supported by equal divisions divisible by 19 such as 152edo, 171edo, and 190edo.
Etymology
This comma was named by Gene Ward Smith in 2001 in terms of the corresponding temperament, enneadecal[1], for the temperament has 19 periods per octave. The comma was at one point dubbed enneadecima[2], though it was enneadeca that stuck.