65/19 atom: Difference between revisions

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'''272629233~~/272629760~~''', the '''65/19 atom''', is ~~an unnoticeable comma in the~~ 2.3.5.13.19 subgroup. It is the ~~amount by which~~ the ~~13-~~comma [[~~6656~~/~~6561]] ("tetris comma") exceeds the~~ 19/~~5-comma [[41553/40960~~]] ~~(an~~ [[~~apotome]] above [[19~~/16]] lowered by [[5/~~4]]). Their difference is small enough that [[sagittal~~]] accidentals equate the 13-comma with the 19/5 comma: the most accurate possible representation of the 13th harmonic in sagittal accidentals (as three octaves above a <code>)/||| P5</code>) accrues this 0.0033{{cent}} error.

'''272629760/272629233''', the '''65/19 atom''', is a [[19-limit]] (2.3.5.13.19 subgroup) [[unnoticeable comma]]. It represents the tiny interval between the pythagorean comma [[pythagorean comma|312/219]] and the wilsorma [[65/64]] lowered by the 19-schisma [[513/512]].

~~Alternatively~~, the 65/19 atom is the ~~difference between~~ the ~~pythagorean~~ comma [[~~pythagorean~~ comma~~|312<~~/~~sup>~~/~~2~~19</~~sup>~~]] ~~raised~~ by [[~~513~~/~~512~~]] and the ~~wilsorma~~ [[65/64]].

Notably, the 65/19 atom is also the amount by which the 13-comma [[6656/6561]] ("tetris comma") exceeds the 19/5-comma [[41553/40960]] (an [[apotome]] above [[19/16]] lowered by [[5/4]]). Their difference is small enough that the untempered Promethian (high precision) and Herculean (ultra precision) [[sagittal]] accidental systems equate the 13-comma with the 19/5 comma: the most accurate possible representation of the [[13/1|13th harmonic]] in JI sagittal accidentals at these precision levels (as three octaves above a {{nowrap|{{sagittal| /||| }}P5}}) accrues this 0.0033{{cent}} error.

[[Category:Commas named systematically]]

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-'''272629233/272629760''', the '''65/19&nbsp;atom''', is an unnoticeable comma in the 2.3.5.13.19 subgroup. It is the amount by which the 13-comma [[6656/6561]] ("tetris comma") exceeds the 19/5-comma [[41553/40960]] (an [[apotome]] above [[19/16]] lowered by [[5/4]]). Their difference is small enough that [[sagittal]] accidentals equate the 13-comma with the 19/5 comma: the most accurate possible representation of the 13th harmonic in sagittal accidentals (as three octaves above a <code>)/||| P5</code>) accrues this 0.0033{{cent}} error.
+'''272629760/272629233''', the '''65/19&nbsp;atom''', is a [[19-limit]] (2.3.5.13.19 subgroup) [[unnoticeable comma]]. It represents the tiny interval between the pythagorean comma [[pythagorean comma|3<sup>12</sup>/2<sup>19</sup>]] and the wilsorma [[65/64]] lowered by the 19-schisma [[513/512]].
-Alternatively, the 65/19&nbsp;atom is the difference between the pythagorean comma [[pythagorean comma|3<sup>12</sup>/2<sup>19</sup>]] raised by [[513/512]] and the wilsorma [[65/64]].
+Notably, the 65/19&nbsp;atom is also the amount by which the 13-comma [[6656/6561]] ("tetris comma") exceeds the 19/5-comma [[41553/40960]] (an [[apotome]] above [[19/16]] lowered by [[5/4]]). Their difference is small enough that the untempered Promethian (high precision) and Herculean (ultra precision) [[sagittal]] accidental systems equate the 13-comma with the 19/5 comma: the most accurate possible representation of the [[13/1|13th harmonic]] in JI sagittal accidentals at these precision levels (as three octaves above a {{nowrap|{{sagittal| /||| }}P5}}) accrues this 0.0033{{cent}} error.
+[[Category:Commas named systematically]]