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.

Alternatively, the 65/19 atom is the difference between the ~~1/19 ~~comma ~~[[19683/19456]] (~~[[pythagorean comma|312/219]] ~~lowered~~ by [[513/512]]) and the wilsorma [[65/64]].

Alternatively, the 65/19 atom is the difference between the pythagorean comma [[pythagorean comma|312/219]] raised by [[513/512]] and the wilsorma [[65/64]].

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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.		'''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.

	Alternatively, the 65/19 atom is the difference between the ~~1/19 ~~comma ~~[[19683/19456]] (~~[[pythagorean comma\|3<sup>12</sup>/2<sup>19</sup>]] ~~lowered~~ by [[513/512]]) and the wilsorma [[65/64]].		Alternatively, the 65/19 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]].