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. | '''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 | 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]]. | ||
Revision as of 06:30, 4 November 2024
| Interval information |
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 )/||| P5) accrues this 0.0033 ¢ error.
Alternatively, the 65/19 atom is the difference between the pythagorean comma 312/219 raised by 513/512 and the wilsorma 65/64.