65/19 atom: Difference between revisions

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Created page with "{{Infobox Interval | name = 65/19 atom | Ratio = 272629760/272629233 | Color name = ss19u3oy2, sasa-nuthoyo 2nd | Comma = yes }} '''272629233/272629760''' is an unnoticeable..."
 
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'''272629233/272629760''' 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]] (the difference between the classical major third [[5/4]] lowered by an [[apotome]] and the novemdecimal minor third [[19/16]]). Their difference is small enough that [[sagittal]] accidentals do not distinguish between the 13-comma and 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]] (the difference between the classical major third [[5/4]] lowered by an [[apotome]] and the novemdecimal minor third [[19/16]]). Their difference is small enough that [[sagittal]] accidentals do not distinguish between the 13-comma and 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.

Revision as of 05:32, 4 November 2024

Interval information
Ratio 272629760/272629233
Factorization 222 × 3-15 × 5 × 13 × 19-1
Monzo [22 -15 1 0 0 1 0 -1
Size in cents 0.003346521¢
Name(s) missing ? 
Color name ss19u3oy2, sasa-nuthoyo 2nd
FJS name [math]\displaystyle{ \text{d2}^{5,13}_{19} }[/math]
Special properties reduced
Tenney norm (log2 nd) 56.0447
Weil norm (log2 max(n, d)) 56.0447
Wilson norm (sopfr(nd)) 126
Comma size unnoticeable
Open this interval in xen-calc

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 (the difference between the classical major third 5/4 lowered by an apotome and the novemdecimal minor third 19/16). Their difference is small enough that sagittal accidentals do not distinguish between the 13-comma and 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.