65/19 atom: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled
18,164 edits
m BudjarnLambeth moved page 272629760/272629233 to 65/19 atom: Long comma name (I didn’t make the name 65/19 atom, it was already in the info box, just didn’t show up for some reason)
No edit summary
Line 1: Line 1:
{{Infobox Interval
{{Infobox Interval
| name = 65/19 atom
| Name = 65/19 atom
| Ratio = 272629760/272629233
| Ratio = 272629760/272629233
| Color name = ss19u3oy2, sasa-nuthoyo 2nd
| Color name = ss19u3oy2, sasa-nuthoyo 2nd
Line 6: Line 6:
}}
}}


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

Revision as of 06:24, 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 65/19 atom
Color name ss19u3oy2, sasa-nuthoyo 2nd
FJS name [math]\displaystyle{ \text{d2}^{5,13}_{19} }[/math]
Special properties reduced
Tenney height (log2 nd) 56.0447
Weil height (log2 max(n, d)) 56.0447
Wilson height (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 (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 1/19 comma 19683/19456 (312/219 lowered by 513/512) and the wilsorma 65/64.

Retrieved from "https://en.xen.wiki/index.php?title=65/19_atom&oldid=164142"